--------- Black holes--------
Perhaps the most mysterious bodies in our entire universe, the existence of black holes was largely theoretical only until recently, with the first ever capture of the supermassive black hole that lies at the centre of our own galaxy, the Milky Way.
In fact, the famous Albert Einstein predicted their existence with his theory of general relativity, which was largely considered to be scrap by most of his peers at the time.
These days, however, the integrity of Einstein's work has been tested time after time, and has been met with resounding success every time.
If you're interested in learning about the particular proofs of his work, then I'd recommend checking out this article here, which investigates the notion of space-time curving due to mass, exactly how Einstein proposed it to.
Make no mistake, what lies at the centre of a black hole is completely unknown, and will likely remain so forever as we seem unable to peer behind the event horizon (which we'll elaborate more on in a minute).
You may have heard that at the centre of a black hole lies a point that's infinitely dense, known as a singularity.
However, just like Schrödinger's cat, the concept of a singularity is more of a mockery to our current model of the universe than an actual realistic outcome - a point of infinite density just doesn't make any sense...
Since we've already mentioned two key "parts" of a black hole, let's take a closer look at how exactly black holes even come into existence.
Formation of black holes
A black hole can be formed from the death of a massive star far beyond the mass of our own star, the Sun, although it's worth bearing in mind that this isn't the only way that they can be formed.
It's currently believed that a star would have to be of at least 20 solar masses, with 1 solar mass being the entire mass of the Sun, in order for a black hole to remain as a stellar remanent at the time of the star's "death".
But what do I mean by the "death of a star" ?
Well, throughout a star's lifetime, it's in a constant turmoil of the forces that govern the universe: gravity, and essentially the energy produced from fusing atomic nuclei together.
I go into more depth of the life-cycle of stars in a different article which again, feel free to check out here , so we'll summarise by saying that when a large enough star runs out of fuel, gravity begins to crush the star.
As the core becomes denser, electrons and protons are eventually forced together to produce a body that's exclusively made from neutrons (a neutron star), which collapses further into matter that is, at the time of writing this, unknown.
When the collapse halts due to the outward pressure of [some form of matter], the surrounding gases explode outward across the cosmos, in an event we call a supernova/hypernova (depending on its intensity).
It's beyond difficult to imagine the scale of compression that we're talking about here, since we're compressing matter down to point of theoretically zero volume...
Which obviously sounds completely absurd, particularly so without knowing just how empty atoms really are.
Again, I do have a separate article that's specifically dedicated to explaining how everything that you can see around you is over 99.9% nothing (a mathematical breakdown is included, although it does assume so experimental values of the dimensions of protons, so I probably wouldn't call it a "proof" , per say... ), which you can check out here.
Briefly though, the relative space between nuclei and orbiting electrons is huge - take note of the word relative here, since obviously we're still talking about tiny volumes.
If the proton at the centre of a hydrogen atom stretched 200 meters across, then the atom as a whole would be the size of the entire planet (Earth), with one electron that occupies zero volume between that space... so nothing!
The significance of this is that all the matter that you can see and interact with around you, including yourself, is over 99.9% nothing... a mere empty vacuum in space.
But what's the big deal with a black hole/neutron star?
Well, because their electrons have been forced to neutralise with protons to form a body that's exclusively made from neutrons with little to no empty space between them, they can be said to be over 99.9% mass-energy!
But let's test this numerically so we can get a better idea of the scale of this.
I said that a hydrogen atom was over 99.9% empty space, but the actual number would be 99.9999999999996%.
Seeing as hydrogen is the most abundant element in the universe and the numbers vary insignificantly from atom to atom anyway, it seems appropriate to use the hydrogen atom as an example for this comparison.
Imagine a block of iron with mass 1kg.
That iron block is 99.9999999999996% empty space.
Now imagine that all that space is now filled with mass, just like the structure of a neutron star and black hole.
We would take our 1kg and now divide it by 0.0000000000004 to calculate how much our new block of the same volume would weigh.
1/0.0000000000004 = 2500000000000000
= 2.5*10¹⁴
= 250 trillion kg
....
The trouble is though, even that doesn't do the density of a black hole justice...
This comparison is far more appropriate for the density of a neutron star, since it's atomically structured in a way that's essentially being replicated in the above thought experiment.
Black holes, however, are somehow even denser...
In fact, to elaborate on a point that I made earlier, black holes are supposedly infinitely dense!
Okay, that just can't be true.... but that's what classical mechanics tells us.
See, the reason why theories like relativity and QM (Quantum Mechanics) exist in the first place is to essentially fill in the gaps of classical physics, such as Newtonian physics.
Einstein wasn't satisfied that gravity was a force, so he proposed the concept of space-time curving due to mass, which is what causes particles within this curvature to accelerate towards the object.
Classical mechanics tells us that electrons would eventually fall into their relative nuclei as they constantly radiate energy and reduce their orbital radius as a result, which obviously can't be right either... so quantum mechanics says that electrons aren't classical particles, they're quantum particles (or waves) that obey completely different rules.
Why am I mentioning any of this?
The point is, we have several models of how the universe operates, but not a single complete one, although quantum mechanics is the most promising at the time of writing this, as it explains 3 of the 4 fundamental forces in the universe:
Strong nuclear force
Weak nuclear force
Electromagnetism (Coulombic force)
But not:
Gravity
Apologies that this is getting a little bit off topic now, but I promise it's all worth it!
Classical physics tells us that the density of a black hole is infinite, which we know simply cannot be true, and besides, all known models of physics break down at the singularity (we'll elaborate on that in a minute ) anyway, so it makes no sense to use classical mechanics when it breaks down - obviously the results are going to be non-sensical.
But let's just break this albeit inaccurate concept down so we can understand just what an infinitely dense region of space even means.
We know that black holes can have different mass values, along with charge and angular momentum.
In fact, just as a quick side note here, those 3 characteristics are the only pieces of information that we have about black holes - everything else (lepton number, baryonic number etc... is lost behind the event horizon, which we're about to come onto).
Interestingly, this is where quantum mechanics fails at explaining black holes, since the concept of information always being preserved is a precursor to quantum mechanics, but we won't go into detail of that here.
So if black holes can have different mass values and the concept of infinite mass is as ludicrous as any, and density is defined as being the amount of mass per volume, then we can see that perhaps the volume of a singularity is the cause of this infinitely high density paradox.
And how do we get to infinity?
Well, that's a difficult question.
The concept of infinity is obviously paradoxical, but whether that's due to some limitation of our conciseness or because it simply doesn't exist is anyone's guess.
In mathematics, the idea of infinity is useful because it allows us to measure the outcomes of functions that tend to infinity (ie as one number gets bigger and bigger/smaller and smaller), but nothing can actually provide any sense at the point of infinity (because there is no point at which infinity is reached.)
Some people argue that mathematically, infinity can achieved by diving by zero, which might make sense at face value.
I mean how many zeros go into one?
At first, it makes sense to assume that it would take an infinite amount of zeros to go into any number in fact, but let's just stop and consider something for a moment.
Don't worry, we're still on the topic of black holes!
We know that as you divide by smaller numbers, the outcome is a larger number, and as you get really close to dividing by zero, the outcome is an incredibly large number.
We can say that as the denominator tends towards zero, the outcome tends towards infinity.
But we can flip this over to the negative size and say that as the denominator tends towards -0, the outcome tends towards -infinity.
There seems to be this point (at zero), where if you go one way you end with an incredibly large number, and the other way an incredibly small number.
So to say that when you divide by zero, you end up with infinity, wouldn't make much sense.
So what is the outcome of dividing by zero?
Nobody really knows, so mathematicians say that's simply undefined - you just can't do it.
It's not infinity, it's not zero etc... it just isn't defined.
Okay, but what does any of this have to do with a black hole?
Well, general relativity predicts that there are points in space where the curvature of space-time (which results in the acceleration that we call gravity) is infinitely high.
Seeing as this curvature is NOT 3 dimensional, as would be depicted in a typical "bowling-ball on a trampoline analogy", it's impossible to imagine it in your head, so don't worry if you're struggling!
I won't spend any time going into metric tensors, the different transformations and the like, but suffice to say that at the centre of black holes, you can imagine the curvature of space-time as being a completely straight line running up/down.
At this point, the rate of change in the x-axis is zero, which presents the paradox that we've been talking about - dividing by zero.
The gradient of the curvature would involve dividing by zero, meaning that the gradient is left as being undefined.
An undefined region of space-time curvature - this, is a singularity.
Okay, so the curvature of space-time is infinite - great. But what does this mean for our singularity?
Causing an infinite curvature of space-time would naturally correspond to other infinite properties for a particle(s), such as density, which also presents further issues.
Since density is a measure of mass per volume, and we know that black holes haver finite mass, then perhaps the volume of the singularity is zero or converges to zero, although mathematically that might result in the density being undefined as opposed to infinitely large.
To make a slight comparison here, we know that electrons themselves essentially have no volume, but that's remarkably different from saying that they have zero volume, despite them perhaps seeming interchangeable.
Electrons are point particles meaning that they DO NOT occupy space in 3 dimensions, and since the volume of a particle involves measuring its area over 3 dimensional space, electrons cannot have volume.
I explain why exactly they don't occupy 3 dimensions in this article here.
But the volume of an electron isn't zero, it just doesn't make any sense to describe them in that way.
The reason why I bring this up is to differentiate between particles that have zero volume, and no volume at all.
In contrast to electrons, singularities supposedly still have volume, just the value of which is zero which is what leads to perhaps an infinite density.
^An important distinction to remember
Alternatively, maybe the volume of a singularity is just so small that its perceived as being zero by our standard models of the universe.
Perhaps a singularity is a point that's somehow smaller than even a point particle, such as the electron.
The point is - nobody knows. Singularities are loopholes in our models of physics, whether they be quantum or classical.
Besides making no sense intuitively, the concept of a singularity does also present some other issues, particularly when we account for other pieces of information, such as angular momentum.
When stars collapse into black holes, angular momentum is conserved, meaning that most black holes rotate incredibly quickly - usually at relativistic speeds (a significant % of the speed of light).
This conservation of angular momentum means that the singularities must have spin, which would give them a ring-shaped structure - a so called ringularity, which contradicts the idea of zero volume.
Theoretically speaking, a static, non-rotating black hole with no charge or angular momentum, dubbed a Schwarzschild black hole could exist, although in reality it would be next to impossible since if even just a single photon of light collided with the singularity, it would cause it to spin slightly.
The conclusion from all this?
Singularities/ringularities are concepts that arise from mathematics essentially misbehaving.
They're non-sensical conclusions drawn from using our current models in situations that we don't yet fully understand.
As we move on beyond the singularity of a black hole, I just want to clarify something here to make sure there's no confusion around which part of the black hole we're talking about.
When you see 3D computer-simulated images of black holes, you might be inclined to think that the region of blackness is the singularity.
However, that region of space that appears black isn't the singularity itself, and instead is the region of space around the singularity where the "force" of gravity is so high that even light cannot escape.
On Earth, the escape velocity is around 11 km/s, meaning that you have to be travelling at least this fast in order to escape the overwhelming attraction to the Earth's centre of mass.
If you're travelling slower than 11 km/s, then your acceleration due to Earth's gravity will eventually bring you back down to the surface.
For a singularity, there's a region of space around this singularity where the escape velocity is higher than the speed of light, meaning that light can never escape.
In the absence of being able to see that light (because it can't reach our eyes) we see a supposedly empty void of blackness, although that "void" would theoretically be full of intense energy that can't escape - but nobody can ever see it, so who knows!
Since nothing can travel faster than the speed of light, as laid out by Einstein's theory of special relativity, anything that enters this region of space can never get back out, meaning that we cannot and probably will never be able to know for sure what's inside of this region.
Since the "force" of gravity decreases with distance from the object, the border where the escape velocity drops below the speed of light is what we call the event horizon.
Once something passes the event horizon, it cannot return.
Ultimately, since information cannot travel faster than the speed of light, we'll never be able to see beyond the event horizon and take a glimpse at the singularity itself.
So we've covered the hypothetical singularity, the region of space where no light can escape, and the event horizon, so let's move on past the black hole itself and talk about some other features before finishing up with the biggest bomb-shell of all - time dilation....
First of all, black holes come in a huge range of mass and volume.
Most black holes are very dormant, remnants of massive stars and often measure mere kilometres in diameter.
These black holes roam through galaxies mostly minding their own business as they traverse through the emptiness of space.
Other black holes however, exist at the centre of galaxies, and are responsible (along with the attractive force of dark matter) for the formation of galaxies themselves.
These black holes are categorised by their inconceivably high mass, and we refer to them as either supermassive or ultramassive black holes, depending on just how massive they really are.
These black holes are millions to even billions of times more massive than the sun, and have a gravitational field strength that often causes nearby stars to be completely shredded down or "spaghetiffied", as physicists like to say.
The matter is then forced into a very close orbit around the black hole travelling at speeds of hundreds of kilometers per second!
Tidal and frictional forces superheat these gases, resulting in an intense glow that surrounds the black hole, and we call this disc of glowing gas and dust the accretion disk of the black hole.
Interestingly, when there's enough gas present in this accretion disk, high energy gamma rays can be ejected from the poles of the black hole, at which point we refer to the black hole as a quasar, although you can read more about them here.
Not all black holes have an accretion disk though, as it requires matter to be present close enough for the black hole to pull in.
At this point, we've covered the structure of a black hole, but let's now elaborate on a term that I mentioned earlier - spaghetiffication.
Spaghettification is the event of an object being completely stretched due to the tidal forces of a black hole, and happens when an object ventures too close to one.
To avoid this article becoming too long, I'd recommend giving this article a read if you're unfamiliar with tidal forces, although as always, I'll give a brief explanation below:
For sake of ease, consider the Moon and the Earth.
The Earth pulls at the Moon with some gravitational "force" and visa versa, but because the Moon has volume, one side of the Moon is technically closer to the Earth than the other side and therefore experiences a stronger "force" of acceleration towards the Earth.
Therefore, the Moon bulges, or stretches slightly as matter is being non uniformly accelerated.
But the Earth's gravity isn't that strong, so the difference in force is fairly minimal.
A black hole however, can have a gradational field far, far stronger, causing objects to not just bulge, but be completely pulled apart into a string of particles... hence the name.
I talk about the relationship between gravity and density in a different article which you can check out here, so I'd recommend giving it a read if what I'm about to say doesn't make much sense to you.
Even-though the mass of a black hole can be less than that of a reasonably massive star (about 4 solar masses), the tidal forces experienced by objects within close proximity to a black hole can be devastating - sphagetifingly devastating.
The reason for this is because all of the mass of a black hole exists within such a tiny space, and since gravity essentially derives from an object's centre of mass, objects can literally get within a few kilometres of a black hole's centre of mass (the singularity).
Because the force of gravity felt between two particles decreases exponentially with distance between them, the "force" that an object would feel only a few kilometres away from an object with more mass than 3 suns would be astronomically high, which is what results in the incredible tidal forces.
This is one of the biggest problems humanity will face in attempting to get satellites close to a black hole - tidal forces will strip them apart long before they get anywhere near close to the event horizon.
Although as we mentioned earlier, sending any satellite past the event horizon wouldn't do much good anyway, since it would no longer be able to communicate with anything outside of the black hole...
With tidal forces covered, I think it's best if I follow-through on that promise I made earlier of explaining what's probably the most fascinating concept associated with black holes - time dilation.
We've seen it in movies like Interstellar, but does it really exist?
How can time literally run differently for people close enough to a black hole?
Don't worry, we'll cover all of that good stuff right now.
I think it's best to begin with defining what time actually is, because I think a lot of the confusion around time dilation essentially stems from people having different "opinions" of time.
I know that sounds crazy, but in essence, time is merely a measurement of change in events.
Time is how we measure changes across the universe, whether those be chemical reactions in our bodies, water flowing down a river, cars driving by, the Sun setting, seasons or whatever...
Think about it - if everything in the universe was static, how would we measure time?
It just wouldn't exist.
How would you be able to separate the past, present and future from each other when everything is completely the same across all 3 time periods?
Well, you wouldn't.
That's the true meaning of time, but if your pre-existing idea of time is that it's some clock that ticks at a certain frequency, then you're right - time is non-changeable, and isn't affected from relativity, which we'll talk more about in minute.
So when we talk about time dilation, we're talking about the rate of change in events becoming variable depending on:
Where in the universe you're observing from and/or;
How fast your travelling
To elaborate on a subject I brought up a moment ago - relativity - the whole concept of time dilation arises from one of the two postulates (a fancy word for hypotheses) made in Einstein's theory of special relativity.
I'll list them both below because why not, but it's the 2nd one that's of interest to us here:
Physics is the same in the universe, no matter where you are
The speed of light (c) is constant.
To help us understand the significance of the second postulate, specifically on time dilation, consider the following thought experiment.
Imagine you're on the high-way travelling at 70mph (the exact speed isn't relevant).
You know you're moving very quickly because you can see perhaps the trees or road signs, which you know are stationary objects, move by incredibly quickly.
Now let's say a car to your right is driving at the exact same speed as you.
If you focus on the person driving the car and not the tyres (because the spinning tyres would indicate speed), then you would essentially have no idea that either one of you are moving.
That's because velocity, just like every other physical quantity is described as being relativistic by Einstein's theory of relativity, although in my opinion it's more than just a theory at this point...
Any object in the universe only has physical quantities because of its relationship with other objects...
Now, this article is about black holes, and we can spend all day and night here talking about relativity, so I want to quickly make the connection this has to time dilation without wasting too much time, but I will just say that this idea of relativistic quantities goes all the way back to Ancient Greece, albeit in a much simpler format.
But relativity really transcends human observation and is more of an underlying foundation of what I would call experience itself.
Perhaps you could use the word interchangeably with "reality" or "existence", but I just want to solidify the idea that it's functional in all scenarios in the universe.
I mean how do you define feelings of emotion?
How do you define happiness?
Surely being happy is just not being sad, in that if you were happy all time, surely you would no longer be truly happy, by virtue of it just being a different feeling to sad?
Even emotions themselves are relativistic - you only feel any of them BECAUSE of their relationship with the other emotions.
You can only be happy if you've been sad, you could only be hungry if you've not been hungry.
By themselves, they simply don't exist.
To summarise relativity in one sentence, there is no " an object is...", only "an object is [less than/greater than]...."
Moving swiftly back to time dilation though...
Another concept I could spend a while talking about is how we've proven time dilation to be true, but I think it would be best if I went over that in a separate article so that anyone who is here purely for black holes doesn't lose their mind!
So consider singing up to be notified when it drops!
So for now, let's just accept that significant time dilation exists when you're travelling either very close to a black hole or near the speed of light.
As I just mentioned, I'm going to swerve the proof for time dilation travelling near the speed of light, but we will talk about time dilation near a black hole since that's obviously very relevant to this article.
Time dilation occurs near a black hole due to how the black hole's gravity, or more specifically the curvature of space-time around a black hole, affects light.
Just like how the expansion of the universe can cause light to be stretched, or "redshifted" as it's commonly referred to as, simply because stretching a visible light wave gets it to or closer to the wavelength of the colour red, light can be stretched by the curvature of space-time due to mass.
At and beyond the event horizon, which hopefully you remember from earlier, photons of light are infinitely redshifted and they can't escape the black hole.
Just outside of the black hole, however, light is just redshifted enough to cause a physical delay to an observer far away from the black hole.
I think this is a good place to stop and clarify something so we're all on the same page.
Let's say there are two people, one of whom is approaching a black hole, and the other is observing far away from say for example, a planet orbiting the black hole.
Time NEVER changes for the person approaching the black hole.
That's not what time dilation says - only time APPEARS to be running differently for that person FROM the perspective of the person on the planet.
The reason for this is because the light coming from the person approaching the black hole is getting redshifted and delayed by the black hole's gravity, which makes it seem as if time is running differently for them from the perspective of the person watching from the planet.
In this example, we can establish two different frames of time:
coordinate time and;
proper time
Coordinate time is the time that's felt by the person observing from the planet, and is variable due to effects on the speed of light, as we just mentioned.
Proper time, however, is the time that's experienced by the person approaching the black hole, and is invariable - it NEVER changes. Time appears to be running exactly the same for the person approaching the black hole because he's not witnessing his own light being redshifted.
Don't worry, if you're struggling to understand the situation with light being redshifted, consider this quick thought experiment.
The person near the black hole is reflecting/emitting photons of light.
Those photons of light are being pulled back towards the black hole with so much "force" that they take a considerable amount of time (depending on how close to the black hole you are) to reach the person observing from the planet.
By the time they do reach the person observing, many minutes/hours.. etc may have passed for the person near the black hole.
The person observing is receiving delayed information from the person near the black hole, which makes it SEEM as if time is running differently.
The closer the approacher gets to the black hole, the longer light takes to reach the observer, until they cross the event horizon and the light is lost forever.
You're never able to see them cross the event horizon - they simply appear to freeze at the point of entry since no light beyond that point can get to you.
Hopefully that clarifies things a bit more!
See, time only APPEARS to be running differently because the observer is receiving delayed light, and as we established earlier that time is a measure of changes in events, and we can only measure changes by or less than the speed of light, because no information can travel any faster, time appears to change.
However, nothing is actually happening for the person near the black hole - that's an important part to remember.
The reason for this is because of the second postulate made by Einstein's theory of special relativity, which we talked about earlier - the fact that the speed of light (s) is always constant for a local observer.
It's crucially important to remember that local time, or proper time never changes for anyone.
You, yourself, will always experience your own local time to be the same no matter where you are (assuming you're alive I suppose...), because the speed of light locally is always constant.
I think another part about time dilation that causes a lot of confusion is the idea that people can venture close to a black hole, age slower, and then return as if a few hours have passed to them, meanwhile 100 years or something passed back on Earth.
You'll see a similar situation to this in the film Interstellar, and perhaps that's the part that's most confusing.
Rest assured however, that this simply cannot happen.
The trouble with this scenario is that you're combing something that's logical with something that's illogical, giving a non-sensical result.
Sure, theoretically speaking you could age slower near a black hole, simply because of how the ageing process works, but the same concept could be applied to your own ability to recognise that you've aged.
Every process that happens in your body is based on the speed of information, whether that be steroid hormones swimming around in the blood stream, or nerve synapses sending signals to the brain - they're all pieces of information, and they would all be affected by the black holes gravity, just like light is.
But again, you wouldn't appear to age any differently yourself; you would only appear to age slower from a far away observer.
However, you could take it even further and say that's not accurate either, because if all physical processes slow down near a black hole, then so would the signals in your brain that's allowing you to even observe your own ageing...
But what's the problem with Interstellar?
Well, time never changes locally.
You can't travel near a black hole, age slower and then return to Earth looking so much younger than everyone, because you never aged any slower!
You only appeared to age slower by someone observing far away.
The paradox here arises from the fact that you can't travel faster than the speed of light, so if the light is being pulled back enough for a far away observer to see that light several years later, then it will take you several years to arrive at them too.
As soon as you scrap the notion that something can't travel faster than light, spend 3 hours near a black hole and then teleport back to Earth, then of course you create a paradox for yourself.
So just remember that time dilation involves changing the coordinate time, not the proper time, so no single person will ever experience their own local time being any different.
In relativity, different observers in different coordinates in space are called reference frames.
With the explanation out of the way with, let's get to the part which you're probably most interested in - we've established that coordinate time changes, but by how much does it change?
Well, there is a formula for it which you'll see below.
Note that this formula is only true for non-rotating, uncharged black holes, since both quantities will affect the level of time dilation.
Where,
t = coordinate time
𝜏 = proper time
r𝗌 = Schwarzschild radius of the black hole
r = distance from the black hole
Remember that coordinate time is the time felt by the observer, while proper time is the time felt by the approacher.
The Schwarzschild radius of a black hole is simply the radius of the sphere that's black, since it's defined as being the region of space around the singularity where the escape velocity is greater than the speed of light.
Escape velocity has it's own formula, but it's easier if we consider changes in time with changes in distance from the black hole where the distance measured is in multiples of the Schwarzschild radius, since black holes with different Schwarzschild radii will dilate time differently.
Take a look a the chart below to see time dilation in action.
Distance from the black hole (in multiples of rₛ) | Time passed on Earth for 24 hours spent near the black hole |
|---|---|
10rₛ | 25.3 hrs |
3rₛ | 29.4 hrs |
1.5rₛ | 42 hrs |
1.05rₛ | 2.45 days |
1.005rₛ | 14.2 days |
1.0005rₛ | 44.2 days |
1.00005rₛ | 141 days |
As you can see, relativistic effects on the coordinate time are relatively small even when objects are approaching what would still be very close to a black hole - the Schwarzschild radius of the average black hole would be around 10km or so, meaning that if you were around 100km away from the average black hole, you would only experience just over an hour of time dilation.
This is quite simply because the speed of light is inconceivably high (300 million m/s), so it takes a huge gravitational "force" to slow it down enough to give significant impressions of time dilations for a far away observer.
What's also interesting though is that, as you can see from the later values, the difference in proper time and coordinate time increases exponentially the closer you get to the black hole.
The reason for this is because the force of gravity is exponentially related to distance, meaning that if you halve the distance between two objects, you don't just double the force of gravity, rather you quadruple it.
This is accounted for by classical mechanics in Isaac Newton's famous universal law of gravitation.
While being 1.00005rₛ away from a black hole would likely be unrealistic due to the tidal forces that would be experienced at that proximity to the black hole (remember from earlier about spaghettification), it's interesting to see just how rapidly coordinate time can slow down for a far away observer.
Again, this is because as light gets closer to the black hole, the amount of "pull" towards the black hole that it feels increases exponentially, resulting in it taking exponentially longer to reach a far away observer.
Because the observer is receiving light that's being delayed, time appears to run differently for him since our whole perception of time is based around seeing the changes in events around us.
So that's time dilation...
The point of this section was not only to clarify what time actually is, and how we define it, but also to bring to light how relativity plays a role in every aspect of our lives, not just in the observations that we make.
Sure, time is relative because time is defined as being changes in events, and we observe changes in events by processing the light that's coming from them. So if the time that light takes to get to an observer changes, then so will the coordinate time that's experienced by that observer.
But relativity is more than that.
I think it's neat to have relativity sit in the back of your mind throughout life, since I find it helps you appreciate the actual value of experience on planet Earth.
You can only ever have the good times because you have the bad times, so just remember that when you're in an uncomfortable position - it's the duality of the world that we live in.
If you were never uncomfortable, you wouldn't ever be comfortable.
Every physical quantity only exists through its relationship with other physical quantities, and how you wish to define "physical quantity" is your prerogative.
So now let's take a step back from everything and asses what we have and haven't covered so far.
We've talked about:
the formation of black holes from the core collapse of massive stars
the structure of black holes
tidal forces
time dilation
But I think there's a few more sub-topics worth mentioning, seeing as we've come this far.
The first one is gravitational lensing.
If you've ever seen a computer simulated image of a black hole, then you'll probably know that one of a black hole's most distinctive features is the blurry disc of light that surrounds it.
While perhaps sounding familiar to the accretion disk which we talked about earlier, the blurring that we're talk about here isn't due to gas and dust being superheated by tidal forces and friction.
Instead, gravitational lensing is a result of the path of photons of light coming from behind the black hole being bent by the extreme curvature of space-time, which is itself due to the mass of the black hole.
In fact, gravitational lensing is one of the strongest proofs that we have for Einstein's theory of general relativity, specifically that gravity is NOT a force.
I mentioned near the beginning of this article that I wouldn't go into details of any proofs of GR (General Relativity), but I will just say the following for the people that want a brief explanation.
For those who wish to obtain a more comprehensive understanding, I'd recommend checking out this article here.
In classical physics, gravity is depicted as being a force just like electromagnetism.
However, if gravity is a force, then a photon of light would be unaffected by gravity, no matter how strong it may be.
The reason for this is because a photon of light has no mass, by virtue of "mass" being a short version for "rest mass", which refers to the mass of an object when it's not moving.
Photons of light are bound to travel at c, the speed of light in an empty vacuum, meaning that they cannot have rest mass.
In the absence of interacting with gravity, photons of light would appear to be unaffected when travelling no matter how close to celestial bodies like black holes and stars, which we know is simply not true.
Gravity is not a force, and acceleration due to gravity is an effect of the very fabric of space-time curving due to an object's mass.
Given this, photons of light are as affected by gravity as anything else, and as they travel extremely close to the event horizon, they bend around and warp which produces the blurry disc that we see.
See below a computer simulated image of a black hole in universe sandbox 2, a space simulation game that 'd highly recommend to anyone interested in astronomy. You can check it out here on our website!
Another idea that I'd like to bring up is that black holes don't only form from the core-collapse of massive stars.
While it's understood that this is the most common method for the formation of a black hole, they can also form when neutron stars collide with each other.
Essentially, neutron stars are like tamer black holes - electrons and protons have been neutralised to form a body almost exclusively made of neutrons with next to no space in between, but that's as far as it goes and there's no physical breakdown of classical mechanics like there is with the singularity of a black hole.
We understand them (or at least we think we do), but they're the most extreme, violent celestial bodies of which can be modelled using classical/quantum physics.
Neutron stars do not undergo nuclear fusion and are held up solely due to the degeneracy pressure of their degenerate neutrons that contests their own gravity.
Degeneracy is a term that's used to describe a particle that can only occupy a single elementary cell. Neutrons, like electrons, obey this degeneracy principal, meaning that they cannot overlap with each other and this resistance causes a pressure that we call degeneracy pressure.
Think of it as a resistance to being compressed any further.
When two neutrons combine to form a single body that has the combined mass, the increase in gravitational strength collapses the neutron star into a singularity, producing a black hole.
Final words
Because black holes can demolish and spaghetify stars with their gravitational strength, they often end up consuming this matter as it falls behind the event horizon, resulting in an increase in mass.
As they do this over a potentially infinite lifespan, they can accumulate incredible quantities of mass.
I briefly mentioned earlier that most black holes simply roam around their galaxies minding their own business, and those black holes might be around 3-4 solar masses (3-4 times the mass of the Sun).
But the black holes that spend their time consuming matter in the form of stars, dust, gas and even other black holes pack on inconceivable amounts of size and mass.
For example, the black hole at the centre of our own galaxy, the Milky Way, called Sagittarius A*, is thought to be around 4 million solar masses!
But it by no means stops there...
The most massive black hole known to date is called TON-618, and this ultra-massive black hole is said to have a mass of 66,000,000,000 solar masses (that's 66 billion...)
66 billion times the mass of the Sun!
In summary, black holes are the single most mysterious objects in our universe, and our current models of physics simply cannot describe the environment beyond the event horizon.
The very fabric of space-time curves to a degree that challenges the fastest particle in the universe - a photon of light - and since our perception of time is based on the changes in events around us, time appears to run differently when observing objects close enough to a back hole.
To end on a point that I've brought up a few times during this article, relativity is currently our only model that predicts the environment and interactions of black holes (although the work of of Stephen Hawking attempts to reconcile them with quantum physics, which you can read more about here), but the significance of relativity transcends celestial bodies like black holes.
Despite its name, it's really not a theory, but rather a concept that's engrained in experience itself.
Duality is a crucial part to our existence, as we naturally analyse through comparison.
To us, even the days exist because of the nights.
It's not about what's physically happening - the MEANING or VALUE of a day is because there is a night.
Positive exists because of negative.
Winter exists because of Summer.
Happiness exists because of sadness.