Hawking radiation & How Hawking radiation work in Black Hole

Hawking radiation, also known as Hawking–Zel'dovich radiation, is blackbody radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after Jacob Bekenstein, who predicted that black holes should have a finite entropy. 

Stephen Hawking

Hawking's work followed his visit to Moscow in 1973 where the Soviet scientists Yakov Zeldovich and Alexei Starobinsky showed him that, according to the quantum mechanical uncertainty principle, rotating black holes should create and emit particles. Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger emitters of radiation than larger black holes and should shrink and dissipate faster.

Stephen Hawking was perhaps the greatest genius of our time Stephen Hawking peered behind the curtain of reality and glimpsed the true workings of the universe he inspired all of us to pursue our curiosity no matter the obstacles however his true legacy is his work he made profound contributions across physics from quantum theory to cosmology our tribute is to bring you Stephen Hawking's most famous discovery 

it's time for Hawking radiation soon after Einstein revealed his great general theory of relativity in 1915 physicists realized that allowed for the possibility of catastrophic gravitational collapse in places of extreme density like the dead core of a massive star space and time could be dragged in words to create a hole in the universe a boundary in space-time called an event horizon. 

That could be entered but from beyond which nothing could return once formed there was nothing in theory or imagination that could bring material consumed back to the outside universe these black holes should exist forever only growing never shrinking or so we thought until 1974 when a young physicist named Stephen Hawking published a paper in nature entitled black hole explosions in this and in a follow-up 1975 paper he attempted a new union of quantum mechanics 

and general relativity to show that black holes should not be so black after all they should leak they should admit what we now know as Hawking radiation there's a popular description of how Hawking radiation works it goes something like this empty space see this with activity as pairs of virtual particles matter and antimatter spontaneously appear and then annihilate each other briefly borrowing energy from the vacuum itself but when this happens near a black hole sometimes one of the pair will be swallowed by the event horizon leaving the other free to escape and taking its toll and energy with that energy can't come from nothing and so the black hole itself pays the debt by slowly leaking away its mass this is a nice picture 

but how accurate is it in fact if we follow the narrative of Hawking's original calculation the story sounds rather different we've come a long way over the past few months building up the knowledge we'll need to follow that calculation rewatching some of those episodes either now or after this video will be helpful 

but if you think you're ready let's take a deep dive into the quantum field theory of curved space-time to glimpse the true nature of Hawking radiation actually a quick qft refresher can't hurt space is filled with quantum fields they can oscillate with different frequencies much like the many possible vibrational modes on the guitar string a particle is like a note on the string and just like a real guitar note real particles tend to be comprised of many vibrational modes those underlying vibrational modes are still present in the absence of real particles they fluctuate an energy due to quantum uncertainty and those fluctuations give us what we think of as virtual particles now don't take the existence of virtual particles too seriously they're really just a tool for calculating the infinite ways in which a fluctuating quantum field can behave one way the quantum fields are very different to guitar strings is that they can have both positive and negative frequencies a negative frequency can be thought of as a mode that travels backwards in time and can be interpreted as corresponding to antimatter 

Now that's a whole level of weird or on its own and we talked about it here when a quantum field is in a vacuum state there's a balance between positive and negative frequency modes which you can crudely think of as a balance between virtual matter and antimatter particles these all virtually annihilate or cancel out so that no real particles exist this is all fine in flat space but spatial curvature can mess with the balance of the underlying quantum field modes by introducing horizons horizons cut off access to certain modes of the quantum fields disturbing the balance that defines the vacuum Stephen Hawking knew that black holes with their insane space-time curvature would wreak havoc on quantum fields in ever Cinna t but what would the effect be to answer that properly he would need a full union of general relativity and quantum mechanics a theory of quantum gravity a theory of everything it didn't exist then and it doesn't exist yet not to be deterred by the impossible Hawking came up with an ingenious workaround the narrative of Hawking's mathematics goes something like this he imagined a single space-time path a Lightspeed trajectory called annul of geodesic 

it extends from far in the past to far in the future this is a perilous path it passes through the location of a black hole in the instant before it forms in fact it is the very last trajectory to do so it emerges barely ahead of the forming event horizon Hawking imagined a simple quantum field tracing this path a field that is in a perfect vacuum state before the formation of the black hole but he found that the close shave with the black hole disturbs the fundamental vibrational modes that define the fluctuations of the vacuum by the time this trajectory has found its way back out into flat space again those fluctuations look like real particles a distant future observer sees radiation coming from the black hole Hawking's imaginary path from the distant past to the distant future was brilliant it allowed him to compare the state of the vacuum in two regions of flat space far from the black hole regions where the nature of vacuums quantum fields 

and particles are perfectly well understood but to understand the effect of the close encounter with the black hole he required an uneasy marriage of quantum mechanics and general relativity in the absence of a theory of quantum gravity Hawking needed a hack that hack was the Bogoliubov transformations said that three times fast these can be used to approximate the effect of curved space-time on quantum fields by smoothly connecting regions of flat space they describe a sort of mixing of the positive and negative frequency vibrational modes that are caused by that curves the physical interpretation of this mixing via the boggle above transformations is tricky in fact there isn't just one valid interpretation Hawking's calculation talks about scattering certain modes of the quantum field are scattered or deflected by the gravitational field of the forming black hole they are nudged off their narrow escape path 

and Sewer lost behind the forming event horizon meanwhile other modes avoid scattering and continue unscathed with the loss of certain fundamental modes the vacuum state must be constructed from the remaining modes that distorted vacuum looks like it's full of particles the nature of the lost modes tells us what Hawking radiation should look like black holes tend to scatter modes with wavelengths similar to their own sizes the quantum field that emerges is distorted in the same wavelength range and so it produces wave packets it produces particles that also have wavelengths about as large as the event horizon so the more massive the black hole the longer the wavelength of its radiation Hawking calculated the frequency distribution of this radiation and found something incredible it should look exactly like thermal radiation black holes would have a heat glow with an apparent temperature that depends on their mass more directly it's proportional to the surface area of the event horizon large black holes should appear cold radiating excruciating  slowly but small black holes should appear hot and the smallest should radiate explosively okay so what about the whole picture of particle-antiparticle pairs being pulled apart by the event horizon 

so Hawking's math describes splitting or mixing of these pure positive and negative frequency modes it's fair to interpret this mixing as the promotion of what were once virtual particles into reality and for the escaping modes there exists a corresponding set of modes linked by quantum entanglement that are trapped behind the event horizon we can interpret those as corresponding to the swallowed antiparticle partner so the split matter antimatter part of the picture is reasonable but there are reasons to dismiss aspects of this picture firstly this radiation is not localized remember the Hawking radiation has wavelength the size of the event horizon the size of the entire black hole well these are the debris wavelengths have created particles and they tell us that there is an enormous quantum uncertainty in the location of these particles 

Hawking radiation must appear to come from the global black hole not from specific points on the event horizon in fact an observer in free fall through the horizon sees nothing to them space is locally flat the vacuum should look like a vacuum this radiation is visible only to distant observers well there is one exception when you turn on your jetpack and hover a fixed distance above the horizon then you do see particles you see Unruh radiation will look at its relationship to Hawking radiation in the future by the way Hawking radiation is mostly going to be photons and other massless particles to produce particles with mass the energy of the radiation has to be high enough to cover the rest mass of the particle so it's okay to interpret the narrative of Hawking's calculation as the splitting of entangled matter and antimatter pairs even if it really is just a heuristic interpretation it's the cause of the splitting that's hard to pin down we can think about positive and negative frequency modes being mixed due to scattering perhaps by the as yet undiscovered graviton other physicists have derived Hawking's result with very different seeming narratives for example in 2001 parikh and will check got the same thermal spectrum for hawking radiation by thinking about particles escaping from beneath the event horizon through quantum tunneling the common thread is quantum uncertainty

for example uncertainty in position or momentum can lead to particle pairs too or once in the same location or merge through once on the same world line becoming separated by the event horizon alternatively uncertainty in energy can lead to particle creation whichever way you interpret it it's hard to avoid the conclusion that black holes emit particles the fact that different derivations lead to exactly the same result or that the radiation looks thermal can't be by chance it's hard to make Hawking radiation go away in the earth and believe me Stephen Hawking himself tried ultimately however these calculations are all hacks albeit asleep brilliant ones without a full quantum theory of gravity the origin of Hawking radiation will remain mysterious and there are other mysteries that we haven't touched on for example what happens to the particles or modes trapped by the black hole how do they end up reducing the black hole's mass instead of increasing it and then there's the famous information paradox in which Hawking radiation appears to destroy what should be a conserved quantity quantum information will tackle all of these in future episodes for now we must conclude that black holes radiate and in doing so evaporate the scariest monsters of general relativity are ultimately unraveled by the brilliant mind of Stephen Hawking and a mysterious quirk of quantum space-time.

How Hawking radiation work in Black Hole?

It all started in 1972 when Jacob Beckenstein theorized that Black Holes should have Entropy. So, maybe you’re asking yourself… What is Entropy?

Entropy is a part of thermodynamics and it basically states that Everything must release heat. Unless it is at 0 degree kelvin( -273 degrees celsius). Now this includes a Black Hole. But as we’ve known that black holes have always appeared to absorb things! It never releases things… Even the light coming out undergoes a high degree of redshift due to which the frequency falls below the visible spectrum!

But Jacob thought that there should be some heat still leaving it according to Thermodynamics! This led Stephen Hawking, in 1973, to go to Moscow to meet 2 Soviet Scientists (Sorry I don’t remember their names :P ). They showed Stephen Hawking that Black Holes should be emitting particles according to the Uncertainty Principle (I’ll write about that in future). This led Stephen Hawking in 1974 to publish his paper on Hawking Radiation! Also known as Black Hole Evaporation!

So, that’s it! Enough of history! Now let’s dig into the Physics of it all…

Lets start off with Quantum Physics! It is a field that is often regarded to be a sort of difficult field a.k.a the field that doesn’t make any sense!

Quantum Mechanics is the physics of everything that is really very very small… Like electrons, atoms, photons etc.

On the other hand General Relativity is for everything BIG! Like Black Holes, stars, planets etc.

Quantum Mechanics appears to be very real…

Stephen Hawking was trying to find a way to demonstrate a Black Hole in the Quantum World!

So, basically, he wasn’t looking at the BIG planets that are being sucked in by the Black Hole….

Hawking Radaition

…. He was rather looking at the tiny little particles and how they interact with the Black Hole. Since General Relativity couldn’t explain why radiation should be coming out of a Black Hole, maybe Quantum Physics could! And most importantly, HE WAS RIGHT!

Stephen Hawking was looking at the specific quantum event called Virtual Particles. Bear with me as I try to explain…

Let’s start off with some basic math…

Let’s think about 0 (zero). 0 is basically nothing, right? And, there are many ways to make 0…

0=0

Let’s play around…

0=1–1 => This is still true and legit!

What you just read is basically what is happening with our Virtual Particles! In our example, 0 was empty. Now, emptiness, when you think about it is something void of everything! I mean there’e nothing in it… But just like 0 also, in space, there are these things called Virtual Particles. These are basically particles of Matter and Anti-Matter!

They’re constantly being created and destroyed immediately! If this doesn’t baffle your mind, then you are devoid of emotions!

A particle of matter appears… and a particle of anti-matter appears. The moment they appear, they also collide and send matter as 1 and anti-matter as -1. They simply annihilate themselves! Just like in our little example… 0=1–1.

Now the reason this can work and doesn’t violate Law of Conservation of Mass, is because anti-matter is the opposite of matter. So, with both of them being created, there is an equal amount of matter and anti-matter, which implied they are literally creating nothing!

For those who are wondering about antimatter…

Anti-Matter is just matter. Only, it is completely opposite! Like, the antimatter equivalent of an electron is a positron! Yeah, it’s positive.

So, what happens when antimatter hits a piece of matter? They annihilate themselves!

Now that we know about Virtual Particles, let’s think about Black Holes!

It’s just a massive cosmic entity that absorbs anything that comes close enough to it!

When scientists directly observe the center of a black hole, they see nothing! This is due to the high degree of redshifting of light. Now, Black Holes, as defined by general relativity, will just keep absorbing and absorbing and just get bigger and bigger!

But that picture changes with Hawking Radiation! Now I strongly recommend you to read this post on the Event Horizon before trying to understand what Hawking Radiation actually is!

Unnikrishnan Menon's post in Black Holes Aren't So Black!

It is the boundary marking the limits of a black hole. With that out of the way, here’s the big question…

How are these so called “Hawking Radiations” able to escape something that even light cannot?

All the physics I just explained is now gonna come together !!!

So what happens is right at the Event Horizon, a virtual particle pair appears. And because of the massive force of the black hole, one of the particles gets sucked into….

….and the other one manages to escape!

So from an outsider’s point of view, one would see particles being radiated out of the black hole! In fact, they are not actually coming out of the Event Horizon, they are actually being created right at the side of the Event Horizon…. and they are seemingly shooting out!

The more these virtual particles pairs, the smaller it will get! Which is why it is also called Black Hole Evaporation. So if a black hole is big enough, it is obviously absorbing a whole lot of things. These radiating particles will be very minor when compared to the massive amount of things it is absorbing. But if it’s a smaller black hole, then that means that it will actually be radiating more than it is absorbing! Which in turn implies that over time, the black hole will get smaller and smaller until eventually it just disappears!

Phew….

That means the black hole, contrary to what general relativity says, if it is small enough to start with, will get smaller and smaller and smaller….

….Until it is gone completely!

And THAT, my friend, is HAWKING RADIATION!!!

Well, here’s one thing that must be bothering you…

Why is it that only the Anti-Matter gets sucked into the Black Hole?

The answer to this is that Virtual particle pairs don’t quiet appear out of nothing! Don’t forget that this is Quantum Mechanics! So things are bound to get weird o.0

When Matter and Anti-Matter collide and annihilate themselves, they release ENERGY! Because even though they are opposites, they’re both still made out of energy. So, the thing is, where does that energy come from? It actually is empty space but that energy that is used to create this particle of matter and this particle of anti-matter, is actually energy taken from the black hole’s potential gravitational energy! So does this crazy fact fit into the puzzle called Hawking Radiation?

It doesn’t matter if it is the anti-matter that or the matter that escapes! Because the energy used to create that particle was energy from the black hole. Which essentially means that the Black Hole is losing energy and therefore losing MASS!