Why Black holes evaporate? Hawking Radiation explained.

Hawking Radiation black holes evaporate.


Hawking Radiation black holes evaporate.

Black holes are one of the most mysterious and intriguing objects in the universe. The name is appropriate because, first, it is black, meaning that it absorbs all the light coming in, and does not reflect anything back.

Hawking Radiation black holes evaporate.

It’s a hole because it is as if it is a puncture in the fabric of space-time. The space inside the event horizon does not behave anything like empty space.

But in 1974, physicist Stephen Hawking theorized that a black hole may not be so black after all. His calculations showed that when you apply the laws of quantum mechanics to the classical physics that had defined our understanding of black holes, you find that they shine. They emit radiation. They give off photons.

But, how is this possible given that black holes can only absorb light.

If it can't reflect light, then where are these photons coming from? How did they get created? Surely these photons could not be coming from nothing. Or can they? 

Hawking Radiation black holes evaporate.

The gravity around a black hole is so strong that it had been thought that nothing could escape from it, including light.
If we ignore quantum mechanics, then in classical physics, the mass of a black hole cannot decrease, it can either stay the same or get larger, because nothing can escape a black hole.

Hawking Radiation black holes evaporate.

But things can fall in it, so it can gain mass that way. But things can’t escape from it. If mass and energy are added to a black hole, then its radius should get bigger.

If the radius gets bigger, then its surface area will get larger as well according to the equation: A = 4πR^2. This is just the formula for the surface area of any sphere.

For a black hole, the R in this equation is called the Schwarzshield radius. And this radius is proportional to the mass of the black hole according to this equation.

To Stephen Hawking and others, this idea of the surface area staying the same or increasing looked very similar to the 2nd law of thermodynamics.

Hawking Radiation black holes evaporate.

The second law of thermodynamics states that “In any natural process, the entropy of a closed system always increases or remains constant, it never decreases.” 


So Hawking postulated an analogous theorem for black holes, and it is called the second law of black hole mechanics. And it says: “In any natural process, the surface area of the event horizon of a black hole always increases, or remains constant. It never decreases." 

Hawking Radiation black holes evaporate.

So now you can see the parallels with the 2nd law of thermodynamics regarding entropy.

Hawking Radiation black holes evaporate.

Similar to the 2nd law, there are also ways to state the other 3 laws of thermodynamics in a way that are true for black holes as well.

The analogy with the laws thermodynamics suggest that perhaps black holes are physically a thermal body.

In thermodynamics, there is something called a black body. A black body is something that doesn’t transmit or reflect any radiation, it only absorbs radiation. Analogously, a black hole is something also doesn’t transmit or reflect any radiation, it only absorbs it. It absorbs photons.

Hawking Radiation black holes evaporate.

If a black hole can be thought of as a black body, then it must have a temperature associated with it,

Hawking Radiation black holes evaporate.

because a black body in thermodynamics always has a temperature.

But if it has a temperature, it must shine in some way. But now we have a conundrum, because according to classical physics, a black hole is not supposed to release anything. Stuff only goes in. No stuff is supposed to come out.

So how do we reconcile these two thoughts? 

Hawking Radiation black holes evaporate.

When Stephen Hawking saw these ideas, he found the idea of shining black holes to be preposterous. He set out to prove why they would NOT shine.

Hawking Radiation black holes evaporate.

But when he applied the laws of quantum mechanics to general relativity, he found the opposite to be true. He realized that stuff can come out near the event horizon.

Hawking Radiation black holes evaporate.

In 1974, he published a paper where he outlined a mechanism for this shine.

So what was the mechanism he outlined that would allow black holes to emit photons? 

Hawking Radiation black holes evaporate.

So the simplest explanation is this. All of space is teaming with virtual particles that come in and out of existence all the time and everywhere.

Hawking Radiation black holes evaporate.

This is based on the Heisenberg uncertainty principle. One version of the Uncertainty Principle can be written as the following: △E.△t is greater than or equal to h (Planck’s constant)/4π .

So basically, what this equation says is that the uncertainty in energy and uncertainty in time are inversely proportional to each other, because the product of the two is equal to a constant. 

In other words, if you know very precisely the energy of a system, then you can’t know the time over which you made that measurement very well. Or visa versa, you can know the time very well, but not the energy. 

Hawking Radiation black holes evaporate.

But what this equation also tells you is that you can get particles with an energy △E and if it occurs for a very short period of time, △t, such that the product of the two is less than h (Planck’s constant)/4π .

That is, particles can exist that violate this uncertainty principle.

How is this possible? 

Hawking Radiation black holes evaporate.

Well, this is one of the crazy things about quantum mechanics. Violations are allowed.

But it’s as if by not obeying this Heisenberg uncertainty principle, the universe really doesn’t register or record its existence because no measuring device would ever be able to measure this directly.

A particle with some finite energy, as long as the change in time is very small, can exist.

Hawking Radiation black holes evaporate.

So what's happening is particle/antiparticle pairs borrow temporary energy from the present, and give it right back in the future by annihilating themselves.

Hawking Radiation black holes evaporate.

This is how virtual particles are formed in empty space. And space is teeming with them. This is called also the quantum foam.

You might ask, if we can’t measure it, how do we know it's actually happening.

Hawking Radiation black holes evaporate.

Well, it does affect the universe in ways that are measurable,
for example, it manifests as a force in something called the Casimir effect.

Hawking Radiation black holes evaporate.

In which the quantum foam outside a set of two plates is greater than the pressure inside the plates, and this creates a force pushing the plates together.

So this virtual particle creation and annihilation does exist, and is a central part of quantum mechanics

Hawking Radiation black holes evaporate.

The severe curvature of space-time near the event horizon of a black hole disturbs this quantum foam in ways that you don’t see in normal empty space. As Neutrinos and antineutrinos, or electrons and positrons, and other particle-antiparticle pairs can get created,

sometimes when two of these particles are close to the horizon, one particle can get sucked into the black hole before the two particles have a chance to annihilate each other.

Hawking Radiation black holes evaporate.

This kind of capture and release by the black hole can happen anywhere in the space around the event horizon - outside it as well as inside it.

Hawking Radiation black holes evaporate.

If the partner is left outside, it will no longer have a partner with which to annihilate, so it will remain and escape from the black hole.

This particle will be carrying energy with it. This is what we perceive as Hawking radiation outside the black hole. This is how a black hole shines.

Hawking Radiation black holes evaporate.

Where did this energy of the escaped particle come from?


Hawking Radiation black holes evaporate.

From our perspective outside the black hole, the particle we got is positive, but this means that the black hole got negative energy.

In other words it lost energy. This is the same thing as losing mass because of mass energy equivalence of Einstein’s famous equation, E=MC^2.

Hawking Radiation black holes evaporate.

So the virtual particles are created in space by borrowing energy, but ultimately, so that nothing violates the law of energy conservation, the energy of the shine is really coming from the mass of the black hole.

So this is a popular way to think of Hawking Radiation but it has some problems.

Hawking Radiation black holes evaporate.

I think the biggest problem with this is that the radiation from black holes is not in all wavelengths, as would be expected with this mechanism.

Hawking Radiation black holes evaporate.

The radiation actually has a wavelength equal to the size of the black hole. So smaller black holes emit shorter wavelengths, or more energy, than larger black holes.

So a more accurate way to look at this the following. Now this is still an approximation, but it is a probably a closer approximation.

In reality, there really are no particles, only fields. This is the crux of quantum field theory.

The actual Hawking calculations considered waves coming in from infinity and being scattered or disrupted because of the black hole event horizon, as it was forming.

Certain vibrations of waves are deflected by the gravitational field of the black hole as it forms in the past.

Some of these get distorted or even absorbed by the event horizon.

Hawking Radiation black holes evaporate.

Some waves do not get deflected at all. Hawking showed that the wave entering the event horizon was disrupted in a way that the wave on the other side, carried away energies corresponding to the size of the black hole.

Particles with waves as large as the event horizon get lost within the event horizon,

Hawking Radiation black holes evaporate.

so the energy we see are about as large as the event horizon. The quantum fields that have wavelengths the size of the black hole get out with more energy than they came in with, because waves that get absorbed by the black hole have to be negative energy in order for us to see positive energy in our universe.

Hawking Radiation black holes evaporate.

This corresponds to an energy spectrum analogous to a black body at a certain temperature.

So this is why Black holes have a temperature and this is what we perceive as Hawking Radiation.

But is Hawking radiation real? Can we measure it? 

Not directly but Hawking found a formula for the temperature of a black hole.

Hawking Radiation black holes evaporate.

Note that the temperature is proportional to the reciprocal or inverse of the mass. As the black hole evaporates over time, the M in the equation becomes smaller and smaller.

This means that the temperature rises as the black hole evaporates. As the black hole evaporates, its mass decreases.
So the hottest black holes are the smallest ones. This is why they lose energy faster.

Hawking Radiation black holes evaporate.

Now here’s the interesting part, as the mass goes to zero, the evaporation rate goes to infinity.

So this tells us that near the end of the evaporation process, we would see an explosion of the black hole as the mass is quickly used up.

Hawking Radiation black holes evaporate.

This would be seen as a burst of high energy photons or gamma rays.

Hawking Radiation black holes evaporate.

The lifetime of a black hole is calculated using this equation:

Hawking Radiation black holes evaporate.

if you do the calculations, it means that anything with mass less than 10^15 grams would have evaporated by now. These would be tiny black holes about as massive as Mount Everest.

Hawking Radiation black holes evaporate.

They would only be about the size of a proton by the way.
Hawking theorized that such tiny black holes could have existed at the time of the big bang.

Hawking Radiation black holes evaporate.

But it also means that black holes slightly larger than 10^15 grams, would be evaporating around this time in our universe.

And if this is happening, it means that we should see a bunch of Gamma Ray bursts.

So do we detect Gamma Ray bursts?

Hawking Radiation black holes evaporate.

We absolutely do. In fact about one gamma ray bursts or GRB occurs per day.

Hawking Radiation black holes evaporate.

However the pattern of gamma rays do not fit with what we would expect to see in a black hole explosion.

What we see are bursts with variations in brightness, from bright to dim to bright again.

Hawking Radiation black holes evaporate.

The black hole evaporation should look like a steady increase in luminosity from a low value to a high value until a final explosion.

Hawking Radiation black holes evaporate.

So these gamma ray bursts are attributed to another phenomenon – probably colliding neutron stars, or explosions of supermassive stars, not evaporating black holes.

Hawking Radiation black holes evaporate.

So the data does not support the idea that very small black holes exist. But despite the fact that no direct evidence of Hawking Radiation exists, it perfectly fits within the laws of quantum mechanics, and few if any physicists dispute its existence.

Here’s what I find incredible about black hole entropy.

First let’s clarify what entropy is – It is a measure of the amount of disorder in a system.


You can scramble an egg, but you can’t unscramble it. A more disordered system, like the scrambled egg, has greater entropy.

Hawking Radiation black holes evaporate.

You need more information to describe the scrambled or disordered state. So information is also proportional to entropy. 

Beckenstein showed that the entropy of a black hole is defined by this equation:

Hawking Radiation black holes evaporate.

A is the area of a black hole. And Z is very large constant.
This means entropy of black holes is a huge number.


A black hole of the size at the center of our Milky Way galaxy, has an entropy on the order of about 10^91.

Hawking Radiation black holes evaporate.

If you take all the entropy in the universe, ignoring gravity and other black holes, I mean, take the entropy of all the matter, stars, burning fossil fuels, all the dark matter, it would only be about 10^88. 

Hawking Radiation black holes evaporate.

So our black hole at the center of just our galaxy has almost 1000 times the entropy of the entire universe. 

And there are at least 100 billion other such black holes in the universe.

So almost all the entropy of the universe is contained in black holes. Anything outside black holes is negligible in comparison. 

Hawking Radiation black holes evaporate.

And if you equate entropy with information, this should tell us that most of the information of the universe also lies within black holes.

Why is this the case? What the heck is going on inside these things? 

Hawking Radiation black holes evaporate.

Since no one can ever go inside and come back out to tell us, it’s hard to say. But before you get too excited, this doesn’t mean that black holes are a giant computer or brain.
It’s not information like in books, or hard drives. But it’s information that defines the various microstates of particles in a system.

It’s mind bending thoughts like this that makes science really interesting.

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