Black holes do actually radiate, this radiation is dubbed hawking radiation after its discoverer Stephen Hawking. The Hawking radiation was discovered when you incorporate the ideas of quantum mechanics into how a black hole would work. To understand hawking radiation, you must first understand two things:
1. Quantum Vacuum Fluctuations
Vacuum is normally described as something completely empty, with no particles what so ever in it. But In quantum mechanics, there’s the heisenbergs uncertainty principal which says that at particle small levels you can’t know every thing to a 100%, the more you know about one thing the less you can know about another thing. This apply for example to energy and time. If you want to know the energy level better you have to measure it under a longer time. The vacuum, which isn’t supposed to have any energy, has particles constantly being created and destroyed. This is because of the above mentioned uncertainty principal. According to it, energy may fluctuate and the higher the energy level of the fluctuations have, the less time they can exist. This makes it possible for a virtual particle/anti-particle pair to be created, move around a bit and then meet and annihilate each other so that the energy borrowed in the creation is returned. The particles created in these fluctuations are said to be virtual, because you can’t detect them directly but you can measure their effect on other things such as the energy levels in atoms. But the virtual particles can become real, detectable, particles if they are able to take some energy from a field of some kind. the problem is that under their short life time they simply haven’t got enough time to become real particles.
2. Tidal Gravity
The longer away you get from earth the weaker its gravitational pull will be, e.g. you’ll fell the pull of gravity stronger on the surface of earth then if you where out in the atmosphere. This is called tidal gravity. For a black holes the tidal gravity near the horizon can be incredibly strong, there may be an immense difference between the pull on your feet then the pull on your head, if your feets are closer to the horizon then your head. But as it turns out for a bigger black hole the difference in tidal gravity is far less then a small black hole. We’ll talk about this later.
If a virtual particle/anti-particle pair is created near the event horizon of a black hole, the tidal gravity can be so strong that the pair gets separated for a long enough time so that the gravitational field give the particles energy and then they can become real particles. Then one of the particles might be sucked into the hole so that it can’t annihilate the other. While the other one escapes and moves away from the hole. So now the hole will have lost half the energy it put into making the two virtual particles real particles.
The amount of radiation should also increase. To see this, we first have to understand something about the intensity of tidal gravity: I said that the pull on your feet and the pull on your head might be very different in the vicinity of a black hole. But if you increased the power of the gravitational field, so the pull would be larger. Then your head and your feet would be pulled faster towards the hole, but since the pull would be stronger you would fell less difference between the pull on your feet and the pull on your head. They would be pulled more in unison.
And the higher tidal gravity the more efficiently are for example the particle pair torn apart. Now as said, the more energy the particles have the less time they can be apart . So for high energy particles the gravity has only a little while to manage to pull them apart and make them into real particles i.e we need a strong tidal gravity. So big black holes can only make virtual particles of low energy into real particle, since it has a very low tidal gravity and needs the particles to exist a longer time in order to be able to give them enough energy so they can become real particles. And then small black holes can radiate particles of both low and high energies because of their high tidal gravity which doesn’t require the particles to exist for such a long time, but instead it can tear them apart efficiently. Therefore as the hole radiates away its mass and gets smaller the intensity of the radiation should increase.
You can also explain Hawking radiation by another quantum mechanical properties called quantum tunnelling. In quantum mechanics a particle doesn’t have a specific state but has a certain probabilities of existing a little bit every were. So even a particle falling into the horizon has a chance of being out side it. And can therefore also suddenly appear out side it, and can escape the hole. Here the amount of radiation would also increase as the black hole decreased, since the smaller hole the less barrier the particle has to tunnel through, the particle has a larger chance of being somewhere outside the horizon.
So the black hole actually has entropy and the amount of entropy is shown be the size of its event horizon.