Black Holes and Quantum Mechanics

The next surprise came about when quantum effects were studied. In quantum mechanics the vacuum is not merely the absence of particles. The vacuum is a very interesting state where all the time we have particle pairs being created and destroyed. In flat space we have no net production of particles since energy has to be conserved. All particles that are produced have to annihilate very quickly. In 1974 Steven Hawking showed that when a horizon is present this is no longer the case. What can happen is that a particle with positive energy and one with negative energy are created in the vicinity of the horizon. The negative energy particle falls into the black hole and the positive energy one flies away. In flat space this is not possible because we cannot have negative energy particles. However, on the other side of the horizon, a particle that has negative energy from the point of view of an observer far away can have positive energy from the point of view of an observer inside the horizon. The net effect is that the black hole emits particles. The emitted particles have a thermal distribution with a temperature that is inversely proportional to the black hole mass. For solar-mass black holes this temperature is too tiny for this effect to be measurable. If the black hole were in empty space, it would slowly lose mass and become smaller. Smaller mass black holes could have higher temperatures. A black hole with a mass of the order of 10¹⁸ Kg (the mass of a mountain range) would have a temperature of a thousand degrees and it would look white. It would emit as much light as a 1 milli-watt light bulb. As its mass becomes smaller and smaller, its temperature would rise and it would evaporate faster and faster until it, presumably, evaporates completely. In fact if we took a mass of a few kilograms and we collapsed it into a black hole (something that would be very hard to do in practice!) it would evaporate completely in less than a millisecond and it would release more energy than a nuclear bomb.

This thermal property of black holes gives rise to a couple of puzzles: 1) What gives rise to the entropy? and 2) the information paradox. I will try to explain these two puzzles in more detail.

Дата добавления: 2015-08-03