JackDole wrote:Energy is also just a mathematical construct so that we can write formulas and describe physical processes in terms of a conserved quantity.
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But what I believe to have been understood is that Hawking radiation has not been proven yet, no one really knows what it is and that it's just a mathematical construct to preserve the entropy!
That black holes have an entropy associated with their event horizons is not controversial. We just calculated it!
That this entropy depends on the energy tells us that black holes have a temperature, and therefore they must radiate photons with a blackbody spectrum. There's really no way around it, and Hawking made the proof even more rigorous. (He did not use matter-antimatter production, but instead the propagation of modes of the vacuum fields by applying quantum field theory. Describing this as "matter-antimatter pairs" is just a convenient but oversimplified narrative, almost as sloppy as saying the Big Bang came from nothing.)
Is there any experimental evidence for concluding Hawking radiation exists? Well, we do observe it in a variety of analogue black holes in the lab. But maybe because we don't measure it directly from real astrophysical black holes, one may still be skeptical. For any reasonably-sized black hole the radiation would be so weak that there is no hope to measure it. However, we can make an observation with real black holes that supports it indirectly. Specifically, we can test the other predictions of black hole thermodynamics. Since the black hole's entropy is proportional to its horizon area, the 2nd law of thermodynamics insists that when two black holes merge together, the total horizon area cannot decrease.This is a strict limit on how big the resulting black hole can be. By conservation of mass, it cannot be bigger than the sum of the masses of the two original black holes. But by law that the entropy and thus area cannot decrease, the square of the resulting mass cannot be less than the sum of the squares of the two original masses.
Example: If two 10 solar mass black holes merge, then the greatest possible result is 10+10=20 solar masses, but the minimum possible result is sqrt(102
) = sqrt(200) = 14.14 solar masses. Whatever difference from 20 solar masses was carried away by gravitational waves.
We can test this by looking at the gravitational waves from black hole mergers with LIGO, and indeed, the gravitational waves never carry more energy than what the laws of black hole thermodynamics allow.
(Aside: what kind of collision would result in the maximum allowed value of just adding the masses together? That happens if the two black holes collide head-on. Otherwise, some orbital angular momentum is shed as gravitational waves, and this reduces the total mass of the system.)