Abstract
The Hawking radiation emits all species of particles, but the Bekenstein–Hawking entropy is independent of the number of the species of particles. This is the so-called species problem—a puzzling problem for a long time. In this paper, we suggest a solution to this problem. A result of the scheme is that the black hole atmosphere has a mass equaling 3/8 mass of a classical Schwarzschild black hole, which agrees with ’t Hooft’s brick wall model.
Highlights
We suggest a solution to the species problem
The entropy of the atmosphere was first calculated by t’ Hooft [1] in the brick wall model, and thereafter some authors pointed out that the entropy of the atmosphere should be regarded as the entanglement entropy [5,6,7]
The species problem arises in the entanglement entropy calculation
Summary
This result tells us that no matter how many species of particles are emitted, the entropy depends only on the total energy of particles rather than the number of the species of particles. The atmosphere accounts for 3/11 of the mass of a Schwarzschild black hole. For the Schwarzschild spacetime, we can arrive at the Bekenstein–Hawking entropy. The key point of this scheme is to regard the atmosphere of a spacetime, which is a pure quantum effect, as a part of. A spacetime consists of two parts: the classical bare spacetime and its atmosphere. The entropy of the spacetime all comes from the atmosphere. The entropy, regardless of the species of particles, is proportional to the energy (mass) and is independent of the species of particles. A by-product of this scheme is that for a Schwarzschild black, the ratio of the mass of the classical bare black hole and its atmosphere is 8:3. Hooft showed that the energy of the bosonic gas outside the Schwarzschild horizon is [1]
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