Victor H. Alencar | Searcharxiv

arXiv2026

Quantum Scattering in Schwarzschild Spacetime: Hawking Radiation and Black Hole Atmospheres

In this paper, we investigate scattering of a scalar field near a Schwarzschild black hole through its $S$-matrix. Within this framework, we obtain a novel derivation of Hawking radiation by computing the emission rate, which yields a Bose--Einstein distribution with temperature $T_H=(8πGM)^{-1}$, the Hawking temperature. In addition to Hawking radiation, the S-matrix exhibits antibound states, corresponding to excitations at the threshold of becoming scattering (bound) states if the potential is decreased (increased). We interpret these excitations as constituents of the black-hole quantum atmosphere: a thermalised region outside of the event horizon, which is the source of the Hawking radiation. Using the spectrum of antibound states, we found the atmospheric radius, $r_{\text{Atm}} \approx 2.77 r_{s}$, which is in good agreement with previous results in the literature obtained through other methods. Our results indicate that, at the macroscopic level, the quantum atmosphere behaves like an ordinary thermalised gas at the Hawking temperature.

hep-th↗

arXiv2026

Black Hole Evaporation as a Topological Tunneling

We present the quantization of the electromagnetic field near the event horizon of a Schwarzschild black hole using Euclidean path integrals. Our result for the vacuum energy describes a black hole surrounded by a finite volume of photons at $T_{H} = \frac{1}{8πG M}$, the black hole quantum atmosphere. The total entropy includes contributions from this atmosphere, and the Bekenstein entropy, which arises from the Gibbons--Hawking--York boundary term, which encodes topological information. We show that the contribution of the quantum atmosphere to the black hole specific heat is positive, indicating that the system may become thermodynamically stable. By analyzing homology groups, we show that the black hole evaporation is a tunneling between topologically distinct spacetimes: Schwarzschild ($χ= 2)$ transitions to the flat spacetime ($χ= 1$) via Hawking radiation, where $χ$ is the Euler characteristic, a topological invariant. This process resembles instanton-driven tunneling in Yang-Mills theories, where topologically non-trivial solutions dominate the vacuum amplitude. In our case, the Gibbons--Hawking--York term dominates the transition amplitude, which induces the evaporation process. These results corroborate the Parikh-Wilczek picture of Hawking radiation and the interpretation of Euclidean black holes as gravitational instantons.

hep-th↗