2023/10/22 by R. G. G. Amorim, Amorim, Ronni, Vinicius Rispoli +5 · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2310.14241
openalex publication_date 2023/10/22 · openalex created_date 2023/10/25 · openalex updated_date 2026/07/28
In this article we analyze the behavior of a non-relativistic spinless particle near the event horizon of a Schwarzschild-like black hole. In this way, the Schrödinger covariant equation that describes the particle is obtained from the Galilean covariance technique. The Schrödinger equation in a Schwarzschild-like spacetime is solved analytically and its solutions are given in terms of the confluent Heun function. As a relevant result, we discovered that the energy levels of the particles are quantized and that the particle does not escape to infinity. We obtain the existing transmission and reflection coefficients for a particle and anti-particle pair at the event horizon. We thus verify that there is no non-relativistic equivalent of Hawking radiation.