Nonrelativistic spinless particle in vicinity of Schwarzschild-like black hole

Abstract

In this paper, we analyze the behavior of a nonrelativistic 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 space–time 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 nonrelativistic equivalent of Hawking radiation.