Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Free-fall Frame

TL;DR

This paper investigates how modified dispersion relations near the Planck scale affect Hawking radiation in a free-fall frame, revealing corrections to temperature and entropy while confirming the standard Hawking temperature at leading order.

Contribution

It introduces a Hamilton-Jacobi approach to analyze dispersive field models in a free-fall frame, calculating quantum corrections to Hawking radiation and entropy.

Findings

Corrections to Hawking temperature are computed for massive and charged particles.

The Hawking temperature matches the standard value at leading order.

The thermal entropy of scalar fields near the horizon is evaluated.

Abstract

Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass $m_{p}$. The corrections to the Hawking temperature are calculated for massive and charged particles to $\mathcal{O}\left( m_{p}^{-2}\right) $ and neutral and massless particles with $\lambda=0$ to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation.