Tunnelling phenomenon near an apparent horizon in two-dimensional dilaton gravity

TL;DR

This paper investigates the tunnelling process at an apparent horizon in two-dimensional dilaton gravity, deriving the radiation spectrum and temperature, and confirming results with an alternative method in stationary cases.

Contribution

It introduces a novel analysis of tunnelling at apparent horizons in 2D dilaton gravity using Hamilton-Jacobi and null geodesic methods, highlighting differences from higher-dimensional theories.

Findings

Radiation spectrum consistent with surface gravity

Temperature matches the expected relation with surface gravity

Null geodesic method confirms Hamilton-Jacobi results

Abstract

Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon of the apparent horizon by using Hamilton-Jacobi method. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. The spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum and it satisfies the usual relationship with the surface gravity. Besides, the calculation with Parikh's null geodesic method for a simple example conforms to our result in general stationary cases.