Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes

Benrong Mu,Haitang Yang,Peng Wang

doi:10.1155/2015/898916

Abstract

We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole’s mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.

Highlights

The classical theory of black holes predicts that nothing, including light, could escape from the black holes
Among them is a semiclassical method of modeling Hawking radiation as a tunneling effect proposed by Kraus and Wilczek [2, 3], which is known as the null geodesic method
We investigate scalars and fermions tunneling across the horizons of black holes using the deformed Hamilton-Jacobi method which incorporates the minimal length via (4) and (5)

Summary

Introduction

The classical theory of black holes predicts that nothing, including light, could escape from the black holes. Stephen Hawking first showed that quantum effects could allow black holes to emit particles. [23] provides a way to incorporate the minimal length with special relativity, a good starting point for studying Hawking radiation as tunnelling effect. The GUP deformed Hamilton-Jacobi equation for fermions in curved spacetime have been introduced and the corrected Hawking temperatures have been derived [32,33,34,35,36]. We investigate scalars and fermions tunneling across the horizons of black holes using the deformed Hamilton-Jacobi method which incorporates the minimal length via (4) and (5).

Deformed Hamilton-Jacobi Equations

Quantum Tunnelling

Thermodynamics of Black Holes

Conclusion