Black hole evaporation in a spherically symmetric non-commutative space-time

TL;DR

This paper investigates how non-commutative geometry modifies the quantum amplitudes involved in black hole evaporation, revealing a multiplicative factor influenced by non-commutativity parameters that alter the classical gravitational analysis.

Contribution

It introduces a novel perspective on black hole evaporation by incorporating non-commutative geometry effects into the quantum amplitude calculations for spherically symmetric black holes.

Findings

Quantum amplitudes are modified by a multiplicative factor F due to non-commutativity.

The factor F depends on a non-commutativity parameter and the radial coordinate limit R.

Limiting forms of F are compatible with the adiabatic approximation.

Abstract

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in noncommutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. Relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, we have considered from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes has been shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F have been derived which are compatible with the adiabatic approximation.