Gravitational amplitudes in black-hole evaporation: the effect of non-commutative geometry

TL;DR

This paper explores how noncommutative geometry influences quantum amplitudes in black hole evaporation, revealing modifications to gravitational amplitudes and particle emission rates due to noncommutativity effects.

Contribution

It introduces a novel approach to incorporate noncommutative geometry into black hole evaporation analysis, modifying gravitational amplitudes with a new multiplicative factor.

Findings

Amplitude modifications depend on noncommutativity parameter

Derived approximate formulas for particle emission rates

Compatible with 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 noncommutativity 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. The present paper, relying on the recently obtained noncommutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is 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 are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework.