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

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.

14 pages, 2 figures, Latex macros. In the final version, section 5 has been amended, the presentation has been improved, and References 21-24 have been added. Last misprints amended in Section 5 and Ref. 24

References in corpus (6)

• A Gravity Theory on Noncommutative Spaces
• Trace Anomaly in Quantum Spacetime Manifold
• Tunneling between de Sitter and anti de Sitter black holes in a noncommutative D3-brane formalism
• Probing quantum gravity effects in black holes at LHC
• Coherent and squeezed states in black-hole evaporation
• Quantum amplitudes in black-hole evaporation: Spins 1 and 2

Cited by in corpus (6)

• Noncommutative Schwarzschild Black Hole and Area Law
• Strong gravitational lensing in a noncommutative black-hole spacetime
• Black hole evaporation in a spherically symmetric non-commutative space-time
• The scalar wave equation in a non-commutative spherically symmetric space-time
• Thermodynamics of Black Holes: Semi-Classical Approaches and Beyond
• Neutrino spin oscillations in gravitational fields in noncommutative higher dimensions