Renormalized stress tensor for massive fields in KerrNewman spacetime
Abstract
In a fourdimensional spacetime, the DeWittSchwinger expansion of the effective action associated with a massive quantum field reduces, after renormalization and in the large mass limit, to a single term constructed from the purely geometrical GilkeyDeWitt coefficient a_{3} and its metric variation provides a good analytical approximation for the renormalized stressenergy tensor of the quantum field. Here, from the general expression of this tensor, we obtain analytically the renormalized stressenergy tensors of the massive scalar field, the massive Dirac field and the Proca field in KerrNewman spacetime. It should be noted that, even if, at first sight, the expressions obtained are complicated, their structure is in fact rather simple, involving naturally spacetime coordinates as well as the mass M, the charge Q and the rotation parameter a of the KerrNewman black hole and permitting us to recover rapidly the results already existing in the literature for the Schwarzschild, ReissnerNordström and Kerr black holes (and to correct them in the latter case). In the absence of exact results in KerrNewman spacetime, our approximate renormalized stressenergy tensors could be very helpful, in particular to study the backreaction of massive quantum fields on this spacetime or on its quasinormal modes.
 Publication:

Physical Review D
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevD.90.044045
 arXiv:
 arXiv:1404.7422
 Bibcode:
 2014PhRvD..90d4045B
 Keywords:

 04.62.+v;
 04.70.Dy;
 Quantum field theory in curved spacetime;
 Quantum aspects of black holes evaporation thermodynamics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 v2: Presentation greatly improved, discussions and references added.v3: Matches the published version