Renormalized stress tensor for massive fields in Kerr-Newman spacetime
Abstract
In a four-dimensional spacetime, the DeWitt-Schwinger 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 Gilkey-DeWitt coefficient a3 and its metric variation provides a good analytical approximation for the renormalized stress-energy tensor of the quantum field. Here, from the general expression of this tensor, we obtain analytically the renormalized stress-energy tensors of the massive scalar field, the massive Dirac field and the Proca field in Kerr-Newman 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 Kerr-Newman black hole and permitting us to recover rapidly the results already existing in the literature for the Schwarzschild, Reissner-Nordström and Kerr black holes (and to correct them in the latter case). In the absence of exact results in Kerr-Newman spacetime, our approximate renormalized stress-energy 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
- E-Print:
- v2: Presentation greatly improved, discussions and references added.v3: Matches the published version