Some general properties of the renormalized stress-energy tensor for static quantum states on (n + 1)-dimensional spherically symmetric black holes

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f (r). As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even d = 4, ..., 10. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.

Section: Introductionmentioning

confidence: 99%

Mode-sum prescription for vacuum polarization in black hole spacetimes in even dimensions

Taylor

Breen²

2017

“…While the renormalised vacuum polarization has been computed for a variety of black hole spacetimes in four dimensions, see for example [3,4,[7][8][9][10][11][12][13][14], there has been comparatively little work carried out in higher dimensional black hole spacetimes. Some general properties of the renormalised stress energy tensor in higher dimensions are derived in [15] while Decanini and Folacci [16] developed a formalism for its computation based on Hadamard renormalization. Another general formalism for computing the renormalised vacuum polariza-arXiv:1609.08166v2 [gr-qc] 14 Oct 2016 tion in higher dimensional spacetimes based on DeWitt-Schwinger renormalization was developed in [17].…”

Section: Introductionmentioning

confidence: 99%

Mode-sum prescription for the vacuum polarization in odd dimensions

Taylor

Breen²

2016

We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function f (r). In fact, we show that inspite the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots for vacuum polarization in the Schwarzschild-Tangherlini spacetime for odd d = 5, ..., 11.

“…Combining these numerical results with the horizon values obtained in this paper will allow us to numerically calculate these derivatives and thereby draw conclusions on the regularity of the equivalent of the Hartle-Hawking state for lukewarm black holes. We note here that the satisfaction of condition 3 can be shown to be equivalent to requiring that hT i ren possess a Taylor series about the horizon, by following the method of Morgan et al [34]. This will also be investigated in Paper II.…”

Section: Renormalized Stress Tensor Componentsmentioning

confidence: 93%

Hadamard renormalization of the stress energy tensor on the horizons of a spherically symmetric black hole space-time

Breen

Ottewill

2012

We consider a quantum field which is in a Hartle-Hawking state propagating in a general spherically symmetric black hole space-time. We make use of uniform approximations to the radial equation to calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, on the horizons of this space-time. We then specialize these results to the case of the ''lukewarm'' Reissner-Nordstrom-de Sitter black hole and derive some conditions on the stress tensor for the regularity of the Hartle-Hawking state.