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

Breen, Cormac; Ottewill, Adrian C.

doi:10.1103/physrevd.85.064026

Cited by 13 publications

(15 citation statements)

References 33 publications

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“…However, one should observe that in a generic curved space-time and for an arbitrary gravitational coupling a logarithmic term is always present in the Hadamard singularity, even though one is dealing with a massless scalar field: as a consequence of the regularization process a finite logarithmic term with an arbitrary mass scale µ 2 is also present. However, if one restricts the analysis to the massless conformally coupled case, one may get rid of the logarithmic term (see for example [47,48]). …”

Section: < φ > As An Observablementioning

confidence: 99%

Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

et al. 2014

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The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat FLRW space-time. Two simple measurement prescriptions are given in order to remove the ambiguity associated with the short distance singularity of the correlation function. In some cases, it turns out that one is dealing with a "quantum thermometer", recovering a proposal due to Buchholz et al. in order to determine local temperature in the framework of quantum field theory. In general, by arranging the detector so that it does not register for inertial motion in flat space, the regularized quantum fluctuation may be used as a probe of space-time geometry and, in particular, may provide informations on the Hubble parameter. As an aside, it is not possible in general to fully decouple the effect of the detector's motion from the universe expansion, a fact that could be interpreted as a kind of Machian effect which can be traced back to the worldwide nature of the vacuum.

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Section: < φ > As An Observablementioning

confidence: 99%

Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

et al. 2014

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“…Anderson, Hiscock and Samuel (AHS) [17,18] developed a general methodology for computing both the VP and RSET for a quantum scalar field with arbitrary mass and coupling to the spacetime curvature, on a static, spherically symmetric black hole background. Their method was subsequently refined by Breen and Ottewill [19][20][21] and has been applied to a variety of spherically symmetric black holes in four spacetime dimensions [22][23][24][25]. There has also been more limited work on alternative approaches for nonspherically symmetric black hole spacetimes for which the AHS method is not applicable [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Vacuum polarization on topological black holes with Robin boundary conditions

2021

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We compute the renormalized vacuum polarization for a massless, conformally coupled scalar field on asymptotically anti-de Sitter black hole backgrounds. Mixed (Robin) boundary conditions are applied on the spacetime boundary. We consider black holes with nonspherical event horizon topology as well as spherical event horizons. The quantum scalar field is in the Hartle-Hawking state, and we employ Euclidean methods to calculate the renormalized expectation values. Far from the black hole, we find that the vacuum polarization approaches a finite limit, which is the same for all boundary conditions except Dirichlet boundary conditions.

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“…For black holes in four-dimensional, 4D, spacetimes, the full stress-energy tensor must be computed numerically. This is a difficult task that has to date only been done without other approximations for the cases of static spherically symmetric black holes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the stationary Kerr metric [16,17]. However, because of the difficulty involved, to our knowledge, no one has numerically computed the full stress-energy tensor for a quantized field in a 4D spacetime in which a black hole forms from collapse.…”

Section: Introductionmentioning

confidence: 99%

Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell

Anderson,

Siahmazgi,

Clark

et al. 2020

Preprint

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A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy tensor for the field in the Unruh state. The method is shown to work in the two-dimensional case where the results are known.

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

Cited by 13 publications

References 33 publications

Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

Vacuum polarization on topological black holes with Robin boundary conditions

Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell

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