Stress tensor from the trace anomaly in Reissner-Nordström spacetimes

Anderson, Paul R.; Mottola, Emil; Vaulin, R.

doi:10.1103/physrevd.76.124028

Cited by 54 publications

(38 citation statements)

References 57 publications

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“…Reisner-Nordstrom black hole as the only possibility, As it is not possible to solve the auxiliary field equations analytically in the black hole geometries when e = 0, and a numerical solution is required, we postpone a full discussion of these results to a future publication [49].…”

Section: B Other Spacetimes With Horizonsmentioning

confidence: 99%

Macroscopic effects of the quantum trace anomaly

2006

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The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field.The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor.

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Section: B Other Spacetimes With Horizonsmentioning

confidence: 99%

Macroscopic effects of the quantum trace anomaly

2006

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“…After subtracting (20) from (18), we obtain an expression for the renormalized Green function, and its full coincidence limit ǫ → 0, which provides the renormalized vacuum polarization, can be taken:…”

Section: Coincidence Limitmentioning

confidence: 99%

“…[12,13,14], Sushkov developed an analytical approximation and obtained φ 2 for Schwarzschild and wormholes spacetimes [15]. The analysis of quantum effects has also been extended to consider various aspects of quantum effects in rotating black hole geometries in [16,17,18,19] and recently further work in the case of Reissner-Nordstrom [20] and lukewarm black holes has also been studied [21].…”

Section: Introductionmentioning

confidence: 99%

Vacuum polarization in asymptotically anti-de Sitter black hole geometries

Flachi

Tanaka

2008

Phys. Rev. D

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We study the polarization of the vacuum for a scalar field, φ 2 , on a asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and pointsplitting regularization, similarly to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counter-terms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result expressed in terms of some generalized zeta-functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes φ 2 as a series in such zeta-functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the 'remainder' of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The general results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semi-classical Einstein's equations taking into account the back-reaction from quantum fields on asymptotically anti-de Sitter black holes.

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“…4,5,6), and one of the most clear ones is the Starobinsky model of inflation 7 . It is interesting that the EA S EH +Γ ind is producing two dS-like solutions for the homogeneous and isotropic metric (for simplicity we consider only spatially-flat case k = 0),…”

Section: Introductionmentioning

confidence: 99%

Quantum Corrections to Gravity and Their Implications for Cosmology and Astrophysics

Fabris

Oliveira

Rodrigues

et al. 2012

Int. J. Mod. Phys. A

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The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the postinflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology a .

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Stress tensor from the trace anomaly in Reissner-Nordström spacetimes

Cited by 54 publications

References 57 publications

Macroscopic effects of the quantum trace anomaly

Macroscopic effects of the quantum trace anomaly

Vacuum polarization in asymptotically anti-de Sitter black hole geometries

Quantum Corrections to Gravity and Their Implications for Cosmology and Astrophysics

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