Effective actions and conformal transformations

Mr, Brown; Ottewill, Adrian C.

doi:10.1103/physrevd.31.2514

Cited by 121 publications

(131 citation statements)

References 19 publications

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“…Since the equation for the second auxiliary field ψ is identical to that for ϕ, its solution for ψ = ψ(r, t) is of the same form as (5.8) and Ottewill [35,36,37] (dashed curves in Figs. 1).…”

Section: A Schwarzschild Spacetimementioning

confidence: 89%

“…We observe that the two parameter fit with the anomalous stress tensor in terms of the auxiliary ϕ and ψ fields is more accurate than the approximation of refs. [35,36,37] for the Boulware state. In the latter case the stress-tensor is approximated by making a special conformal transformation σ = 1 2 ln f = 1 2 ln(−K a K a ) to the optical metric, obtained from the Schwarzschild line element (4.17) by dividing by f (r) = 1 − 2M r .…”

Section: A Schwarzschild Spacetimementioning

confidence: 99%

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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: A Schwarzschild Spacetimementioning

confidence: 89%

Section: A Schwarzschild Spacetimementioning

confidence: 99%

Macroscopic effects of the quantum trace anomaly

2006

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“…A simple polynomial approximation to the non-vanishing quantities appearing in a stress energy tensor of the form given in (2.4) can be obtained for the Boulware vacuum [9], by combining Page's approximation [33] with the results of Brown and Ottewill [34]. These are [9]: 33) and…”

Section: Boulware Vacuummentioning

confidence: 99%

“…Furthermore, setting z = 2M/r, (cf the Brown-Ottewill approximation [34], see also [8], and [31]), in the Boulware vacuum we have:…”

Section: General Analysis Of the Form Of The Stress-energy Tensormentioning

confidence: 99%

Semiclassical energy conditions for quantum vacuum states

Martín–Moruno

Visser

2013

J. High Energ. Phys.

106

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We present and develop several nonlinear energy conditions suitable for use in the semiclassical regime. In particular, we consider the recently formulated "flux energy condition" (FEC), and the novel "trace-of-square" (TOSEC) and "determinant" (DETEC) energy conditions. As we shall show, these nonlinear energy conditions behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects. Moreover, whereas the quantum extensions of these nonlinear energy conditions seem to be quite widely satisfied as one enters the quantum realm, at least for quantum vacuum states, analogous quantum extensions are generally not useful for the linear classical energy conditions.

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“…Jensen and Ottewill [18] have computed the vacuum stress-energy of a massless vector field in Schwarzschild. Approximation methods have been developed by Page, Brown, and Ottewill [19,20,21] for conformally invariant fields in Schwarzschild spacetime, Frolov and Zel'nikov [22] for conformally invariant fields in a general static spacetime, Anderson, Hiscock and Samuel [13] for massless arbitrarily coupled scalar fields in a general static spherically symmetric spacetime. Furthermore the DeWitt-Schwinger approximation has been derived by Frolov and Zel'nikov [23,24] for massive fields in Kerr spacetime, Anderson Hiscock and Samuel [13] for a general (arbitrary curvature coupling and mass) scalar field in a general static spherically symmetric spacetime and have applied their method to the Reissner-Nordström geometry [14].…”

Section: Introductionmentioning

confidence: 99%

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Sinha

Raval

2003

Foundations of Physics

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We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein-Langevin equation. Once the thermal Green's function in a Schwarzschild background becomes available to the required accuracy the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories.

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Effective actions and conformal transformations

Cited by 121 publications

References 19 publications

Macroscopic effects of the quantum trace anomaly

Macroscopic effects of the quantum trace anomaly

Semiclassical energy conditions for quantum vacuum states

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