Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method

Christensen, Steven M.

doi:10.1103/physrevd.14.2490

Cited by 561 publications

(654 citation statements)

References 2 publications

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“…Indeed, the ultraviolet cutoff can be generalized to "point-splitting" regularization, where T (or, historically more often, a Green function for the wave equation) and its derivatives in (2)-(3) are expanded in powers of the displacement tu ν ≡ x ν − x ν (historically, its generalization to curved space-time as a tangent vector). The result in curved space-time (with signature g 00 < 0) is 4 T µν = 1 2π 2 t 4 g µν − 4 u µ u ν u ρ u ρ (5) for the leading term, which is the entirety when T = T 0 . Eq.…”

Section: Basic Formalism and Empty Spacementioning

confidence: 99%

Energy Density and Pressure in Power-Wall Models

Fulling

Milton

Wagner

2012

Int. J. Mod. Phys. Conf. Ser.

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A finite ultraviolet cutoff near a reflecting boundary yields a stress tensor that violates the basic energy-pressure relation. Therefore, a "soft" wall described by a power-law potential, which needs no ad hoc cutoff, is being investigated by the collaboration centered at Texas A&M University and the University of Oklahoma. Progress is reported here.Keywords: vacuum energy; stress tensor; boundary; soft wall. PACS numbers: 03.70.+k, 11.10.Gh Hard Walls: The Pressure Paradox Basic formalism and empty spaceWe model the electromagnetic vacuum-energy problem by a massless scalar field in three space dimensions, subjected to the Dirichlet boundary condition on the "conducting" boundaries. The vacuum energy can be calculated from a Green function, such as the "cylinder kernel", 1,2,3where the φ n are the normalized eigenfunctions with frequencies ω n . The classical formulas for the components of the vacuum expectation value of the stress-energy

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Section: Basic Formalism and Empty Spacementioning

confidence: 99%

Energy Density and Pressure in Power-Wall Models

Fulling

Milton

Wagner

2012

Int. J. Mod. Phys. Conf. Ser.

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“…This allows us to develop recursive algorithms for the symbolic manipulations. The lowest order terms in the series expansions are known [23,35]. For example, Christensen's work on the stress tensor goes to second order in σ a (ending up creating results spanning a page and a half in his manuscript).…”

Section: B Symbolic Computationmentioning

confidence: 99%

“…Further details on these objects and discussions of the definitions and properties are contained in [23] and [32]. There it is shown how the defining equations for σ and ∆ 1/2 are used to determine the coincident limit expression for the various covariant derivatives of the world function ([σ ;a ], [σ ;ab ], etc.)…”

Section: A N-tensors and End-point Expansionsmentioning

confidence: 99%

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Noise kernel in stochastic gravity and stress energy bitensor of quantum fields in curved spacetimes

Phillips¹,

2001

Phys. Rev. D

124

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The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum and/or extended nature of spacetime. It reflects the medium energy (referring to Planck energy as high energy) or mesoscopic behavior of any viable theory of quantum gravity, including string theory. The stress energy bi-tensor could be the starting point for a new quantum field theory constructed on spacetimes with extended structures. In the coincidence limit we use the method of point-separation to derive a regularized noise-kernel for a scalar field in general curved spacetimes. It is useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in the early universe and black holes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for specific cases of physical interest such as the Robertson-Walker and Schwarzschild spacetimes.

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“…This anomaly is obtained in terms of geometrical objects such as R µν R µν , R µναβ R µναβ , ✷R, and R 2 for conformaly coupling massless quantum field propagated on four dimensional curved space time (Christensen 1976;Adler, Liberman and Ng 1977;Wald 1978;Birrell and Davies 1982;Brown 1984;Bernard and Folacci 1986;Ghafarnejad and Salehi 1997;Parker and Toms 2009). In two dimension the conformal coupling reduces to minimal coupling and so the quantity of trace anomaly is obtained in terms of the Ricci scalar R = R β β which for a massless scalar matter field become:…”

Section: Introductionmentioning

confidence: 99%

Evaporating quantum Lukewarm black holes final state from back-reaction corrections of quantum scalar fields

Ghaffarnejad

Neyad

Mojahedi

2013

Astrophys Space Sci

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We obtain renormalized stress tensor of a mass-less, charge-less dynamical quantum scalar field, minimally coupled with a spherically symmetric static Lukewarm black hole. In two dimensional analog the minimal coupling reduces to the conformal coupling and the stress tensor is found to be determined by the nonlocal contribution of the anomalous trace and some additional parameters in close relation to the work presented by Christensen and Fulling. Lukewarm black holes are a special class of Reissner-Nordström-de Sitter space times where its electric charge is equal to its mass. Having the obtained renormalized stress tensor we attempt to obtain a time-independent solution of the well known metric back reaction equation. Mathematical derivations predict that the final state of an evaporating quantum Lukewarm black hole reduces to a remnant stable mini black hole with moved locations of the horizons. Namely the perturbed black hole (cosmological) horizon is compressed (extended) to scales which is smaller (larger) than the corresponding classical radius of the event horizons. Hence there is not obtained an deviation on the cosmic sensor-ship hypothesis.

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Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method

Cited by 561 publications

References 2 publications

Energy Density and Pressure in Power-Wall Models

Energy Density and Pressure in Power-Wall Models

Noise kernel in stochastic gravity and stress energy bitensor of quantum fields in curved spacetimes

Evaporating quantum Lukewarm black holes final state from back-reaction corrections of quantum scalar fields

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