Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction

The total vacuum stress-energy tensor of nonconformal scalar field is calculated in a nonsingular metric determined by some background matter with the effective negative energy density and pressure. The corrections due to the field nonconformity are shown to dominate the conformal contributions for some cases. The back reaction problem of vacuum stress-energy tensor upon the background metric is also discussed.

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AdS2×S2 GEOMETRIES AND THE EXTREME QUANTUM-CORRECTED BLACK HOLES

Modern Physics Letters A ◽

10.1142/s0217732309031910 ◽

2009 ◽

Vol 24 (31) ◽

pp. 2517-2530 ◽

Cited By ~ 8

Author(s):

JERZY MATYJASEK ◽

DARIUSZ TRYNIECKI

Keyword(s):

Order Term ◽

Second Order ◽

Energy Tensor ◽

Stress Energy Tensor ◽

Field Equations ◽

Massive Scalar Field ◽

Stress Energy ◽

Consistent Solution ◽

Leading Term ◽

Horizon Geometry

The second-order term of the approximate stress–energy tensor of the quantized massive scalar field in the Bertotti–Robinson and Reissner–Nordström spacetimes is constructed within the framework of the Schwinger–DeWitt method. It is shown that although the Bertotti–Robinson geometry is a self-consistent solution of the (Λ = 0) semiclassical Einstein field equations with the source term given by the leading term of the renormalized stress–energy tensor, it does not remain so when the next-to-leading term is taken into account and requires the introduction of a cosmological term. The addition of the electric charge to the system does not change this behavior. The near horizon geometry of the extreme quantum-corrected Reissner–Nordström black hole is analyzed. It has the AdS2 ×S2 topology and the sum of the curvature radii of the two-dimensional submanifolds is proportional to the trace of the second-order term. It suggests that the "minimal" approximation should be constructed from the first two terms of the Schwinger–DeWitt expansion

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THE EXTENDED ALGEBRA OF OBSERVABLES FOR DIRAC FIELDS AND THE TRACE ANOMALY OF THEIR STRESS-ENERGY TENSOR

Reviews in Mathematical Physics ◽

10.1142/s0129055x09003864 ◽

2009 ◽

Vol 21 (10) ◽

pp. 1241-1312 ◽

Cited By ~ 37

Author(s):

CLAUDIO DAPPIAGGI ◽

THOMAS-PAUL HACK ◽

NICOLA PINAMONTI

Keyword(s):

Back Reaction ◽

Energy Tensor ◽

Quantum Field ◽

Stress Energy Tensor ◽

Covariant Quantum ◽

Algebra Of Observables ◽

Spinor Fields ◽

Trace Anomaly ◽

Stress Energy ◽

Dirac Spinors

We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.

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EXACT SOLUTIONS OF BRANS–DICKE WORMHOLES IN THE PRESENCE OF MATTER

Modern Physics Letters A ◽

10.1142/s021773231103739x ◽

2011 ◽

Vol 26 (40) ◽

pp. 3067-3076 ◽

Cited By ~ 9

Author(s):

NADIEZHDA MONTELONGO GARCIA ◽

FRANCISCO S. N. LOBO

Keyword(s):

Scalar Field ◽

Vacuum Solution ◽

Energy Condition ◽

Null Energy Condition ◽

Exotic Matter ◽

Energy Tensor ◽

Stress Energy Tensor ◽

Normal Matter ◽

Stress Energy

A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In this work, we find exact wormhole solutions in Brans–Dicke theory where the normal matter threading the wormhole satisfies the null energy condition throughout the geometry. Thus, the latter implies that it is the effective stress–energy tensor containing the scalar field, that plays the role of exotic matter, that is responsible for sustaining the wormhole geometry. More specifically, we consider a zero redshift function and a particular choice for the scalar field and determine the remaining quantities, namely, the stress–energy tensor components and the shape function. The solution found is not asymptotically flat, so that this interior wormhole spacetime needs to be matched to an exterior vacuum solution.

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Schwarzschild radial perturbations in Eddington–Finkelstein and Painlevé–Gullstrand coordinates

International Journal of Modern Physics D ◽

10.1142/s0218271815420067 ◽

2015 ◽

Vol 24 (09) ◽

pp. 1542006 ◽

Cited By ~ 3

Author(s):

Dennis Philipp ◽

Volker Perlick

Keyword(s):

Dark Matter ◽

Scalar Field ◽

Exact Solutions ◽

Dark Matter Candidate ◽

Massive Scalar ◽

Open Domain ◽

Schwarzschild Spacetime ◽

Massive Scalar Field ◽

Massless Case ◽

Central Singularity

In a previous paper, we have considered the Regge–Wheeler equation for fields of spin s = 0, 1 or 2 on the Schwarzschild spacetime in coordinates that are regular at the horizon. In particular, we have constructed in Eddington–Finkelstein (EF) coordinates exact solutions in terms of series that are regular at the horizon and converge on the entire open domain from the central singularity to infinity. Here, we extend this earlier work in two different directions. First, we consider in EF coordinates a massive scalar field that can serve as a dark matter candidate. Second, we extend the treatment of the massless case to Painlevé–Gullstrand (PG) coordinates, which are associated with radially infalling observers.

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