Quantum scalar field on the massless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn /><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>-dimensional black hole background

Binosi, Daniele; Moretti, Valter; Vanzo, Luciano; Zerbini, Sergio

doi:10.1103/physrevd.59.104017

Cited by 20 publications

(25 citation statements)

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“…Some of them have a constant curvature and can be obtained as quotients of AdS by a discrete subgroup of its isometry group, SO(N − 1, 2); the most popular are the Bañados-Teitelboim-Zanelli solutions in three dimensions [17], but higher dimensional generalizations exist [8,18]. These black holes are locally isometric to AdS, and quantum corrections due to the propagation of scalar fields on the background of these black holes have been considered by various authors, for the BTZ black hole [19][20][21][22], for the singular background of toroidal black holes in four dimensions [23], while the propagation of photons in topological black hole spacetimes has been investigated in [24]. In this paper we shall study the propagation of a scalar quantum field, with arbitrary coupling, on AdS spacetime, in the framework of euclidean field theory.…”

Section: Introductionmentioning

confidence: 99%

Quantum scalar fields on anti-de Sitter space-time

Caldarelli

1999

Nuclear Physics B

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We investigate the propagation of arbitrarily coupled scalar fields on the N -dimensional hyperbolic space H N . Using the ζ-function regularization we compute exactly the one loop effective action. The vacuum expectation value of quadratic field fluctuations and the one loop renormalized stress tensor are then computed using the recently proposed direct ζ-function technique. Our computation tests the validity of this approach in presence of a continuous spectrum. Our results apply as well to the N -dimensional anti-de Sitter spacetime, whose appropriate euclidean section is the hyperbolic space H N .

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Section: Introductionmentioning

confidence: 99%

Quantum scalar fields on anti-de Sitter space-time

Caldarelli

1999

Nuclear Physics B

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“…On the other hand, one could investigate Hawking radiation in this context and its interplay with the rotation of the black hole, by using the method of Parikh and Wilczek [33], recently extended to the framework of algebraic quantum field theory in [34]. A more long term and ambitious goal is the explicit construction of a regularized stress-energy tensor, to be used in the analysis of the semiclassical Einstein's equations, extending the work of [35]. We hope to come back to these problems in the near future.…”

Section: Discussionmentioning

confidence: 99%

“…To conclude this section we comment on the physical significance of the two-point functions obtained in (35) and (37). In the first case, we are dealing with a generalization of (32) to Robin boundary conditions.…”

Section: Case ζ ∈ [ζ * π)mentioning

confidence: 95%

Ground state for a massive scalar field in the BTZ spacetime with Robin boundary conditions

et al. 2017

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We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Secondly, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible. * francesco.bussola01@ateneopv.it † claudio.dappiaggi@unipv.it ‡ hugo.ferreira@pv.infn.it § igor.khavkine@unimi.it arXiv:1708.00271v1 [gr-qc] 1 Aug 2017

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“…However, it should be noticed that in this case, it is not reasonable to neglect the back-reaction effects. In fact, in [24][25][26] it has been shown that there is a quantum implementation of the Cosmic Censorship Principle due to the back-reaction on the metric.…”

Section: Discussionmentioning

confidence: 99%

“…where ζ R is the Riemann ζ-function, and we have introduced the horizon cutoff ε, and the cusp regularization δ > 0. It should be noticed the divergence for δ = 0, which is usually present when one is dealing with parabolic elements [25]. As far as the field fluctuations are concerned, we only need the expression of the local ζ-function near the horizon.…”

Section: B Exteme Casementioning

confidence: 99%

Quantum scalar field in D-dimensional static black hole space–times

Binosi

Zerbini

1999

Journal of Mathematical Physics

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An Euclidean approach for investigating quantum aspects of a scalar field living on a class of D-dimensional static black hole space-times, including the extremal ones, is reviewed. The method makes use of a near horizon approximation of the metric and ζ-function formalism for evaluating the partition function and the expectation value of the field fluctuations φ 2 (x) . After a review of the non-extreme black hole case, the extreme one is considered in some details. In this case, there is no conical singularity, but the finite imaginary time compactification introduces a cusp singularity. It is found that the ζ-function regularized partition function can be defined, and the quantum fluctuations are finite on the horizon, as soon as the cusp singularity is absent, and the corresponding temperature is T = 0. 04.70.Dy,04.20.Cv,04.60.Kz I. INTRODUCTION.The issue of determining the equilibrium (Unruh-Hawking) temperature of a black hole, is important. In fact, one can extract thermodynamical informations from its knowledge: for example the Bekenstein-Hawking entropy (i.e. the tree-level contribution to the entropy) can be defined as the response of the free energy of the black hole to the change of this equilibrium temperature. Furthermore, it defines the admissible temperatures of thermal states of free scalar fields in a static and globally hyperbolic space-time region with horizons.As is well known, there exist several methods for evaluating the possible equilibrium temperature of a stationary black hole. Whithin the simplest of these methods, one has to make a Wick rotation of the time coordinate (passing in this way to the Euclidean time τ = it), and eliminate all the metric (conical) singularities connected to the horizon by an opportune choice of the time periodicity β M [1]. Then, one has to impose the KMS condition for thermal states [2,3], i.e. to impose the periodicity condition on the imaginary time dependence of the thermal Wightman functions, and interprete the common period β T as the inverse of the temperature T of the state. Although this procedure determines the correct Unruh-Hawking temperature in the case of a non-extreme black hole, it does not apply to the extreme case (for example to the case of an extreme Reissner-Nordström black hole), since one is unable to determine the time periodicity of the manifold β M .Later, a more sophisticated Lorentzian method was introduced in [4] and successively developed in [5] and [6,8]. Without entering in the details of this approach, we only recall that the method is connected to the well known Hadamard expansion of the two-point Green functions in a curved background and in the limit of coincidence of the arguments. Basically in [4] was proved that assuming fairly standard axioms of quantum (quasi-free) field theory (such as local definitness and local stability in a stationary space-time region), then, when the distance between the two arguments vanishes, the thermal Wightman functions in the interior of this region will transform into non-thermal and mas...

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Quantum scalar field on the massless(2+1)-dimensional black hole background

Cited by 20 publications

References 50 publications

Quantum scalar fields on anti-de Sitter space-time

Quantum scalar fields on anti-de Sitter space-time

Ground state for a massive scalar field in the BTZ spacetime with Robin boundary conditions

Quantum scalar field in D-dimensional static black hole space–times

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