We provide a mode-sum prescription to directly compute the renormalized stress-energy tensor (RSET) for scalar fields in the Boulware vacuum. The method generalizes the recently developed extended coordinate method which was previously only applicable to Hartle-Hawking states. We exhibit the accuracy and efficiency of the method by calculating the RSET in sub-extremal and extremal Reissner-Nordström spacetimes. We find numerical evidence for the regularity of the RSET at the extremal horizon regardless of the field mass and its coupling. We employ our numerical results of the RSET to source the semi-classical Einstein equations, demonstrating that if the RSET is considered as a static perturbation, it will either de-extremalize the black hole, or convert it into a horizonless object.
We consider the problem of quantum field theory on the Bertotti-Robinson space-time, which arises naturally as the near horizon geometry of an extremal Reissner-Nordstrom black hole but can also arise in certain near-horizon limits of non-extremal Reissner Nordstrom space-time. The various vacuum states have been considered in the context of $AdS_{2}$ black holes by Spradlin and Strominger who showed that the Poincare vacuum, the Global vacuum and the Hartle-Hawking vacuum are all equivalent, while the Boulware vacuum and the Schwarzschild vacuum are equivalent. We verify this by explicitly co…
We study a quantum fermion field on a background non-extremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and anti-particle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate `Boulware'-like state, empty at both past and future null infinity; and a candidate `Hartle-Ha…
We derive constraints on the form of the renormalized stress tensor for states on Kerr space-time based on general physical principles: symmetry, the conservation equations, the trace anomaly and regularity on (sections of) the event horizon. This is then applied to the physical vacua of interest. We introduce the concept of past and future Boulware vacua and discuss the non-existence of a state empty at both scri- and scri+. By calculating the stress tensor for the Unruh vacuum at the event horizon and at infinity, we are able to check our earlier conditions. We also discuss the difficulties …
We point out how to construct the Hartle-Hawking-Israel state for the minimaly coupled massless quantum real scalar field in the two dimensional BTZ black hole. We also calculate the renormalized energy-momentum tensor for the same field in the eternal CGHS black hole, AdS, Robertson-Walker and Rindler spacetime in two dimensions. We also discuss the Boulware, the Hartle-Hawking-Israel and the Unruh state for the eternal CGHS black hole.
Vacuum polarization and renormalized stress-energy tensor of spherical thin shells
SISSA, International School for Advanced Studies（国际高等研究院）；INFN Sezione di Trieste（的里雅斯特INFN分部）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Technological University Dublin（都柏林科技大学）；University College Dublin（都柏林大学学院）；Dublin City University（都柏林城市大学）
We consider the response of an Unruh-DeWitt detector near an extremal charged black hole, modeling the near-horizon region of this extremal spacetime by the Bertotti-Robinson spacetime. The advantage of employing the Bertotti-Robinson limit is that the two-point functions for a massless scalar field are obtainable in closed form for the field in a number of quantum states of interest. We consider the detector coupled to a massless field in both the Boulware vacuum state and arbitrary thermal states, including the Hartle-Hawking state, and analyse the detector's response for a broad range of tr…
We investigate the canonical quantization of the electromagnetic field on the Kerr background. We give new expressions for the expectation value of the electromagnetic stress-energy tensor in various vacua states and give a physical interpretation of the separate terms appearing in them. We numerically calculate the luminosity in these states. We also study the form of the renormalized stress-energy tensor close to the horizon when the electromagnetic field is in the past Boulware state.
We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum s…
Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds
Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Institut für Theoretische Physik（理论物理研究所）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息研究中心）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究系宇宙早期研究センター(RESCEU)）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学前沿研究机构 Kavli宇宙物理数学研究所(WPI)）
A short derivation is given of the weak gravitational field approximation to the scalar massless propagator in Schwarzschild spacetime obtained by Paszko using the path-integral approach. The contribution from the direct coupling of the quantum field to the scalar curvature is explictly included. The propagator complies with Hadamard's pattern, and the vacuum state is consistent with the perturbative version of the Boulware vacuum. The momentum space propagator is computed for massless or massive particles to the same perturbative order. The renormalized value of $\ < ϕ^2(x)\ >$ for the massle…
The computation of the renormalized stress-energy tensor or $\left\langleϕ^{2}\right\rangle_{ren}$ in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically-flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute $\left\langle ϕ^{2}\right\rangle _{ren}$ in a stationary spacetime using t-splitting, namely splitting in the time-translation direction. Here we …
We consider the entropy of a quantum scalar field on a background black hole geometry in asymptotically anti-de Sitter space-time, using the ``brick wall'' approach. In anti-de Sitter space, the theory has no infra-red divergences, and all ultra-violet divergences can be absorbed into a renormalization of the coupling constants in the one-loop effective gravitational Lagrangian. We then calculate the finite renormalized entropy for the Schwarzschild-anti-de Sitter and extremal Reissner-Nordstrom-anti-de Sitter black holes, and show that, at least for large black holes, the entropy is entirely …
We derive the BPS type of first order differential equations for the rotating black hole solutions in the three-dimensional Einstein gravity coupled minimally with a self-interacting scalar field, using fake supersymmetry formalism. It turns out that the formalism is not complete and should be augmented by an additional equation to imply the full equations of motion. We identify this additional equation as a constraint by using an effective action method. By computing the renormalized boundary stress tensor, we obtain the mass and angular momentum of the black hole solutions of these first ord…
In the framework of quantum field theory in curved space-time, we study the quantization of a massless fermion field on a non-extremal Kerr black hole. The key theme in this note is the fundamental difference between scalar and fermion fields for the process of defining quantum states. In particular, we define two new states for fermions on Kerr which cannot be defined for quantum scalar fields on Kerr. These two states are the analogues of the standard Boulware and Hartle-Hawking states on a Schwarzschild black hole.
Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to $\left\langle ϕ^{2}\right\rangle _{ren}$, namely the renormalized …
We construct the gravitational dual, in the Unruh state, of the "jammed" phase of a CFT at strong coupling and infinite N on a fixed five-dimensional rotating Myers-Perry black hole with equal angular momenta. When the angular momenta are all zero, the solution corresponds to the five-dimensional generalization of the solution first studied by Figueras, Lucietti, and Wiseman. In the extremal limit, when the angular momenta of the Myers-Perry black hole are maximum, the Unruh, Boulware and Hartle-Hawking states degenerate. We give a detailed analysis of the corresponding holographic stress ener…
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in…
We study classical and quantum aspects of electromagnetic perturbations on black hole space-times. We develop an elegant formalism introduced by Wald, which sets up the theory of linear perturbations in a Type-D background in a compact and transparent manner. We derive expressions for the electromagnetic potential in terms of the single Newman-Penrose scalar ϕ_0.This enables the formulation of the quantum theory of the electromagnetic field as that of a complex scalar field. We study the separable field equations obeyed by the various Newman-Penrose scalars in the Kerr-Newman background and fi…
We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker "rough" version of the conjecture is respected. We calculate the renorm…
The semiclassical approximation takes into account the gravitational contribution of zero-point energies. We model this contribution via the renormalized stress-energy tensor (RSET) of a massless scalar field, which we compute in a cutoff-regularized version of the Polyakov approximation. When the field is in the Boulware vacuum state (the natural vacuum for stellar geometries), the RSET works in favor of violating the Buchdahl compactness limit. We review the family of classical constant-density stellar solutions, paying particular attention to the notion of criticality -- the presence of off…
Semiclassical regularity of compact trapped regions: From dynamical horizons to inner extremality
Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；Institut für Theoretische Physik（理论物理研究所）；SISSA - International School for Advanced Studies（国际高等研究院）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；School of Mathematics and Statistics, Victoria University of Wellington（惠灵顿维多利亚大学数学与统计学院）
We examine quantum properties of topological black holes which are asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors which propagate in the background of an anti--de Sitter black hole are considered in an exactly soluble two--dimensional toy model. The Boulware--, Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide with the Unruh vacuum due to the boundary conditions necessary in asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum represents a thermal equilibrium state with the temperature found in the Euclidean formula…
We find an exact spherically symmetric regular Bardeen-like solutions by considering the coupling between Einstein-Gauss-Bonnet theory and nonlinear electrodynamics (NED) in five-dimensional spacetime. These solutions, with an additional parameter $g$ apart from the mass $M$, represent black holes with Cauchy and event horizons, extremal black holes with degenerate horizons or no black holes in the absence of the horizons, and encompasses as a special case Boulware-Deser black holes which can be recovered in the absence of magnetic charge ($g=0$). Owing to the NED corrected black hole, the the…
We analyze the rather unusual properties of some exact solutions in 2D dilaton gravity for which infinite quantum stresses on the Killing horizon can be compatible with regularity of the geometry. In particular, the Boulware state can support a regular horizon. We show that such solutions are contained in some well-known exactly solvable models (for example, RST). Formally, they appear to account for an additional coefficient $B$ in the solutions (for the same Lagrangian which contains also ''traditional'' solutions) that gives rise to the deviation of temperature $T$ from its Hawking value $T…
We extend the recent microscopic analysis of extremal dyonic Kaluza-Klein (D0-D6) black holes to cover the regime of fast rotation in addition to slow rotation. Fastly rotating black holes, in contrast to slow ones, have non-zero angular velocity and possess ergospheres, so they are more similar to the Kerr black hole. The D-brane model reproduces their entropy exactly, but the mass gets renormalized from weak to strong coupling, in agreement with recent macroscopic analyses of rotating attractors. We discuss how the existence of the ergosphere and superradiance manifest themselves within the …
We compute the Renormalized Stress-Energy Tensor (RSET) of a massless minimally coupled scalar field in the Regularized Polyakov approximation, as well as its backreaction, on the classical Reissner-Nordström spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with the classical counterparts. The semiclassical Reissner-Nordström family involves three kinds of geometries that depend on the charge-to-mass ratio of the spacetime. In the under-charged regime, the geometry has its external horizon replaced by a wormhole neck that leads to…
We carry out the holographic renormalization of Einstein-Maxwell theory with curvature-squared corrections. In particular, we demonstrate how to construct the generalized Gibbons-Hawking surface term needed to ensure a perturbatively well-defined variational principle. This treatment ensures the absence of ghost degrees of freedom at the linearized perturbative order in the higher-derivative corrections. We use the holographically renormalized action to study the thermodynamics of R-charged black holes with higher derivatives and to investigate their mass to charge ratio in the extremal limit.…
The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient $a_{3}.$ The result is compared with the analogous result derived for the Reissner-Nordström black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the…
The approximate renormalized one-loop effective action of the quantized massive scalar, spinor and vector field in a large mass limit, i.e., the lowest order of the DeWitt-Schwinger expansion involves the coincidence limit of the Hadamard-DeWitt coefficient a3. Building on this and using Wald's approach we shall construct the general expression describing entropy of the spherically-symmetric static black hole being the solution of the semi-classical field equations. For the concrete case of the quantum-corrected Reissner-Nordstrom black hole this result coincides, as expected, with the entropy…
AdS black holes in two-dimensional dilaton gravity and holography
Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学）；Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理与数学科学学院）；Instituto de Física, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理研究所）
Strong cosmic censorship for the spherically symmetric Einstein-Maxwell-charged-Klein-Gordon system with positive $Λ$: stability of the Cauchy horizon and $H^1$ extensions
