In this work we analyse the backreaction of a quantum field on a spherically symmetric black hole geometry with an inner horizon, i.e. an internal boundary of the trapped region. We start with a black hole background with an inner horizon which remains static after its formation. We quantise a massless scalar field on it and calculate its renormalised stress-energy tensor in the Polyakov approximation. We use this tensor as a source of perturbation on top of the background spacetime. We find that the inner horizon has a tendency to evaporate outward much more quickly than the outer one evaporates inward through the Hawking effect. This suggests a revised picture of a semiclassically self-consistent evaporation in which the dominant dynamical effect comes from the inner horizon. We also look at backreaction on backgrounds which resemble gravitational collapse, where the inner horizon moves toward the origin. There we find that, depending on the nature of the background dynamics, horizon-related semiclassical effects can become dominant and invert the collapse.
Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large $D$, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds co…
We point out that two-dimensional Russo-Susskind-Thorlacius (RST) model for evaporating black holes is locally equivalent - at the full quantum level - to flat-space Jackiw-Teitelboim (JT) gravity that was recently shown to be unitary. Globally, the two models differ by a reflective spacetime boundary added in the RST model. Treating the boundary as a local and covariant deformation of quantum JT theory, we develop sensible semiclassical description of evaporating RST black holes. Nevertheless, our semiclassical solutions fail to resolve the information recovery problem, and they do not indica…
We argue that the semiclassical analysis of the black hole information paradox is incomplete and has to be completed by an explicit entanglement of matter and quantum gravity degrees of freedom. We study in detail the evaporation process from beginning to end in the light of our extension and show that a pure initial state remains pure over the full evaporation process, including the final state which remains after the black hole has completely evaporated. By the same token we show how the quantum hair is encoded in the micro structure of the (final) gravitational state which is entangled with…
We discuss semiclassical Nariai black holes in the framework of $f(T)$-gravity. For a diagonal choice of tetrades, stable Nariai metrics can be found, emitting Bekenstein-Hawking radiation in semiclassical limit. However, for a non-diagonal choice of tetrades, evaporation and antievaporation instabilities are turned on. In turn, this causes a back-reaction effect suppressing the Bekenstein-Hawking radiation. In particular, evaporation instabilities produce a new radiation -- different by Bekenstein-Hawking emission -- non-violating unitarity in particle physics sector.
In case of spherical symmetry, the assumptions of finite-time formation of a trapped region and regularity of its boundary --- the apparent horizon --- are sufficient to identify the form of the metric and energy-momentum tensor in its vicinity. By comparison with the known results for quasistatic evaporation of black holes, we complete the identification of their parameters. Consistency of the Einstein equations allows only two possible types of higher-order terms in the energy-momentum tensor. By using its local conservation, we provide a method of calculation of the higher-order terms, expl…
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, $f(R)$-gravity, $f(T)$-gravity, string inspired black holes and brane-world cosmology. Evaporating and antievaporating black holes seem to have completely different thermodynamical features compared to standard semiclassical black holes. The purpose of this review is to provide an introduction to conceptual and technical aspects of (anti)evaporation …
We analyse the geometry of a spherically symmetric black hole with an inner and outer apparent horizon which is perturbed by spherical null shells of matter. On a classical level we observe that the mass inflation instability is triggered, resulting in a growth of curvature and an inward displacement of the inner horizon. We study in detail the inner structure of the mass-inflated region and compare it with previous results obtained for the case in which the perturbing matter content has a continuous distribution. We then perform an approximate calculation of the renormalised stress-energy ten…
We consider the black hole information problem in an explicitly defined spacetime modelling black hole evaporation. Using this context we review basic aspects of the problem, with a particular effort to be unambiguous about subtle topics, for instance precisely what is meant by entropy in various circumstances. We then focus on questions of unitarity, and argue that commonly invoked semiclassical statements of long term, evaporation time, and Page time "unitarity" may all be violated even if physics is fundamentally unitary. This suggests that there is no horizon firewall. We discuss how the p…
The evaporation of four-dimensional spherically symmetric black holes is presented in the framework of quantum field theory in curved spacetimes and semiclassical gravity. It is discussed how the evaporation process can be sourced by the presence of the trace anomaly of a massless, conformally coupled scalar field outside the apparent horizon of the black hole.
Explicitly computed Penrose diagrams are plotted for a classical model of black hole formation and evaporation, in which black holes form by the accretion of infalling spherical shells of matter and subsequently evaporate by emitting spherical shells of Hawking radiation. This model is based on known semiclassical effects, but is not a full solution of semiclassical gravity. The method allows arbitrary interior metrics of the form $ds^2=-f(r)\,dt^2+f(r)^{-1}\,dr^2+r^2\,dΩ^2$, including singular and nonsingular models. Matter dynamics are visualized by explicitly plotting proper density in the …
Renormalization of the Quantum Stress Tensor Fluctuations and the Limits of Semiclassical Gravity
Aix-Marseille Université, Université de Toulon, CNRS, CPT（艾克斯-马赛大学, 土伦大学, 法国国家科学研究中心, 理论物理中心）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（核科学学院, 墨西哥国立自治大学）；Departament de Física Quantica i Astrofísica, Universidad de Barcelona（量子物理与天体物理学系, 巴塞罗那大学）
We explore the Hawking evaporation of two-dimensional anti-de Sitter (AdS$_2$), dilatonic black hole coupled with conformal matter, and derive the Page curve for the entanglement entropy of radiation. We first work in a semiclassical approximation with backreaction. We show that the end-point of the evaporation process is AdS$_2$ with a vanishing dilaton, i.e. a regular, singularity-free, zero-entropy state. We explicitly compute the entanglement entropies of the black hole and the radiation, as functions of the horizon radius, using the conformal field theory (CFT) dual to AdS$_2$ gravity. We…
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）
Approximate solution to the CGHS field equations for two-dimensional evaporating black holes
Callan，Giddings，Harvey and Strominger（CGHS）以前介绍了一个耦合到重子和物质场的二维半经典引力模型。他们的模型产生了一个场方程组，可以描述黑洞在引力坍缩中的形成以及随后的蒸发。本文给出了半经典CGHS场方程的近似解析解。这个解决方案是使用最近推出的形式主义的通量守恒双曲系统。我们还讨论了蒸发黑洞在视界处的渐近行为。
It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.
One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S-matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile tha…
