Alessandro Fabbri

Modeling black hole evaporation

Classical Black Holes The Hawking Effect Near-Horizon Approximation and Conformal Symmetry Stress Tensor, Anomalies and Effective Actions Models for Evaporating Black Holes.

Quantum Black Holes as Holograms in AdS Braneworlds

We propose a new approach for using the AdS/CFT correspondence to study quantum black hole physics. The black holes on a brane in an AdSD+1 braneworld that solve the classical bulk equations are interpreted as duals of quantum-corrected D-dimensional black holes, rather than classical ones, of a conformal field theory coupled to gravity. We check this explicitly in D = 3 and D = 4. In D = 3 we reinterpret the existing exact solutions on a flat membrane as states of the dual 2+1 CFT. We show that states with a sufficiently large mass really are 2+1 black holes where the quantum corrections dress the classical conical singularity with a horizon and censor it from the outside. On a negatively curved membrane, we reinterpret the classical bulk solutions as quantum-corrected BTZ black holes. In D = 4 we argue that the bulk solution for the brane black hole should include a radiation component in order to describe a quantum-corrected black hole in the 3+1 dual. Hawking radiation of the conformal field is then dual to classical gravitational bremsstrahlung in the AdS5 bulk.

New black holes in the brane world

It is known that the Einstein field equations in five dimensions admit more general spherically symmetric black holes on the brane than four-dimensional general relativity. We propose two families of analytic solutions (with g_ttnot=-1/g_rr), parameterized by the ADM mass and the PPN parameter beta, which reduce to Schwarzschild for beta=1. Agreement with observations requires |beta-1| |eta| 0). In the latter case, we find a family of black hole space-times completely regular.

Critical collapse in (2+1)-dimensional AdS spacetime: quasi-CSS solutions and linear perturbations

Abstract We construct a one-parameter family of exact time-dependent solutions to 2+1 gravity with a negative cosmological constant and a massless minimally coupled scalar field as source. These solutions present a continuously self-similar (CSS) behavior near the central singularity, as observed in critical collapse, and an asymptotically AdS behavior at spatial infinity. We consider the linear perturbation analysis in this background, and discuss the crucial question of boundary conditions. These are tested in the special case where the scalar field decouples and the linear perturbations describe exactly the small-mass static BTZ black hole. In the case of genuine scalar perturbations, we find a growing mode with a behavior characteristic of supercritical collapse, the spacelike singularity and apparent horizon appearing simultaneously and evolving towards the AdS boundary. Our boundary conditions lead to the value of the critical exponent γ =0.4.

Quantum gravitational corrections to black hole geometries

We calculate perturbative quantum gravity corrections to eternal two-dimensional black holes. We estimate the leading corrections to the AdS_2 black hole entropy and determine the quantum modification of N-dimensional Schwarzschild spacetime.

Brane cosmology with an anisotropic bulk

In the context of brane cosmology, a scenario where our universe is a 3+1-dimensional surface (the ``brane) embedded in a five-dimensional spacetime (the ``bulk), we study geometries for which the brane is anisotropic — more specifically Bianchi I — though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to be empty but endowed with a negative cosmological constant. We then embed Z2-symmetric branes in the anisotropic spacetimes and discuss the constraints on the brane energy-momentum tensor due to the five-dimensional anisotropic geometry. We show that if the bulk is static, an anisotropic brane cannot support a perfect fluid. However, we find that for some of our bulk solutions it is possible to embed a brane with a perfect fluid though its energy density and pressure are completely determined by the bulk geometry.In the context of brane cosmology, a scenario where our universe is a 3+1-dimensional surface (the ``brane) embedded in a five-dimensional spacetime (the ``bulk), we study geometries for which the brane is anisotropic - more specifically Bianchi I - though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to be empty but endowed with a negative cosmological constant. We then embed Z_2-symmetric branes in the anisotropic spacetimes and discuss the constraints on the brane energy-momentum tensor due to the five-dimensional anisotropic geometry. We show that if the bulk is static, an anisotropic brane cannot support a perfect fluid. However, we find that for some of our bulk solutions it is possible to embed a brane with a perfect fluid though its energy density and pressure are completely determined by the bulk geometry.

Analytical treatment of critical collapse in (2+1)-dimensional AdS spacetime: a toy model

We present an exact collapsing solution to 2 + 1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation to those of the corresponding continuously self-similar solution derived in the Λ = 0 case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be γ = (2/5).

The cosmological gravitating σ model: solitons and black holes

We derive and analyse exact static solutions to the gravitating O(3) σ model with a cosmological constant in (2+1) dimensions. Both signs of the gravitational and cosmological constants are considered. Our solutions include geodesically complete spacetimes, and two classes of black holes.

Quantum evolution of near-extremal Reissner–Nordström black holes

Abstract We study the near-horizon AdS 2 × S 2 geometry of evaporating near-extremal Reissner–Nordstrom black holes interacting with null matter. The non-local (boundary) terms t ± , coming from the effective theory corrected with the quantum Polyakov–Liouville action, are treated as dynamical variables. We describe analytically the evaporation process which turns out to be compatible with the third law of thermodynamics, i.e., an infinite amount of time is required for the black hole to decay to extremality. Finally we comment briefly on the implications of our results for the information loss problem.

Approximately self-similar critical collapse in 2+1 dimensions

Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional spacetime with negative cosmological constant seems to be dominated by a continuously self-similar solution of the field equations without cosmological constant. However, previous studies of linear perturbations in this background were inconclusive. We extend the continuously self-similar solutions to solutions of the field equations with negative cosmological constant, and analyse their linear perturbations. The extended solutions are characterized by a continuous parameter. A suitable choice of this parameter seems to improve the agreement with the numerical results. We also study the dynamics of the apparent horizon in the extended background.