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This is an introduction into the problem of how to set up black hole initial-data for the matter-free field equations of General Relativity. The approach is semi-pedagogical and addresses a more general audience of astrophysicists and…
We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an SO(4,2) group. Of these, a…
Three dimensional black holes in a generalized dilaton gravity action theory are analysed. The theory is specified by two fields, the dilaton and the graviton, and two parameters, the cosmological constant and the Brans-Dicke parameter. It…
Fast variability studies of accreting black holes in the Galaxy offer us a unique opportunity to measure the spins of black holes and test the strong-field behavior of general relativity. In this review, I summarize the arguments often used…
We establish that the Einstein tensor takes on a highly symmetric form near the Killing horizon of any stationary but non-static (and non-extremal) black hole spacetime. [This follows up on a recent article by the current authors,…
Black holes are important astrophysical objects describing an end state of stellar evolution, which are observed frequently. There are theoretical predictions that Kerr black holes with high spins expel magnetic fields. However, Kerr black…
We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity. After an introduction that discusses the main conceptual issues we present some details about the classical…
A pedagogical discussion is given of some aspects of \lq\lq quantum black holes", primarily using recently developed two-dimensional models. After a short preliminary concerning classical black holes, we give several motivations for…
Analytic approximations for the stress-energy of quantized fields in the Hartle-Hawking state in static black hole spacetimes predict divergences on the event horizon of the black hole for a number of important cases. Such divergences, if…
We investigate the possibility to localize scalar field configurations as a model for black hole accretion. We analyze and resolve difficulties encountered when localizing scalar fields in General Relativity. We illustrate this ability with…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential…
In this paper, the Killing vector will be constructed for the $R$-spacetime metric. The symmetry transformations corresponding to this vectors are obtained explicitly. Their coincidence with the transformations of the Poincar\'e group in a…
Recent applications of Operator Algebras to Quantum Field Theory on a Curved Spacetime show that the incremental entropy associated with a quantum black hole, due the addition of a short range charge, is quantized proportionally to the…
Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we…
The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\tilde…
This article outlines the search for an exact general relativistic description of the exterior (vacuum) gravitational field of a rotating spheroidal black hole surrounded by a realistic axially symmetric disc of matter. The problem of…
In 4-dimensional General Relativity, black holes are described by the Kerr solution and are completely specified by their mass $M$ and by their spin angular momentum $J$. A fundamental limit for a black hole in General Relativity is the…
The general parametrization of a black-hole spacetime in arbitrary metric theories of gravity includes an infinite set of parameters. It is natural to suppose that essential astrophysically observable quantities, such as quasinormal modes,…
We determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second…