12 research outputs found
Bounds on the force between black holes
We treat the problem of N interacting, axisymmetric black holes and obtain
two relations among physical parameters of the system including the force
between the black holes. The first relation involves the total mass, the
angular momenta, the distances and the forces between the black holes. The
second one relates the angular momentum and area of each black hole with the
forces acting on it.Comment: 13 pages, no figure
Conformally flat black hole initial data, with one cylindrical end
We give a complete analytical proof of existence and uniqueness of
extreme-like black hole initial data for Einstein equations, which possess a
cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and
extreme Bowen-York's initial data. This extends and refines a previous result
\cite{dain-gabach09} to a general case of conformally flat, maximal initial
data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published
version in Class. Quantum Grav. (2010). Results unchange
Proof of the area-angular momentum-charge inequality for axisymmetric black holes
We give a comprehensive discussion, including a detailed proof, of the
area-angular momentum-charge inequality for axisymmetric black holes. We
analyze the inequality from several viewpoints, in particular including aspects
with a theoretical interest well beyond the Einstein-Maxwell theory.Comment: 31 pages, 2 figure
Horizon area-angular momentum inequality in higher dimensional spacetimes
We consider -dimensional spacetimes which are axisymmetric--but not
necessarily stationary (!)--in the sense of having isometry group ,
and which satisfy the Einstein equations with a non-negative cosmological
constant. We show that any black hole horizon must have area A \ge 8\pi |J_+
J_-|^\half, where are distinguished components of the angular momentum
corresponding to linear combinations of the rotational Killing fields that
vanish somewhere on the horizon. In the case of , where there is only one
angular momentum component , we recover an inequality of 1012.2413
[gr-qc]. Our work can hence be viewed as a generalization of this result to
higher dimensions. In the case of with horizon of topology , the quantities are the same angular momentum component (in the
direction). In the case of with horizon topology , the
quantities are the distinct components of the angular momentum. We
also show that, in all dimensions, the inequality is saturated if the metric is
a so-called ``near horizon geometry''. Our argument is entirely quasi-local,
and hence also applies e.g. to any stably outer marginally trapped surface.Comment: 16 pages, Latex, no figure
Geometric inequalities for axially symmetric black holes
A geometric inequality in General Relativity relates quantities that have
both a physical interpretation and a geometrical definition. It is well known
that the parameters that characterize the Kerr-Newman black hole satisfy
several important geometric inequalities. Remarkably enough, some of these
inequalities also hold for dynamical black holes. This kind of inequalities
play an important role in the characterization of the gravitational collapse,
they are closed related with the cosmic censorship conjecture. Axially
symmetric black holes are the natural candidates to study these inequalities
because the quasi-local angular momentum is well defined for them. We review
recent results in this subject and we also describe the main ideas behind the
proofs. Finally, a list of relevant open problem is presented.Comment: 65 pages, 5 figures. Review article, to appear in Class. Quantum
Grav. as Topical Review. Improved presentation, minor corrections, references
updat
Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black-hole solutions to the stationary Einstein
equations has been steadily increasing, sometimes in unexpected ways. In
particular, it has turned out that not all black-hole-equilibrium
configurations are characterized by their mass, angular momentum and global
charges. Moreover, the high degree of symmetry displayed by vacuum and
electro-vacuum black-hole spacetimes ceases to exist in self-gravitating
non-linear field theories. This text aims to review some developments in the
subject and to discuss them in light of the uniqueness theorem for the
Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998.
Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's
authorship. Significantly restructured and updated all sections; changes are
too numerous to be usefully described here. The number of references
increased from 186 to 32