30 research outputs found
The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory
We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8\pi J)2+(4\pi Q2)2=A+ A-, where A+ and A- denote the areas of event and Cauchy horizon respectively
Universal properties of distorted Kerr-Newman black holes
We discuss universal properties of axisymmetric and stationary configurations
consisting of a central black hole and surrounding matter in Einstein-Maxwell
theory. In particular, we find that certain physical equations and inequalities
(involving angular momentum, electric charge and horizon area) are not
restricted to the Kerr-Newman solution but can be generalized to the situation
where the black hole is distorted by an arbitrary axisymmetric and stationary
surrounding matter distribution.Comment: 7 page
The interior of axisymmetric and stationary black holes: Numerical and analytical studies
We investigate the interior hyperbolic region of axisymmetric and stationary
black holes surrounded by a matter distribution. First, we treat the
corresponding initial value problem of the hyperbolic Einstein equations
numerically in terms of a single-domain fully pseudo-spectral scheme.
Thereafter, a rigorous mathematical approach is given, in which soliton methods
are utilized to derive an explicit relation between the event horizon and an
inner Cauchy horizon. This horizon arises as the boundary of the future domain
of dependence of the event horizon. Our numerical studies provide strong
evidence for the validity of the universal relation \Ap\Am = (8\pi J)^2 where
\Ap and \Am are the areas of event and inner Cauchy horizon respectively,
and denotes the angular momentum. With our analytical considerations we are
able to prove this relation rigorously.Comment: Proceedings of the Spanish Relativity Meeting ERE 2010, 10 pages, 5
figure
Non-existence of stationary two-black-hole configurations
We resume former discussions of the question, whether the spin-spin repulsion
and the gravitational attraction of two aligned black holes can balance each
other. To answer the question we formulate a boundary value problem for two
separate (Killing-) horizons and apply the inverse (scattering) method to solve
it. Making use of results of Manko, Ruiz and Sanabria-G\'omez and a novel black
hole criterion, we prove the non-existence of the equilibrium situation in
question.Comment: 15 pages, 3 figures; Contribution to Juergen Ehlers Memorial Issue
(GeRG journal
Mass, angular-momentum, and charge inequalities for axisymmetric initial data
We present the key elements of the proof of an upper bound for
angular-momentum and charge in terms of the mass for electro-vacuum
asymptotically flat axisymmetric initial data sets with simply connected orbit
space
Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes
We study general S2xS1 Gowdy models with a regular past Cauchy horizon and
prove that a second (future) Cauchy horizon exists, provided that a particular
conserved quantity is not zero. We derive an explicit expression for the
metric form on the future Cauchy horizon in terms of the initial data on the
past horizon and conclude the universal relation A\p A\f=(8\pi J)^2 where
A\p and A\f are the areas of past and future Cauchy horizon respectively.Comment: 17 pages, 1 figur
Area-charge inequality for black holes
The inequality between area and charge for dynamical black
holes is proved. No symmetry assumption is made and charged matter fields are
included. Extensions of this inequality are also proved for regions in the
spacetime which are not necessarily black hole boundaries.Comment: 21 pages, 2 figure
Non-existence of stationary two-black-hole configurations: The degenerate case
In a preceding paper we examined the question whether the spin-spin repulsion
and the gravitational attraction of two aligned sub-extremal black holes can
balance each other. Based on the solution of a boundary value problem for two
separate (Killing-) horizons and a novel black hole criterion we were able to
prove the non-existence of the equilibrium configuration in question. In this
paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 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
Mass and Angular Momentum in General Relativity
We present an introduction to mass and angular momentum in General
Relativity. After briefly reviewing energy-momentum for matter fields, first in
the flat Minkowski case (Special Relativity) and then in curved spacetimes with
or without symmetries, we focus on the discussion of energy-momentum for the
gravitational field. We illustrate the difficulties rooted in the Equivalence
Principle for defining a local energy-momentum density for the gravitational
field. This leads to the understanding of gravitational energy-momentum and
angular momentum as non-local observables that make sense, at best, for
extended domains of spacetime. After introducing Komar quantities associated
with spacetime symmetries, it is shown how total energy-momentum can be
unambiguously defined for isolated systems, providing fundamental tests for the
internal consistency of General Relativity as well as setting the conceptual
basis for the understanding of energy loss by gravitational radiation. Finally,
several attempts to formulate quasi-local notions of mass and angular momentum
associated with extended but finite spacetime domains are presented, together
with some illustrations of the relations between total and quasi-local
quantities in the particular context of black hole spacetimes. This article is
not intended to be a rigorous and exhaustive review of the subject, but rather
an invitation to the topic for non-experts. In this sense we follow essentially
the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84,
and refer the reader interested in further developments to the existing
literature, in particular to the excellent and comprehensive review by Szabados
(2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on
Mass" (June 2008) in Orleans, France. To appear as proceedings in the book
"Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and
B. Whiting. Some comments and references added