25 research outputs found
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
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
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
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
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
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
Smooth Gowdy symmetric generalized Taub-NUT solutions
We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon
which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In
particular, we prove existence of such solutions by formulating a singular
initial value problem with asymptotic data on the past Cauchy horizon. The
result of our investigations is that a future Cauchy horizon exists for generic
asymptotic data. Moreover, we derive an explicit expression for the metric on
the future Cauchy horizon in terms of the asymptotic data on the past horizon.
This complements earlier results about S2xS1 Gowdy models.Comment: 56 pages, 1 figure. The new version contains a detailed explanation
of the Fuchsian method on the 2-spher
Gravitating Opposites Attract
Generalizing previous work by two of us, we prove the non-existence of
certain stationary configurations in General Relativity having a spatial
reflection symmetry across a non-compact surface disjoint from the matter
region. Our results cover cases such that of two symmetrically arranged
rotating bodies with anti-aligned spins in () dimensions, or
two symmetrically arranged static bodies with opposite charges in 3+1
dimensions. They also cover certain symmetric configurations in
(3+1)-dimensional gravity coupled to a collection of scalars and abelian vector
fields, such as arise in supergravity and Kaluza-Klein models. We also treat
the bosonic sector of simple supergravity in 4+1 dimensions.Comment: 13 pages; slightly amended version, some references added, matches
version to be published in Classical and Quantum Gravit