26,235 research outputs found
Linear perturbations for the vacuum axisymmetric Einstein equations
In axial symmetry, there is a gauge for Einstein equations such that the
total mass of the spacetime can be written as a conserved, positive definite,
integral on the spacelike slices. This property is expected to play an
important role in the global evolution. In this gauge the equations reduce to a
coupled hyperbolic-elliptic system which is formally singular at the axis. Due
to the rather peculiar properties of the system, the local in time existence
has proved to resist analysis by standard methods. To analyze the principal
part of the equations, which may represent the main source of the difficulties,
we study linear perturbation around the flat Minkowski solution in this gauge.
In this article we solve this linearized system explicitly in terms of integral
transformations in a remarkable simple form. This representation is well suited
to obtain useful estimates to apply in the non-linear case.Comment: 13 pages. We suppressed the statements about decay at infinity. The
proofs of these statements were incomplete. The complete proofs will require
extensive technical analysis. We will studied this in a subsequent work. We
also have rewritten the introduction and slighted changed the titl
A Dain Inequality with charge
We prove 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
Angular momentum-mass inequality for axisymmetric black holes
In these notes we describe recent results concerning the inequality for axially symmetric black holes.Comment: 7 pages, 1 figur
The Yamabe invariant for axially symmetric two Kerr black holes initial data
An explicit 3-dimensional Riemannian metric is constructed which can be
interpreted as the (conformal) sum of two Kerr black holes with aligned angular
momentum. When the separation distance between them is large we prove that this
metric has positive Ricci scalar and hence positive Yamabe invariant. This
metric can be used to construct axially symmetric initial data for two Kerr
black holes with large angular momentum.Comment: 14 pages, 2 figure
Initial data for black hole collisions
I describe the construction of initial data for the Einstein vacuum equations
that can represent a collision of two black holes. I stress in the main
physical ideas.Comment: 5 pages, 2 figures. To appear in the Proceedings of the Spanish
Relativity Meeting Gravitation and Cosmology ERE - 2002; isbn: 978844752738
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