10 research outputs found
Periodic analogues of the Kerr solutions: a numerical study
In recent years black hole configurations with non standard topology or with
non-standard asymptotic have gained considerable attention. In this article we
carry out numerical investigations aimed to find periodic coaxial
configurations of co-rotating 3+1 vacuum black holes, for which existence and
uniqueness has not yet been theoretically proven. The aimed configurations
would extend Myers/Korotkin-Nicolai's family of non-rotating (static) coaxial
arrays of black holes. We find that numerical solutions with a given value for
the area A and for the angular momentum J of the horizons appear to exist only
when the separation between consecutive horizons is larger than a certain
critical value that depends only on A and |J|. We also establish that the
solutions have the same Lewis's cylindrical asymptotic as Stockum's infinite
rotating cylinders. Below the mentioned critical value the rotational energy
appears to be too big to sustain a global equilibrium and a singularity shows
up at a finite distance from the bulk. This phenomenon is a relative of
Stockum's asymptotic's collapse, manifesting when the angular momentum (per
unit of axial length) reaches a critical value compared to the mass (per unit
of axial length), and that results from a transition in the Lewis's class of
the cylindrical exterior solution. This remarkable phenomenon seems to be
unexplored in the context of coaxial arrays of black holes. Ergospheres and
other global properties are also presented in detail.Comment: 25 page
Black hole Area-Angular momentum inequality in non-vacuum spacetimes
We show that the area-angular momentum inequality A\geq 8\pi|J| holds for
axially symmetric closed outermost stably marginally trapped surfaces. These
are horizon sections (in particular, apparent horizons) contained in otherwise
generic non-necessarily axisymmetric black hole spacetimes, with non-negative
cosmological constant and whose matter content satisfies the dominant energy
condition.Comment: 5 pages, no figures, updated to match published versio
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
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
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