81 research outputs found
A Double Myers-Perry Black Hole in Five Dimensions
Using the inverse scattering method we construct a six-parameter family of
exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum
Einstein equations, with U(1)^2 rotational symmetry. It describes the
superposition of two Myers-Perry black holes, each with a single angular
momentum parameter, both in the same plane. The black holes live in a
background geometry which is the Euclidean C-metric with an extra flat time
direction. This background possesses conical singularities in two adjacent
compact regions, each corresponding to a set of fixed points of one of the U(1)
actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the
black holes geometry, including the conical singularities arising from force
imbalance, and the torsion singularity arising from torque imbalance. The
double Myers-Perry solution presented herein is considerably simpler than the
four dimensional double Kerr solution and might be of interest in studying
spin-spin interactions in five dimensional general relativity.Comment: 23 pages, 7 figures, LaTeX. v2: minor changes, references added;
version published in JHE
Black hole binaries: ergoregions, photon surfaces, wave scattering, and quasinormal modes
Closed photon orbits around isolated black holes are related to important
aspects of black hole physics, such as strong lensing, absorption cross section
of null particles and the way that black holes relax through quasinormal
ringing. When two black holes are present -- such as during the inspiral and
merger events of interest for gravitational-wave detectors -- the concept of
closed photon orbits still exists, but its properties are basically unknown.
With these applications in mind, we study here the closed photon orbits of two
different static black hole binaries. The first one is the Majumdar-Papapetrou
geometry describing two extremal, charged black holes in equilibrium, while the
second one is the double sink solution of fluid dynamics, which describes (in a
curved-spacetime language) two "dumb" holes. For the latter solution, we also
characterize its dynamical response to external perturbations, and study how it
relates to the photon orbits. In addition, we compute the ergoregion of such
spacetime and show that it does not coincide with the event horizon.Comment: 13 pages, 11 figures. v3: minor edits, to appear in Physical Review
Black holes in a box: towards the numerical evolution of black holes in AdS
The evolution of black holes in "confining boxes" is interesting for a number
of reasons, particularly because it mimics the global structure of Anti-de
Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy
problem may only be well defined if the initial data is supplemented by
boundary conditions at the time-like conformal boundary. Here, we explore the
active role that boundary conditions play in the evolution of a bulk black hole
system, by imprisoning a black hole binary in a box with mirror-like boundary
conditions. We are able to follow the post-merger dynamics for up to two
reflections off the boundary of the gravitational radiation produced in the
merger. We estimate that about 15% of the radiation energy is absorbed by the
black hole per interaction, whereas transfer of angular momentum from the
radiation to the black hole is only observed in the first interaction. We
discuss the possible role of superradiant scattering for this result. Unlike
the studies with outgoing boundary conditions, both the Newman-Penrose scalars
\Psi_4 and \Psi_0 are non-trivial in our setup, and we show that the numerical
data verifies the expected relations between them.Comment: REvTex4, 17 pages, 12 Figs. v2: Minor improvements. Published
version. Animation of a black hole binary in a box can be found at
http://blackholes.ist.utl.pt
Black holes in a box
The evolution of BHs in "confining boxes" is interesting for a number of reasons, particularly because it mimics some aspects of anti-de Sitter spacetimes. These admit no Cauchy surface and are a simple example of a non-globally hyperbolic spacetime. We are here interested in the potential role that boundary conditions play in the evolution of a BH system. For that, we imprison a binary BH in a box, at which boundary we set mirror-like boundary conditions. © 2010 IOP Publishing Ltd
Numerical relativity in higher dimensions
We give a status report on our project targeted at performing numerical simulations of a head-on collision of non-spinning black holes in higher dimensional non-compact space-times. These simulations should help us understand black objects in higher dimensions and their stability properties. They are also relevant for the problem of black hole formation and evaporation in particle accelerators and cosmic rays. We use the symmetries of the system to reduce the problem to an effective 3+1 problem, allowing the use of existing numerical codes. As a simple application of the formalism, we present the results for the evolution of a five dimensional single black hole space-time. © 2010 IOP Publishing Ltd
Higher dimensional Numerical Relativity: code comparison
The nonlinear behavior of higher dimensional black hole spacetimes is of
interest in several contexts, ranging from an understanding of cosmic
censorship to black hole production in high-energy collisions. However,
nonlinear numerical evolutions of higher dimensional black hole spacetimes are
tremendously complex, involving different diagnostic tools and "dimensional
reduction methods". In this work we compare two different successful codes to
evolve Einstein's equations in higher dimensions, and show that the results of
such different procedures agree to numerical precision, when applied to the
collision from rest of two equal-mass black holes. We calculate the total
radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in
six dimensions.Comment: 7 pages, RevTex
Gauge structure of the Einstein field equations in Bondi-like coordinates
The characteristic initial (boundary) value problem has numerous applications
in general relativity (GR) involving numerical studies, and is often formulated
using Bondi-like coordinates. Recently it was shown that several prototype
formulations of this type are only weakly hyperbolic. Presently we examine the
root cause of this result. In a linear analysis we identify the gauge,
constraint and physical blocks in the principal part of the Einstein field
equations in such a gauge, and show that the subsystem related to the gauge
variables is only weakly hyperbolic. Weak hyperbolicity of the full system
follows as a consequence in many cases. We demonstrate this explicitly in
specific examples, and thus argue that Bondi-like gauges result in weakly
hyperbolic free evolution systems under quite general conditions. Consequently
the characteristic initial (boundary) value problem of GR in these gauges is
rendered ill-posed in the simplest norms one would like to employ. The
possibility of finding good alternative norms, in which well-posedness is
achieved, is discussed. So motivated, we present numerical convergence tests
with an implementation of full GR which demonstrate the effect of weak
hyperbolicity in practice.Comment: 23 pages, 3 figures, ancillary files, data and more supplemental
material at 10.5281/zenodo.5618007, updated to match published versio
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