158 research outputs found
Singularity in 2+1 dimensional AdS-scalar black hole
We study the spacetime singularity in 2+1 dimensional AdS-scalar black hole
with circular symmetry using a quasi-homogeneous model. We show that this is a
spacelike, scalar curvature, deformationally strong singularity.Comment: 4 pages, RevTeX, submitted to PRD (brief report
Late-time Kerr tails: generic and non-generic initial data sets, "up" modes, and superposition
Three interrelated questions concerning Kerr spacetime late-time scalar-field
tails are considered numerically, specifically the evolutions of generic and
non-generic initial data sets, the excitation of "up" modes, and the resolution
of an apparent paradox related to the superposition principle. We propose to
generalize the Barack-Ori formula for the decay rate of any tail multipole
given a generic initial data set, to the contribution of any initial multipole
mode. Our proposal leads to a much simpler expression for the late-time power
law index. Specifically, we propose that the late-time decay rate of the
spherical harmonic multipole moment because of an initial
multipole is independent of the azimuthal number , and is
given by , where for and
for . We also show explicitly that the angular symmetry group of
a multipole does not determine its late-time decay rate.Comment: 12 pages, 13 figures, 4 tables. Substantially revised manuscrip
Singularity deep inside the spherical charged black hole core
We study analytically the spacelike singularity inside a
spherically-symmetric, charged black hole coupled to a self-gravitating
spherical massless scalar field. We assume spatial homogeneity, and find a
generic solution in terms of a formal series expansion. This solution is tested
against fully-nonlinear and inhomogeneous numerical simulations. We find full
compliance between our analytical solution and the pointwise behavior of the
singularity in the numerical simulations. This is a strong scalar-curvature
monotonic spacelike singularity, which connects to a weak null singularity at
asymptotically-late advanced time.Comment: 6 pages, to be published in Phys. Rev.
On the falloff of radiated energy in black hole spacetimes
The goal of much research in relativity is to understand gravitational waves
generated by a strong-field dynamical spacetime. Quantities of particular
interest for many calculations are the Weyl scalar , which is simply
related to the flux of gravitational waves far from the source, and the flux of
energy carried to distant observers, . Conservation laws guarantee
that, in asympotically flat spacetimes, and as . Most calculations extract these quantities at
some finite extraction radius. An understanding of finite radius corrections to
and allows us to more accurately infer their asymptotic
values from a computation. In this paper, we show that, if the final state of
the system is a black hole, then the leading correction to is , and that to the energy flux is --- not and as one might naively guess. Our argument only
relies on the behavior of the curvature scalars for black hole spacetimes.
Using black hole perturbation theory, we calculate the corrections to the
leading falloff, showing that it is quite easy to correct for finite extraction
radius effects.Comment: 5 pages, no figures, accepted to Phys. Rev. D. This version corrects
several typos and minor errors in the earlier submissio
Self force on static charges in Schwarzschild spacetime
We study the self forces acting on static scalar and electric test charges in
the spacetime of a Schwarzschild black hole. The analysis is based on a direct,
local calculation of the self forces via mode decomposition, and on two
independent regularization procedures: A spatially-extended particle model
method, and on a mode-sum regularization prescription. In all cases we find
excellent agreement with the known exact results.Comment: 21 pages, 9 Encapsulated PostScript figures, submitted to Class.
Quantum Gra
The Central Singularity in Spherical Collapse
The gravitational strength of the central singularity in spherically
symmetric space-times is investigated. Necessary conditions for the singularity
to be gravitationally weak are derived and it is shown that these are violated
in a wide variety of circumstances. These conditions allow conclusions to be
drawn about the nature of the singularity without having to integrate the
geodesic equations. In particular, any geodesic with a non-zero amount of
angular momentum which impinges on the singularity terminates in a strong
curvature singularity.Comment: 17 pages; revised and corrected with improved result
Numerical investigation of the late-time Kerr tails
The late-time behavior of a scalar field on fixed Kerr background is examined
in a numerical framework incorporating the techniques of conformal
compactification and hyperbolic initial value formulation. The applied code is
1+(1+2) as it is based on the use of the spectral method in the angular
directions while in the time-radial section fourth order finite differencing,
along with the method of lines, is applied. The evolution of various types of
stationary and non-stationary pure multipole initial states are investigated.
The asymptotic decay rates are determined not only in the domain of outer
communication but along the event horizon and at future null infinity as well.
The decay rates are found to be different for stationary and non-stationary
initial data, and they also depend on the fall off properties of the initial
data toward future null infinity. The energy and angular momentum transfers are
found to show significantly different behavior in the initial phase of the time
evolution. The quasinormal ringing phase and the tail phase are also
investigated. In the tail phase, the decay exponents for the energy and angular
momentum losses at future null infinity are found to be smaller than at the
horizon which is in accordance with the behavior of the field itself and it
means that at late times the energy and angular momentum falling into the black
hole become negligible in comparison with the energy and angular momentum
radiated toward future null infinity. The energy and angular momentum balances
are used as additional verifications of the reliability of our numerical
method.Comment: 33 pages, 12 figure
Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits
Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be
computed using time--domain methods with accuracy that is fast approaching that
of frequency--domain methods. We study in detail the computational efficiency
of these methods for equatorial orbits of fast spinning Kerr black holes, and
find the number of modes needed in either method --as functions of the orbital
parameters-- in order to achieve a desired accuracy level. We then estimate the
total computation time and argue that for high eccentricity orbits the
time--domain approach is more efficient computationally. We suggest that in
practice low-- modes are computed using the frequency--domain approach, and
high-- modes are computed using the time--domain approach, where is the
azimuthal mode number.Comment: 19 figures, 6 table
The interior structure of rotating black holes 1. Concise derivation
This paper presents a concise derivation of a new set of solutions for the
interior structure of accreting, rotating black holes. The solutions are
conformally stationary, axisymmetric, and conformally separable.
Hyper-relativistic counter-streaming between freely-falling collisionless
ingoing and outgoing streams leads to mass inflation at the inner horizon,
followed by collapse. The solutions fail at an exponentially tiny radius, where
the rotational motion of the streams becomes comparable to their radial motion.
The papers provide a fully nonlinear, dynamical solution for the interior
structure of a rotating black hole from just above the inner horizon inward,
down to a tiny scale.Comment: Version 1: 8 pages, 3 figures. Version 2: Extensively revised to
emphasize the derivation of the solution rather than the solution itself. 11
pages, 4 figures. Version 3: Minor changes to match published version.
Mathematica notebook available at
http://jila.colorado.edu/~ajsh/rotatinginflationary/rotatinginflationary.n
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