60 research outputs found
Non-linear perturbation of black branes at large
The Einstein equations describing the black-brane dynamics both in Minkowski
and AdS background were recently recast in the form of coupled diffusion
equations in the large-(imension) limit. Using such results in the
literature, we formulate a higher-order perturbation theory of black branes in
time domain and present the general form of solutions for arbitrary initial
conditions. For illustrative purposes, the solutions up to the first or second
order are explicitly written down for several kind of initial conditions, such
as a Gaussian wave packet, shock wave, and rather general superposed sinusoidal
waves. These could be the first examples describing the non-trivial evolution
of black-brane horizons in time domain. In particular, we learn some
interesting aspects of black-brane dynamics such as the Gregory-Laflamme (GL)
instability and non-equilibrium steady state (NESS). The formalism presented
here would be applicable to the analysis of various black branes and their
holographically dual field theories.Comment: 1+22 pages, 6 figure
Stability of non-uniform liquid bridges in all dimensions
Static equilibrium configurations of continuum supported by surface tension
are given by constant-mean-curvature (CMC) surfaces which are the critical
points of a variational problem to extremize the area with keeping the volume
fixed. The geometry of CMC surfaces and their properties such as stability are
of special importance in differential geometry and a variety of physical
science. In this paper, we examine the stability of CMC hypersurfaces in
general dimensions possibly having boundaries on two parallel hyperplanes, by
investigating the second variation of area functional. We reveal the stability
of non-uniform liquid bridges or unduloids for the first time in all dimensions
and all parameter (the ratio of the neck radius to bulge radius) regimes. The
analysis is assisted by numerical computations.Comment: 36 pages, 3 figures, 3 table
Stability of branes trapped by d-dimensional black holes
The system of extended objects interplaying with a black hole describes or
mimics various gravitational phenomena. In this brief paper, we report the
results of stability analysis of codimension-one Dirac-Nambu-Goto branes rest
at the equatorial plane of -dimensional spherical black holes, including the
Schwarzschild and Schwarzschild-(anti-)de Sitter black holes. For the
Schwarzschild and Schwarzschild-anti-de Sitter backgrounds the stability of
branes is shown analytically by means of a deformation technique. In contrast,
for the Schwarzschild-de Sitter background we demonstrate with the help of
numerics that the brane is unstable (only) against the s-wave sector of
perturbations.Comment: 13 pages, no figure, 1 table; v2: typos corrected, refs and minor
comments adde
Quantum Effect and Curvature Strength of Naked Singularities
There are many solutions to the Einstein field equations that demonstrate
naked singularity (NS) formation after regular evolution. It is possible,
however, that such a quantum effect as particle creation prevents NSs from
forming. We investigate the relation between the curvature strength and the
quantum effects of NSs in a very wide class of spherical dust collapse. Through
a perturbative calculation, we find that if the NS is very strong, the quantum
particle creation diverges as the Cauchy horizon is approached, while if the NS
is very weak, the creation should be finite. In the context of cosmic
censorship, strong NSs will be subjected to the backreaction of quantum effects
and may disappear or be hidden behind horizons, while weak NSs will not.Comment: 21 pages, 1 table, 3 figures. Final version to appear in Progress of
Theoretical Physic
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