Non-linear perturbation of black branes at large DD

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-$D$(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 $d$-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