Bekenstein-Hawking entropy from a phenomenological membrane

It is pointed out that the entropy of a membrane which is quantized perturbatively around a background position of fixed radius in a black hole spacetime is equal to the Bekenstein-Hawking entropy, if 1) the membrane surface is the horizon surface plus one Planck unit, and 2) its temperature is the Hawking temperature. (This is a comment on gr-qc 9411037.)Comment: 1 journal page, Revte

Critical collapse of a rotating scalar field in 2+12+1 dimensions

We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving rise to an axisymmetric metric, in 2+1 spacetime dimensions with cosmological constant $\Lambda<0$, for $m=0,1,2$, for four 1-parameter families of initial data. We look for the familiar scaling of black hole mass and maximal Ricci curvature as a power of $|p-p_*|$, where $p$ is the amplitude of our initial data and $p_*$ some threshold. We find evidence of Ricci scaling for all families, and tentative evidence of mass scaling for most families, but the case $m>0$ is very different from the case $m=0$ we have considered before: the thresholds for mass scaling and Ricci scaling are significantly different (for the same family), scaling stops well above the scale set by $\Lambda$, and the exponents depend strongly on the family. Hence, in contrast to the $m=0$ case, and to many other self-gravitating systems, there is only weak evidence for the collapse threshold being controlled by a self-similar critical solution and no evidence for it being universal.Comment: Version accepted for publication in PR

Critical collapse of rotating radiation fluids

We present results from the first fully relativistic simulations of the critical collapse of rotating radiation fluids. We observe critical scaling both in subcritical evolutions, in which case the fluid disperses to infinity and leaves behind flat space, and in supercritical evolutions that lead to the formation of black holes. We measure the mass and angular momentum of these black holes, and find that both show critical scaling with critical exponents that are consistent with perturbative results. The critical exponents are universal; they are not affected by angular momentum, and are independent of the direction in which the critical curve, which separates subcritical from supercritical evolutions in our two-dimensional parameter space, is crossed. In particular, these findings suggest that the angular momentum decreases more rapidly than the square of the mass, so that, as criticality is approached, the collapse leads to the formation of a non-spinning black hole. We also demonstrate excellent agreement of our numerical data with new closed-form extensions of power-law scalings that describe the mass and angular momentum of rotating black holes formed close to criticality.Comment: 5 pages, 4 figures; version accepted for publication in PR

Einstein-Vlasov system in spherical symmetry: Reduction of the equations of motion and classification of single-shell static solutions in the limit of massless particles

We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable z (radial over angular momentum). This regularizes the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables (t,r,z) only. Similarly, in this limit the Vlasov density function f for static solutions depends on a single variable Q (energy over angular momentum). This reduction allows us to show that any given static metric that has vanishing Ricci scalar, is vacuum at the center and for r&gt;3M and obeys certain energy conditions uniquely determines a consistent f=¯k(Q) (in closed form). Vice versa, any ¯k(Q) within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ordinary differential equations). Hence the space of static spherically symmetric solutions of the Einstein-Vlasov system is locally a space of functions of one variable. For a simple two-parameter family of functions ¯k(Q), we construct the corresponding static spherically symmetric solutions, finding that their compactness is in the interval 0.7?maxr(2M/r)?8/9. This class of static solutions includes one that agrees with the approximately universal type-I critical solution recently found by Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what singles it out as the critical solution found by fine-tuning generic data to the collapse threshold, given that AC also found that all static solutions are one-parameter unstable and sit on the threshold of collapse

Scalar field critical collapse in 2+1 dimensions

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the $n=4$ Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of $\Lambda<0$. This approximation is only $C^3$ at the lightcone and has three growing modes. We {\em conjecture} that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.Comment: 27 page

Fractal Threshold Behavior in Vacuum Gravitational Collapse

We present the numerical evidence for fractal threshold behavior in the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a butterfly may influence the process of the black hole formation.Comment: 4 pages, 6 figures, minor change