The nature of gravitational singularities

The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and the singularity behaves locally like a homogeneous oscillatory spacetime.Comment: received "honorable mention" in Gravity Research Foundation essay contes

Numerical simulations of generic singuarities

Numerical simulations of the approach to the singularity in vacuum spacetimes are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities. It is found that the singularity is spacelike and that as it is approached, the spacetime dynamics becomes local and oscillatory.Comment: typos correcte

An exact solution for 2+1 dimensional critical collapse

We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions. This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.Comment: 5 pages, 5 figures, Revtex. New comparison of analytic and numerical solutions beyond the past light cone of the singularity added. Two new references added. Error in equation (21) correcte

On the relation of the gravitino mass and the GUT parameters

In this article we consider the local supersymmetry breaking and the broken SU(5) symmetry permisible by dilaton vacuum configuration in supergravity theories. We establish the parameter relation of spontaneuos breaking of supersymmetry and of the GUT theory.Comment: 12 pages, file written in Revtex forma

High velocity spikes in Gowdy spacetimes

We study the behavior of spiky features in Gowdy spacetimes. Spikes with velocity initially high are, generally, driven to low velocity. Let n be any integer greater than or equal to 1. If the initial velocity of an upward pointing spike is between 4n-3 and 4n-1 the spike persists with final velocity between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the spiky feature eventually disappears. For downward pointing spikes the analogous rule is that spikes with initial velocity between 4n-4 and 4n-2 persist with final velocity between 0 and 1, while spikes with initial velocity between 4n-2 and 4n eventually disappear.Comment: discussion of constraints added. Accepted for publication in Phys. Rev.

Thick planar domain wall: its thin wall limit and dynamics

We consider a planar gravitating thick domain wall of the $\lambda \phi^4$ theory as a spacetime with finite thickness glued to two vacuum spacetimes on each side of it. Darmois junction conditions written on the boundaries of the thick wall with the embedding spacetimes reproduce the Israel junction condition across the wall in the limit of infinitesimal thickness. The thick planar domain wall located at a fixed position is then transformed to a new coordinate system in which its dynamics can be formulated. It is shown that the wall's core expands as if it were a thin wall. The thickness in the new coordinates is not constant anymore and its time dependence is given.Comment: 11 pages, to appear in IJMP

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

Conserved masses in GHS Einstein and string black holes

We analyze the relationship between quasilocal masses calculated for solutions of conformally related theories. We show that the ADM mass of a static, spherically symmetric solution is conformally invariant (up to a constant factor) only if the background action functional is conformally invariant. Thus, the requirement of conformal invariance places restrictions on the choice of reference spacetimes. We calculate the mass of the black hole solutions obtained by Garfinkle, Horowitz, and Strominger (GHS) for both the string and the Einstein metrics. In addition, the quasilocal thermodynamic quantities in the string metrics are computed and discussed.Comment: 16 pages REVTeX with packages amsfonts and amssym

d=4 Attractors, Effective Horizon Radius and Fake Supergravity

We consider extremal black hole attractors (both BPS and non-BPS) for N=3 and N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled N=3 theory are similar to attractors in N=2 supergravity minimally coupled to Abelian vector multiplets. On the other hand, N=5 attractors are similar to attractors in N=4 pure supergravity, and in such theories only 1\N-BPS non-degenerate solutions exist. All the above mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d=5 uplift. Finally we comment on the "duality" relations among the attractor solutions of N\geq2 supergravities sharing the same full bosonic sector.Comment: 1+47 pages, 2 Tables. v2: Eqs. (2.3),(2.4) and Footnote 3 added; minor cosmetic changes; to appear in PR