Developments in General Relativity: Black Hole Singularity and Beyond

At the 20-th Texas Symposium on Relativistic Astrophysics there was a plenary talk devoted to the recent developments in classical Relativity. In that talk the problems of gravitational collapse, collisions of black holes, and of black holes as celestial bodies were discussed. But probably the problems of the internal structure of black holes are a real great challenge. In my talk I want to outline the recent achievements in our understanding of the nature of the singularity (and beyond!) inside a realistic rotating black hole. This presentation also addresses the following questions: Can we see what happens inside a black hole? Can a falling observer cross the singularity without being crushed? An answer to these questions is probably "yes".Comment: 13 page

Three-Dimensional Billiards with Time Machine

Self-collision of a non-relativistic classical point-like body, or particle, in the spacetime containing closed time-like curves (time-machine spacetime) is considered. A point-like body (particle) is an idealization of a small ideal elastic billiard ball. The known model of a time machine is used containing a wormhole leading to the past. If the body enters one of the mouths of the wormhole, it emerges from another mouth in an earlier time so that both the particle and its "incarnation" coexist during some time and may collide. Such self-collisions are considered in the case when the size of the body is much less than the radius of the mouth, and the latter is much less than the distance between the mouths. Three-dimensional configurations of trajectories with a self-collision are presented. Their dynamics is investigated in detail. Configurations corresponding to multiple wormhole traversals are discussed. It is shown that, for each world line describing self-collision of a particle, dynamically equivalent configurations exist in which the particle collides not with itself but with an identical particle having a closed trajectory (Jinnee of Time Machine).Comment: 20 pages (LATEX), 5 figures (EPS

Silhouettes of wormholes traversed for radiation

The problem of the passage of light through the mouth of a zero-mass wormhole and the possibility of observing the objects from another asymptotically flat space-time through the mouth of a wormhole are considered. It is shown that an individual star can have several images and the fact that the image of a flat Lambertian screen has a complex brightness distribution for an observer located on the opposite side of the throat. Images of two such screens visible inside the silhouette of a massless wormhole and the distribution of radiation intensity in their images are constructed.Comment: 11 pages, 12 figure

Homogeneous singularities inside collapsing wormholes

We analyze analytically and numerically the origin of the singularity in the course of the collapse of a wormhole with the exotic scalar field Psi with negative energy density, and with this field Psi together with the ordered magnetic field H. We do this under the simplifying assumptions of the spherical symmetry and that in the vicinity of the singularity the solution of the Einstein equations depends only on one coordinate (the homogeneous approximation). In the framework of these assumptions we found the principal difference between the case of the collapse of the ordinary scalar field Phi with the positive energy density together with an ordered magnetic field H and the collapse of the exotic scalar field Psi together with the magnetic field H. The later case is important for the possible astrophysical manifestation of the wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To be published in "Physical review. D, Particles, fields, gravitation, and cosmology

Numerical simulations of wind-driven protoplanetary nebulae – I. near-infrared emission

To understand how the circumstellar environments of post-Active Giant Branch (AGB) stars develop into planetary nebulae, we initiate a systematic study of 2D axisymmetric hydrodynamic simulations of protoplanetary nebula (pPN) with a modified ZEUS code. The aim of this first work is to compare the structure of prolate ellipsoidal winds into a stationary ambient medium where both media can be either atomic or molecular. We specifically model the early twin-shock phase which generates a decelerating shell. A thick deformed and turbulent shell grows when an atomic wind expands into an atomic medium. In all other cases, the interaction shell region fragments into radial protrusions due to molecular cooling and chemistry. The resulting fingers eliminate any global slip parallel to the shell surface. This rough surface implies that weak shocks are prominent in the excitation of the gas despite the fast speed of advance. This may explain why low-excitation molecular hydrogen is found towards the front of elliptical pPN. We constrain molecular dissociative fractions and time-scales of fast H2 winds and the pPN lifetime with wind densities ∼105cm−3 and shock speeds of 80∼200kms−1⁠. We identify a variety of stages associated with thermal excitation of H2 near-infrared emission. Generated line emission maps and position–velocity diagrams enable a comparison and distinction with post-AGB survey results. The 1→0S(1)&2→1S(1) lines are lobe-dominated bows rather than bipolar shells