Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

We study the internal structure of a two-dimensional dilatonic evaporating black hole, based on the CGHS model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well-defined at the semiclassical singularity. A well-localized initial wave-packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.Comment: Accepted to Phys. Rev.

Outgoing gravitational shock-wave at the inner horizon: The late-time limit of black hole interiors

We investigate the interiors of 3+1 dimensional asymptotically flat charged and rotating black holes as described by observers who fall into the black holes at late times, long after any perturbations of the exterior region have decayed. In the strict limit of late infall times, the initial experiences of such observers are precisely described by the region of the limiting stationary geometry to the past of its inner horizon. However, we argue that late infall-time observers encounter a null shockwave at the location of the would-be outgoing inner horizon. In particular, for spherically symmetric black hole spacetimes we demonstrate that freely-falling observers experience a metric discontinuity across this shock, that is, a gravitational shock-wave. Furthermore, the magnitude of this shock is at least of order unity. A similar phenomenon of metric discontinuity appears to take place at the inner horizon of a generically-perturbed spinning black hole. We compare the properties of this null shockwave singularity with those of the null weak singularity that forms at the Cauchy horizon.Comment: 23 pages, 4 figures, minor change

Ground States of S-duality Twisted N=4 Super Yang-Mills Theory

We study the low-energy limit of a compactification of N=4 U(n) super Yang-Mills theory on $S^1$ with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the $T^2$ compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a related twisted compactification in terms of the (2,0)-theory, where the recent solution by Gaiotto and Witten of the boundary conditions describing D3-branes ending on a (p,q) 5-brane plays a crucial role.Comment: 104 pages, 5 figures. Revisions to subsection (6.6) and other minor corrections included in version

The Ori-Soen time machine

Ori and Soen have proposed a spacetime which has closed causal curves on the boundary of a region of normal causality, all within a region where the weak energy condition (positive energy density) is satisfied. I analyze the causal structure of this spacetime in some simplified models, show that the Cauchy horizon is compactly generated, and argue that any attempt to build such a spacetime with normal matter might lead to singular behavior where the causality violation would otherwise take place.Comment: 5 pages, RevTeX, 7 figures with epsf, miscellaneous clarifications in v2, minor updates to correspond to version to appear in PR

Are physical objects necessarily burnt up by the blue sheet inside a black hole?

The electromagnetic radiation that falls into a Reissner-Nordstrom black hole develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We consider classical electromagnetic fields (that were produced during the collapse and then backscattered into the black hole), and investigate the blue-sheet effects of these fields on infalling objects within a simplified model. These effects are found to be finite and even negligible for typical parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters

A new time-machine model with compact vacuum core

We present a class of curved-spacetime vacuum solutions which develope closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically-flat, and topologically-trivial. Stability remains the main open question.Comment: 7 page

Evaporation of a two-dimensional charged black hole

We construct a dilatonic two-dimensional model of a charged black hole. The classical solution is a static charged black hole, characterized by two parameters, $m$ and $q$, representing the black hole's mass and charge. Then we study the semiclassical effects, and calculate the evaporation rate of both $m$ and $q$, as a function of these two quantities. Analyzing this dynamical system, we find two qualitatively different regimes, depending on the electromagnetic coupling constant $g_{A}$. If the latter is greater than a certain critical value, the charge-to-mass ratio decays to zero upon evaporation. On the other hand, for $g_{A}$ smaller than the critical value, the charge-to-mass ratio approaches a non-zero constant that depends on $g_{A}$ but not on the initial values of $m$ and $q$.Comment: Latex, 30 pages, accepted for publication in Phys. Rev.

Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

Peningkatan Aktivitas Pembelajaran Ilmu Pengetahuan Sosial Menggunakan Media Puzzle di Kelas V Sekolah Dasar

: This study aims to determine the results of learning activities in the classroom learning social studies V.Media research is descriptive in the form of classroom action research ( PTK ) . This study was conducted in two cycles . The sample was 20 students consisting of 9 men and 11 women in a class V SDS Usaba Sepotong . This study was conducted in two cycles . Based on the first cycle obtained in classical learning activity is 16.67 % . While in the second cycle percentage classical activity of 88.89 % . An increase in activity in the classical style in the second cycle studies . Student learning activities can be enhanced by using a puzzle media on learning social studies class V SDS Usaba Sepotong