We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. The field equations admit two types of singularities, and their local asymptotic structure is investigated. One of these singularities is found to develop, as a spacelike singularity, inside the black hole. We then study the internal structure of the evaporating black hole from the horizon to the singularity.PACS numbers:

Misner space is a two-dimensional (2D) locally-flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of safe time-travel orbits free of any self-collisions.

We consider a simple dissipative system with spatial structure in contact with a heat bath. The system always exhibits correlations except in the cases of zero and maximal dissipation. We explicitly calculate the correlation function and the nonlocal response function of the system and show that they have the same spatial dependence. Finally, we examine heat transfer in the model, which agrees qualitatively with simulations of vibrated granular gases.PACS numbers: 05.40.a, 44.10.+i, 45.70.-n Driven dissipative systems (DDS) occur in many different contexts, from collections of macroscopic particles to biological systems. Such systems are intrinsically out of equilibrium, and need the input of energy in order to remain functional. One prototype DDS is a granular gas[1], a collection of inelastic grains which dissipate energy through collisions; these have been examined extensively, both experimentally [2,3], numerically [4,5,6], and analytically [7]. Because of the difficulty in treating granular gasses analytically, stochastic mean-field models have been studied. One such is the Maxwell model [8], which assumes a velocity independent collision rate and no spatial structure; this facilitates analytical calculation [9] of quantities such as the velocity distribution function and its moments.The introduction of spatial dependence complicates and enriches the behavior, and may lead to correlations: for example, actual granular gasses exhibit spatial clustering and velocity correlations because of the dissipative collisions, as is seen in simulational studies [10]. Williams and MacKintosh[11] have shown numerically that correlations exist in a 1D driven dissipative gas provided the restitution coefficient is different from one, and Soto, et al [12] have used the BBGKY hierarchy to study the appearance of velocity correlations in inelastic hardsphere systems. Baldassarri, et al [13], and Ben-Naim and Krapivsky[14] consider a lattice variant of the Maxwell model which they solve in the freely cooling case (no driving); the latter authors calculate the spatially dependent velocity correlations which exhibit gaussian decay with distance.In this Rapid Communication we study a model of a driven system with spatial structure: the constituent "particles" are constrained to lie on a 1D lattice with nearest-neighbor coupling. Our main goal will be to understand the connection between the system's dissipative nature and spatial correlations. The system is coupled to a heat reservoir at temperature T , and the model is chosen so that it has a well-defined equilibrium limit for certain values of the system parameters. The meanfield version of the model, which has no spatial structure, can be solved exactly [15], in the sense that all the moments of the energy distribution may be calculated. For the model of this Rapid Communication, we calculate the two-point correlations of the system analytically, and demonstrate that non-zero correlations always exist except for the cases (a) in which there is no dissipation (in agreement ...

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger 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.

No abstract