Back Reaction of Hawking Radiation on Black Hole Geometry

We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiation results from tunnelling between the two geometries. Using this model, the back reaction correction from Hawking radiation is calculated.Comment: Latex file, 15 pages, 4 figures enclosed, uses eps

Trapped Surfaces in Vacuum Spacetimes

An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future.Comment: 14 page

Stress Tensor Correlators in the Schwinger-Keldysh Formalism

We express stress tensor correlators using the Schwinger-Keldysh formalism. The absence of off-diagonal counterterms in this formalism ensures that the +- and -+ correlators are free of primitive divergences. We use dimensional regularization in position space to explicitly check this at one loop order for a massless scalar on a flat space background. We use the same procedure to show that the ++ correlator contains the divergences first computed by `t Hooft and Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio

Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification added, typos corrected, to appear in JHE

Constraints on Cosmic Strings due to Black Holes Formed from Collapsed Cosmic String Loops

The cosmological features of primordial black holes formed from collapsed cosmic string loops are studied. Observational restrictions on a population of primordial black holes are used to restrict $f$, the fraction of cosmic string loops which collapse to form black holes, and $\mu$, the cosmic string mass-per-unit-length. Using a realistic model of cosmic strings, we find the strongest restriction on the parameters $f$ and $\mu$ is due to the energy density in $100 MeV$ photons radiated by the black holes. We also find that inert black hole remnants cannot serve as the dark matter. If earlier, crude estimates of $f$ are reliable, our results severely restrict $\mu$, and therefore limit the viability of the cosmic string large-scale structure scenario.Comment: (Plain Tex, uses tables.tex -- wrapped lines corrected), 11 pages, FERMILAB-Pub-93/137-

van Vleck determinants: traversable wormhole spacetimes

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.

Radiating black hole solutions in arbitrary dimensions

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in $N$-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.Comment: RevTeX 9 pages, no figure

The Worldvolume Action of Kink Solitons in AdS Spacetime

A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters--associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.Comment: 32 pages, 3 figures, typos corrected and additional comments adde

Designed Single-Step Synthesis, Structure, and Derivative Textural Properties of Well-Ordered Layered Penta-coordinate Silicon Alcoholate Complexes

The controllable synthesis of well-ordered layered materials with specific nanoarchitecture poses a grand challenge in materials chemistry. Here the solvothermal synthesis of two structurally analogous 5-coordinate organosilicate complexes through a novel transesterification mechanism is reported. Since the polycrystalline nature of the intrinsic hypervalent Si complex thwarts the endeavor in determining its structure, a novel strategy concerning the elegant addition of a small fraction of B species as an effective crystal growth mediator and a sacrificial agent is proposed to directly prepare diffraction-quality single crystals without disrupting the intrinsic elemental type. In the determined crystal structure, two monomeric primary building units (PBUs) self-assemble into a dimeric asymmetric secondary BU via strong Na+[BOND]O2− ionic bonds. The designed one-pot synthesis is straightforward, robust, and efficient, leading to a well-ordered (10ī)-parallel layered Si complex with its principal interlayers intercalated with extensive van der Waals gaps in spite of the presence of substantial Na+ counter-ions as a result of unique atomic arrangement in its structure. However, upon fast pyrolysis, followed by acid leaching, both complexes are converted into two SiO2 composites bearing BET surface areas of 163.3 and 254.7 m2 g−1 for the pyrolyzed intrinsic and B-assisted Si complexes, respectively. The transesterification methodology merely involving alcoholysis but without any hydrolysis side reaction is designed to have generalized applicability for use in synthesizing new layered metal–organic compounds with tailored PBUs and corresponding metal oxide particles with hierarchical porosity.United States. Defense Advanced Research Projects Agency (control No. 0471-1627)National Institute for Biomedical Imaging and Bioengineering (U.S.) (award No. EB-001960)National Institutes of Health (U.S.) (NIBIB award No. EB-002026)National Science Foundation (U.S.) (Grant No. CHE-0946721

Reduced phase space formalism for spherically symmetric geometry with a massive dust shell

We perform a Hamiltonian reduction of spherically symmetric Einstein gravity with a thin dust shell of positive rest mass. Three spatial topologies are considered: Euclidean (R^3), Kruskal (S^2 x R), and the spatial topology of a diametrically identified Kruskal (RP^3 - {a point at infinity}). For the Kruskal and RP^3 topologies the reduced phase space is four-dimensional, with one canonical pair associated with the shell and the other with the geometry; the latter pair disappears if one prescribes the value of the Schwarzschild mass at an asymptopia or at a throat. For the Euclidean topology the reduced phase space is necessarily two-dimensional, with only the canonical pair associated with the shell surviving. A time-reparametrization on a two-dimensional phase space is introduced and used to bring the shell Hamiltonians to a simpler (and known) form associated with the proper time of the shell. An alternative reparametrization yields a square-root Hamiltonian that generalizes the Hamiltonian of a test shell in Minkowski space with respect to Minkowski time. Quantization is briefly discussed. The discrete mass spectrum that characterizes natural minisuperspace quantizations of vacuum wormholes and RP^3-geons appears to persist as the geometrical part of the mass spectrum when the additional matter degree of freedom is added.Comment: 36 pages, REVTeX v3.1 with amsfonts. (References updated; minor typos corrected.