A non-singular black hole model as a possible end-product of gravitational collapse

In this paper we present a non-singular black hole model as a possible end-product of gravitational collapse. The depicted spacetime which is type [II,(II)], by Petrov classification, is an exact solution of the Einstein equations and contains two horizons. The equation of state in the radial direction, is a well-behaved function of the density and smoothly reproduces vacuum-like behavior near r=0 while tending to a polytrope at larger r, low density, values. The final equilibrium configuration comprises of a de Sitter-like inner core surrounded by a family of 2-surfaces of matter fields with variable equation of state. The fields are all concentrated in the vicinity of the radial center r=0. The solution depicts a spacetime that is asymptotically Schwarzschild at large r, while it becomes de Sitter-like for vanishing r. Possible physical interpretations of the macro-state of the black hole interior in the model are offered. We find that the possible state admits two equally viable interpretations, namely either a quintessential intermediary region or a phase transition in which a two-fluid system is in both dynamic and thermodynamic equilibrium. We estimate the ratio of pure matter present to the total energy and in both (interpretations) cases find it to be virtually the same, being 0.83. Finally, the well-behaved dependence of the density and pressure on the radial coordinate provides some insight on dealing with the information loss paradox.Comment: 12 Pages, 1 figure. Accepted for publication in Phys. Rev.

The K-Server Dual and Loose Competitiveness for Paging

This paper has two results. The first is based on the surprising observation that the well-known ``least-recently-used'' paging algorithm and the ``balance'' algorithm for weighted caching are linear-programming primal-dual algorithms. This observation leads to a strategy (called ``Greedy-Dual'') that generalizes them both and has an optimal performance guarantee for weighted caching. For the second result, the paper presents empirical studies of paging algorithms, documenting that in practice, on ``typical'' cache sizes and sequences, the performance of paging strategies are much better than their worst-case analyses in the standard model suggest. The paper then presents theoretical results that support and explain this. For example: on any input sequence, with almost all cache sizes, either the performance guarantee of least-recently-used is O(log k) or the fault rate (in an absolute sense) is insignificant. Both of these results are strengthened and generalized in``On-line File Caching'' (1998).Comment: conference version: "On-Line Caching as Cache Size Varies", SODA (1991

Hansenula polymorpha NMR2 and NMR4, two new loci involved in nitrogen metabolite repression

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Radiation reaction and the self-force for a point mass in general relativity

A point particle of mass m moving on a geodesic creates a perturbation h, of the spacetime metric g, that diverges at the particle. Simple expressions are given for the singular m/r part of h and its quadrupole distortion caused by the spacetime. Subtracting these from h leaves a remainder h^R that is C^1. The self-force on the particle from its own gravitational field corrects the worldline at O(m) to be a geodesic of g+h^R. For the case that the particle is a small non-rotating black hole, an approximate solution to the Einstein equations is given with error of O(m^2) as m approaches 0.Comment: 4 pages, RevTe

An approximate binary-black-hole metric

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric is presented in a single coordinate system valid up to the apparent horizons of the black holes. This metric could be useful in numerical simulations of binary black holes. Initial data extracted from this metric have the advantages of being linked to the early inspiral phase of the binary system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.

Retarded coordinates based at a world line, and the motion of a small black hole in an external universe

In the first part of this article I present a system of retarded coordinates based at an arbitrary world line of an arbitrary curved spacetime. The retarded-time coordinate labels forward light cones that are centered on the world line, the radial coordinate is an affine parameter on the null generators of these light cones, and the angular coordinates are constant on each of these generators. The spacetime metric in the retarded coordinates is displayed as an expansion in powers of the radial coordinate and expressed in terms of the world line's acceleration vector and the spacetime's Riemann tensor evaluated at the world line. The formalism is illustrated in two examples, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer in circular motion in the Schwarzschild spacetime. The main application of the formalism is presented in the second part of the article, in which I consider the motion of a small black hole in an empty external universe. I use the retarded coordinates to construct the metric of the small black hole perturbed by the tidal field of the external universe, and the metric of the external universe perturbed by the presence of the black hole. Matching these metrics produces the MiSaTaQuWa equations of motion for the small black hole.Comment: 20 pages, revtex4, 2 figure

Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation

The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in the time domain within the framework of black-hole perturbation theory. Two such prescriptions are presented. The first is based on the Teukolsky equation and it applies to general (rotating) black holes. The second is based on the Regge-Wheeler and Zerilli equations and it applies to nonrotating black holes. The second objective of this work is to apply the time-domain absorption formalisms to situations in which the black hole is either small or slowly moving. In the context of this small-hole/slow-motion approximation, the equations of black-hole perturbation theory can be solved analytically, and explicit expressions can be obtained for the absorption of mass and angular momentum. The changes in the black-hole parameters can then be understood in terms of an interaction between the tidal gravitational fields supplied by the external universe and the hole's tidally-induced mass and current quadrupole moments. For a nonrotating black hole the quadrupole moments are proportional to the rate of change of the tidal fields on the hole's world line. For a rotating black hole they are proportional to the tidal fields themselves.Comment: 36 pages, revtex4, no figures, final published versio

Factoring by electronic mail

Describes a distributed implementation of two factoring algorithms, the elliptic curve method (ECM) and the multiple polynomial quadratic sieve algorithm (MPQS). The authors' ECM-implementation on a network of DEC MicroVAX processors has factored several numbers from the Cunningham project. The authors have also implemented the multiple polynomial quadratic sieve algorithm on the same network. On this network alone, they are now able to factor any 100 digit integer, or to find 35 digit factors of numbers up to 150 digits long within one month. To allow an even wider distribution of their programs they made use of electronic mail networks for the distribution of the programs and for inter-processor communication. Even during the initial stage of this experiment, machines all over the United States and at various places in Europe and Australia contributed 15 percent of the total factorization effort. At all the sites where the program is running, the authors only use cycles that would otherwise have been idle. This shows that the enormous computational task of factoring 100 digit integers with the current algorithms can be completed almost for free. Since they use a negligible fraction of the idle cycles of all the machines on the worldwide electronic mail networks, the authors could factor 100 digit integers within a few days with a little more hel