What is the maximum rate at which entropy of a string can increase?

According to Susskind, a string falling toward a black hole spreads exponentially over the stretched horizon due to repulsive interactions of the string bits. In this paper such a string is modeled as a self-avoiding walk and the string entropy is found. It is shown that the rate at which information/entropy contained in the string spreads is the maximum rate allowed by quantum theory. The maximum rate at which the black hole entropy can increase when a string falls into a black hole is also discussed.Comment: 11 pages, no figures; formulas (18), (20) are corrected (the quantum constant is added), a point concerning a relation between the Hawking and Hagedorn temperatures is corrected, conclusions unchanged; accepted by Physical Review D for publicatio

Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies

Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the {\it same relative} post-Newtonian order form the basis of the {\it standard adiabatic} approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new {\it complete adiabatic} approximant constructed from the energy and flux functions. At the leading order it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the {\it effectualness} at lower PN ($<$ 3PN) orders, while standard approximants of order $\geq$ 3PN provide a good lower-bound to the complete approximants for the construction of effectual templates. {\it Faithfulness} of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant. Gra

Radiative Falloff in Neutron Star Spacetimes

We systematically study late-time tails of scalar waves propagating in neutron star spacetimes. We consider uniform density neutron stars, for which the background spacetime is analytic and the compaction of the star can be varied continously between the Newtonian limit 2M/R << 1 and the relativistic Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off neutron stars of different compactions 2M/R and find that a Newtonian, an intermediate, and a highly relativistic regime can be clearly distinguished. In the highly relativistic regime, the reflected signal is dominated by quasi-periodic peaks, which originate from the wave packet bouncing back and forth between the center of the star and the maximum of the background curvature potential at R ~ 3 M. Between these peaks, the field decays according to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between the center and the maximum or the curvature potential grows without bound, so that the first peak arrives only at infinitely late time. The modes of neutron stars can therefore no longer be excited in the ultra-relativistic limit, and it is in this sense that the late-time radiative decay from neutron stars looses all its features and gives rise to power-law tails reminiscent of Schwarzschild black holes.Comment: 10 pages, 7 figures, to appear in PR

The Stretched Horizon and Black Hole Complementarity

Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution. We explain how these postulates may be implemented in a ``stretched horizon'' or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black hole complementarity is advocated. The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.Comment: (some misprints in equations have been fixed), 48 pages (including figures), SU-ITP-93-1

On the back reaction of gravitational and particle emission and absorption from straight thick cosmic strings: A toy model

The emission and absorption of gravitational waves and massless particles of an infinitely long straight cosmic string with finite thickness are studied. It is shown in a general term that the back reaction of the emission and absorption {\em always} makes the symmetry axis of the string singular. The singularity is a scalar singularity and cannot be removed.Comment: To appear in Gen. Relativ. Gra

Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.Comment: 25 pages, phyzzx, CALT-68-188

Relativistic orbits and Gravitational Waves from gravitomagnetic corrections

Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.Comment: 6 pages, 10 figures; Multifrequency Behaviour of High-Energy Cosmic Sources, Vulcano Workshop 200

Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations

We present a self-contained framework called Direct Integration of the Relaxed Einstein Equations (DIRE) for calculating equations of motion and gravitational radiation emission for isolated gravitating systems based on the post-Newtonian approximation. We cast the Einstein equations into their ``relaxed'' form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve the equations formally as a retarded integral over the past null cone of the field point (chosen to be within the near zone when calculating equations of motion, and in the far zone when calculating gravitational radiation). The ``inner'' part of this integral(within a sphere of radius $\cal R \sim$ one gravitational wavelength) is approximated in a slow-motion expansion using standard techniques; the ``outer'' part, extending over the radiation zone, is evaluated using a null integration variable. We show generally and explicitly that all contributions to the inner integrals that depend on $\cal R$ cancel corresponding terms from the outer integrals, and that the outer integrals converge at infinity, subject only to reasonable assumptions about the past behavior of the source. The method cures defects that plagued previous ``brute-force'' slow-motion approaches to motion and gravitational radiation for isolated systems. We detail the procedure for iterating the solutions in a weak-field, slow-motion approximation, and derive expressions for the near-zone field through 3.5 post-Newtonian order in terms of Poisson-like potentials.Comment: 43 pages, RevTeX, 3 figures, submitted to Physical Review

The holographic fluid dual to vacuum Einstein gravity

We present an algorithm for systematically reconstructing a solution of the (d+2)-dimensional vacuum Einstein equations from a (d+1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al in arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion which are the incompressible Navier-Stokes equations, corrected by specific higher derivative terms. The uniqueness and regularity of this solution is established to all orders and explicit results are given for the bulk metric and the stress tensor of the dual fluid through fifth order in the hydrodynamic expansion. We establish the validity of a relativistic hydrodynamic description for the dual fluid, which has the unusual property of having a vanishing equilibrium energy density. The gravitational results are used to identify transport coefficients of the dual fluid, which also obeys an interesting and exact constraint on its stress tensor. We propose novel Lagrangian models which realise key properties of the holographic fluid.Comment: 31 pages; v2: references added and minor improvements, published versio