The Rotating Quantum Thermal Distribution

We show that the rigidly rotating quantum thermal distribution on flat space-time suffers from a global pathology which can be cured by introducing a cylindrical mirror if and only if it has a radius smaller than that of the speed-of-light cylinder. When this condition is met, we demonstrate numerically that the renormalized expectation value of the energy-momentum stress tensor corresponds to a rigidly rotating thermal bath up to a finite correction except on the mirror where there are the usual Casimir divergences.Comment: 8 pages, 2 PostScript figure

Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String

We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added the calculation of the stress tensor. 28 pages, 7 figure

Detection of Anisotropies in the Gravitational-Wave Stochastic Background

By correlating the signals from a pair of gravitational-wave detectors, one can undertake sensitive searches for a stochastic background of gravitational radiation. If the stochastic background is anisotropic, then this correlated signal varies harmonically with the earth's rotation. We calculate how the harmonics of this varying signal are related to the multipole moments which characterize the anisotropy, and give a formula for the signal-to-noise ratio of a given harmonic. The specific case of the two LIGO (Laser Interferometric Gravitational Observatory) detectors, which will begin operation around the year 2000, is analyzed in detail. We consider two possible examples of anisotropy. If the gravitational-wave stochastic background contains a dipole intensity anisotropy whose origin (like that of the Cosmic Background Radiation) is motion of our local system, then that anisotropy will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if \Omega_{gw} > 5.3 \times 10^{-8} h_{100}^{-2}. We also study the signal produced by stochastic sources distributed in the same way as the luminous matter in the galactic disk, and in the same way as the galactic halo. The anisotropy due to sources distributed as the galactic disk or as the galactic halo will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if \Omega_{gw} > 1.8 \times 10^{-10} h_{100}^{-2} or \Omega_{gw} > 6.7 \times 10^{-8} h_{100}^{-2}, respectively.Comment: 25 pages, Latex with RevTeX and epsfig, now includes S/N ratio calculations, expected response from anisotropy due to local motion & sources in galax

Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops

Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.Comment: 15 pages, RevTex 3.0, 7 figures available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-1

Diffusion in Curved Spacetimes

Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and therefore provides a microscopic justification for his phenomenological heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of the mean square displacement of Brownian motion in static spacetimes. Beyond general relativity itself, this result has potential applications in analogue gravitational systems.Comment: 14 pages, substantially revised versio

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

Quantum corrections to critical phenomena in gravitational collapse

We investigate conformally coupled quantum matter fields on spherically symmetric, continuously self-similar backgrounds. By exploiting the symmetry associated with the self-similarity the general structure of the renormalized quantum stress-energy tensor can be derived. As an immediate application we consider a combination of classical, and quantum perturbations about exactly critical collapse. Generalizing the standard argument which explains the scaling law for black hole mass, $M \propto |\eta-\eta^*|^\beta$, we demonstrate the existence of a quantum mass gap when the classical critical exponent satisfies $\beta \geq 0.5$. When $\beta < 0.5$ our argument is inconclusive; the semi-classical approximation breaks down in the spacetime region of interest.Comment: RevTeX, 6 pages, 3 figures included using psfi

Effective source approach to self-force calculations

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG special issue - 22 pages, 8 figure

Black hole determinants and quasinormal modes

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde

How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.Comment: 30 pages, 1 figure. v3: Added references and minor clarification