A momentum-space representation of Green's functions with modified dispersion on ultra-static space-time

We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series representation of the Green's functions is doomed to failure, because of higher order spatial derivatives in the Klein-Gordon operator. We show how to overcome this difficulty by considering a preferred frame, associated to a unit time-like vector. With respect to this frame, we can express the Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, as a series with geometric coefficients similar to the deWitt-Schwinger's ones. By integrating over all frequencies, we finally find the expansion of the Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed.Comment: revtex, version accepted for publication in Phys. Rev.

Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling

Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired accuracy requires calculation of the second-order gravitational perturbations produced by the compact object. At the point particle limit the second-order gravitational perturbation equations turn out to have highly singular source terms, for which the standard retarded solutions diverge. Here we study a simplified scalar toy-model in which a point particle induces a nonlinear scalar field in a given curved spacetime. The corresponding second-order scalar perturbation equation in this model is found to have a similar singular source term, and therefore its standard retarded solutions diverge. We develop a regularization method for constructing well-defined causal solutions for this equation. Notably these solutions differ from the standard retarded solutions, which are ill-defined in this case.Comment: 14 page

Nonsingular Black Hole Evaporation and ``Stable'' Remnants

We examine the evaporation of two--dimensional black holes, the classical space--times of which are extended geometries, like for example the two--dimensional section of the extremal Reissner--Nordstrom black hole. We find that the evaporation in two particular models proceeds to a stable end--point. This should represent the generic behavior of a certain class of two--dimensional dilaton--gravity models. There are two distinct regimes depending on whether the back--reaction is weak or strong in a certain sense. When the back--reaction is weak, evaporation proceeds via an adiabatic evolution, whereas for strong back--reaction, the decay proceeds in a somewhat surprising manner. Although information loss is inevitable in these models at the semi--classical level, it is rather benign, in that the information is stored in another asymptotic region.Comment: 23 pages, 6 figures, harvmac and epsf, RU-93-12, PUPT-1399, NSF-ITP-93-5

Band-aid for information loss from black holes

We summarize, simplify and extend recent work showing that small deviations from exact thermality in Hawking radiation, first uncovered by Kraus and Wilczek, have the capacity to carry off the maximum information content of a black hole. This goes a considerable way toward resolving a long-standing "information-loss paradox"

Ultrastable lasers based on vibration insensitive cavities

We present two ultra-stable lasers based on two vibration insensitive cavity designs, one with vertical optical axis geometry, the other horizontal. Ultra-stable cavities are constructed with fused silica mirror substrates, shown to decrease the thermal noise limit, in order to improve the frequency stability over previous designs. Vibration sensitivity components measured are equal to or better than 1.5e-11 per m.s^-2 for each spatial direction, which shows significant improvement over previous studies. We have tested the very low dependence on the position of the cavity support points, in order to establish that our designs eliminate the need for fine tuning to achieve extremely low vibration sensitivity. Relative frequency measurements show that at least one of the stabilized lasers has a stability better than 5.6e-16 at 1 second, which is the best result obtained for this length of cavity.Comment: 8 pages 12 figure

Perspective on gravitational self-force analyses

A point particle of mass $\mu$ moving on a geodesic creates a perturbation $h_{ab}$, of the spacetime metric $g_{ab}$, that diverges at the particle. Simple expressions are given for the singular $\mu/r$ part of $h_{ab}$ and its distortion caused by the spacetime. This singular part h^\SS_{ab} is described in different coordinate systems and in different gauges. Subtracting h^\SS_{ab} from $h_{ab}$ leaves a regular remainder $h^\R_{ab}$. The self-force on the particle from its own gravitational field adjusts the world line at \Or(\mu) to be a geodesic of $g_{ab}+h^\R_{ab}$; this adjustment includes all of the effects of radiation reaction. For the case that the particle is a small non-rotating black hole, we give a uniformly valid approximation to a solution of the Einstein equations, with a remainder of \Or(\mu^2) as $\mu\to0$. An example presents the actual steps involved in a self-force calculation. Gauge freedom introduces ambiguity in perturbation analysis. However, physically interesting problems avoid this ambiguity.Comment: 40 pages, to appear in a special issue of CQG on radiation reaction, contains additional references, improved notation for tensor harmonic

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure

Excited by a quantum field: Does shape matter?

The instantaneous transition rate of an arbitrarily accelerated Unruh-DeWitt particle detector on four-dimensional Minkowski space is ill defined without regularisation. We show that Schlicht's regularisation as the zero-size limit of a Lorentz-function spatial profile yields a manifestly well-defined transition rate with physically reasonable asymptotic properties. In the special case of stationary trajectories, including uniform acceleration, we recover the results that have been previously obtained by a regularisation that relies on the stationarity. Finally, we discuss evidence for the conjecture that the zero-size limit of the transition rate is independent of the detector profile.Comment: 7 pages, uses jpconf. Talk given at NEB XII (Nafplio, Greece, 29 June - 2 July 2006

Fermi Coordinates and Penrose Limits

We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant description of the expansion around the plane wave metric in terms of components of the curvature tensor of the original metric, and generalises the covariant description of the lowest order Penrose limit metric itself, obtained in hep-th/0312029. We describe in some detail the construction of null Fermi coordinates and the corresponding expansion of the metric, and then study various aspects of the higher order corrections to the Penrose limit. In particular, we observe that in general the first-order corrected metric is such that it admits a light-cone gauge description in string theory. We also establish a formal analogue of the Weyl tensor peeling theorem for the Penrose limit expansion in any dimension, and we give a simple derivation of the leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page