A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.

In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild–de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild–de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity—the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild–de Sitter space-time, we apply the method of complex paths to three different coordinate systems—spherically symmetric, Painlevé, and Lemaître. We show that the equilibrium temperature in Schwarzschild–de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild–de Sitter space-time satisfies the D-bound conjecture.

We prove the uniqueness theorem for a static higher dimensional charged black hole spacetime containing an asymptotically flat spacelike hypersurface with a compact interior and with both degenerate and nondegenerate components of the event horizon.

We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension $5<~d<~9.$ We prove that all the Bohm metrics on $S^3\times S^2$ and $S^3\times S^3$ have negative eigenvalue modes of the Lichnerowicz operator acting on transverse traceless symmetric tensors, and by numerical methods we establish that Bohm metrics on $S^5$ have negative eigenvalues too. General arguments suggest that all the Bohm metrics will have negative Lichnerowicz modes. These results imply that generalized higher-dimensional black-hole spacetimes, in which the Bohm metric replaces the usual round sphere metric, are classically unstable. We also show that the classical stability criterion for Freund-Rubin solutions, which are products of Einstein metrics with anti–de Sitter spacetimes, is the same in all dimensions as that for black-hole stability, and hence such solutions based on the Bohm metrics will also be unstable. We consider possible end points of the instabilities, and in particular we show that all Einstein-Sasaki manifolds give stable solutions. Next, we show how analytic continuation of Bohm metrics gives Lorentzian metrics that provide counterexamples to a strict form of the cosmic baldness conjecture, but they are nevertheless consistent with the intuition behind the cosmic no-hair conjectures. We indicate how these Lorentzian metrics may be created “from nothing” in a no-boundary setting. We argue that Lorentzian Bohm metrics are unstable to decay to de Sitter spacetime. Finally, we argue that noncompact versions of the Bohm metrics have infinitely many negative Lichnerowicz modes, and we conjecture a general relationship between Lichnerowicz eigenvalues and nonuniqueness of the Dirichlet problem for Einstein’s equations.

Numerical relativity has faced the problem that standard 3+1 simulations of black hole spacetimes without singularity excision and with singularity avoiding lapse and vanishing shift fail early on due to the so-called slice stretching. We discuss lapse and shift conditions for the nonexcision case that effectively cure slice stretching and allow run times of $1000M$ and more.

We derive the low energy effective theory for a two branes system solving the bulk geometry formally in the covariant curvature formalism developed by Shiromizu, Maeda, and Sasaki. As expected, the effective theory looks like an Einstein-scalar system. Using this theory we can discuss the cosmology and nonlinear gravity at low energy scales.

We calculate analytically and numerically the production of superheavy dark matter (scalar field $X)$ when it is coupled to the inflaton field $\phi$ within the context of a slow-roll $m_{\phi }^2{\phi }^2/2\mathrm{}$ inflationary model with coupling $g^2{X}^2{\phi }^2/2.\mathrm{}$ We find that X particles with a mass as large as ${1000H}_i,$ where $H_i$ is the value of the Hubble expansion rate at the end of inflation, can be produced in sufficient abundance to be cosmologically significant today. This means that superheavy dark matter may have a mass of up to ${10}^{-3}{M}_{\mathrm{Pl}}.$ We also derive a simple formula that can be used to estimate particle production as a result of a quantum field’s interaction with a general class of homogeneous classical fields. Finally, we note that the combined effect of the inflaton field and the gravitational field on the X field causes the production to be a nonmonotonic function of $g^2.$

We show that a suitable interaction between a scalar field and a matter fluid in a spatially homogeneous and isotropic spacetime can drive the transition from a matter dominated era to an accelerated expansion phase and simultaneously solve the coincidence problem of our present Universe. For this purpose we study the evolution of the energy density ratio of these two components. We demonstrate that a stationary attractor solution is compatible with an accelerated expansion of the Universe. We extend this study to account for dissipation effects due to interactions in the dark matter fluid. Finally, type Ia supernovae and primordial nucleosynthesis data are used to constrain the parameters of the model.

A new method for predicting inflationary cosmological perturbations, based on the Wentzel-Kramers-Brillouin (WKB) approximation, is presented. A general expression for the WKB scalar and tensor power spectra is derived. The main advantage of the new scheme of approximation is that it is valid even if the slow-roll conditions are violated. The method is applied to power-law inflation, which allows a comparison with an exact result. It is demonstrated that the WKB approximation predicts the spectral indices exactly and the amplitude with an error lower than 10%, even in regimes far from scale invariance. The new method of approximation is also applied to a situation where the slow-roll conditions hold. It is shown that the result obtained bears close resemblance with the standard slow-roll calculation. Finally, some possible improvements are briefly mentioned.

The recent measurements of the power spectrum of cosmic microwave background anisotropies are consistent with the simplest inflationary scenario and big bang nucleosynthesis constraints. However, these results rely on the assumption of a class of models based on primordial adiabatic perturbations, cold dark matter and a cosmological constant. In this paper we investigate the need for deviations from the $\Lambda$-CDM scenario by first characterizing the spectrum using a phenomenological function in a $15$ dimensional parameter space. Using a Monte Carlo Markov chain approach to Bayesian inference and a low curvature model template we then check for the presence of new physics and/or systematics in the CMB data. We find an almost perfect consistency between the phenomenological fits and the standard $\Lambda$-CDM models. The curvature of the secondary peaks is weakly constrained by the present data, but they are well located. The improved spectral resolution expected from future satellite experiments is warranted for a definitive test of the scenario.

The asymptotic properties of the Bianchi type II cosmological model in the brane-world scenario are investigated. The matter content is assumed to be a combination of a perfect fluid and a minimally coupled scalar field that is restricted to the brane. The isotropic brane-world solution is determined to represent the initial singularity in all brane-world cosmologies. Additionally, it is shown that it is the kinetic energy of the scalar field which dominates the initial dynamics in these brane-world cosmologies. It is important to note that the dynamics of these brane-world cosmologies is not necessarily asymptotic to general relativistic cosmologies to the future in the case of a zero four-dimensional cosmological constant.

We study the cosmological evolution of a scalar field that couples to the trace ${T=T}_a^a$ of the energy momentum tensor of all the fields (including itself). In the case of a shallow exponential potential, the presence of coupling to the trace T in the field equation makes the energy density of the scalar field decrease faster, thereby hastening the commencement of radiation domination. This effect gradually diminishes at later epochs, allowing the scalar field to dominate the energy density again. We interpret this phase as the current epoch of cosmic acceleration with ${\Omega }_{\phi }=\mathrm{0.7.}\mathrm{}$ A variant of this model can lead to accelerated expansion at the present epoch, followed by an $a\left(t\right)\mathrm{}\propto t^{2/3}$ behavior as $\overrightarrow{t}\infty ,$ making the model free from a future event horizon. The main features of the model are independent of initial conditions. However, fine-tuning of parameters is necessary for viable evolution.

We have earlier shown that cosmic strings moving through the plasma at the time of a first order quark-hadron transition in the early universe can generate large scale baryon inhomogeneities. In this paper, we calculate detailed structure of these inhomogeneities at the quark-hadron transition. Our calculations show that the inhomogeneities generated by cosmic string wakes can strongly affect nucleosynthesis calculations. A comparison with observational data suggests that such baryon inhomogeneities should not have existed at the nucleosynthesis epoch. If this disagreement holds with more accurate observations, then it will lead to the conclusions that cosmic string formation scales above ${10}^{14}–{10}^{15}$ GeV may not be consistent with nucleosynthesis and CMBR observations. Alternatively, some other input in our calculation should be constrained, for example, if the average string velocity remains sufficiently small so that significant density perturbations are never produced at the QCD scale, or if strings move ultrarelativistically so that string wakes are very thin, trapping negligible amount of baryons. Finally, if the quark-hadron transition is not of first order then our calculations do not apply.

Gravitational lensing of the microwave background by the intervening dark matter mainly arises from large-angle fluctuations in the projected gravitational potential and hence offers a unique opportunity to study the physics of the dark sector at large scales. Studies with surveys that cover greater than a percent of the sky will require techniques that incorporate the curvature of the sky. We lay the groundwork for these studies by deriving the full sky minimum variance quadratic estimators of the lensing potential from the CMB temperature and polarization fields. We also present a general technique for constructing these estimators, with harmonic space convolutions replaced by real space products, that is appropriate for both the full sky limit and the flat sky approximation. This also extends previous treatments to include estimators involving the temperature-polarization cross-correlation and should be useful for next generation experiments in which most of the additional information from polarization comes from this channel due to sensitivity limitations.

The first scientific runs of kilometer scale laser interferometric detectors such as LIGO are under way. Data from these detectors will be used to look for signatures of gravitational waves from astrophysical objects such as inspiraling neutron-star–black-hole binaries using matched filtering. The computational resources required for online flat-search implementation of the matched filtering are large if searches are carried out for a small total mass. A flat search is implemented by constructing a single discrete grid of densely populated template waveforms spanning the dynamical parameters—masses, spins—which are correlated with the interferometer data. The correlations over the kinematical parameters can be maximized a prioriwithout constructing a template bank over them. Mohanty and Dhurandhar showed that a significant reduction in computational resources can be accomplished by using a hierarchy of such template banks where candidate events triggered by a sparsely populated grid are followed up by the regular, dense flat-search grid. The estimated speedup in this method was a factor $\sim 25$ over the flat search. In this paper we report an improved implementation of the hierarchical search, wherein we extend the domain of hierarchy to an extra dimension—namely, the time of arrival of the signal in the bandwidth of the interferometer. This is accomplished by lowering the Nyquist sampling rate of the signal in the trigger stage. We show that this leads to further improvement in the efficiency of data analysis and speeds up the online computation by a factor of $\sim 65–70$ over the flat search. We also take into account and discuss issues related to template placement, trigger thresholds, and other peculiar problems that do not arise in earlier implementation schemes of the hierarchical search. We present simulation results for 2PN waveforms embedded in the noise expected for initial LIGO detectors.

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant $hiss,$ and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Recent studies of the ultraviolet behavior of pure gravity suggest that it admits a non-Gaussian attractive fixed point, and therefore that the theory is asymptotically safe. We consider the effect on this fixed point of massless minimally coupled matter fields. The existence of a UV attractive fixed point puts bounds on the type and number of such fields.

A phenomenological description of diffractive dijet hadroproduction via double Pomeron exchange is presented. This description is based on a modified version of the Ingelman-Schlein model which includes the evolution of the Pomeron structure function and corrections regarding rapidity gap suppression effects. The same quark-dominant Pomeron structure function employed in a previous report to describe diffractive dijet and W production via single Pomeron processes is shown here to yield results consistent with the available data for double Pomeron processes as well.

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics (QQED) at finite temperature in the bare vertex approximation, using Schwinger-Dyson equations (SDE’s). Motivated by perturbation theory, a further simplification is introduced by taking the wave function renormalization to be unity. In the zeroth mode approximation, the SDE for the fermion propagator resembles QED in 2+1 dimensions $\left({\mathrm{QED}}_3\right)$ at zero temperature with an effective dimensionful coupling ${\alpha }^{\prime }=\alpha T.\mathrm{}$ For a fixed temperature, the mass is dynamically generated above a certain critical value of this coupling. As expected, raising the temperature restores chiral symmetry and fermions become massless again. We also argue that by summing over the frequency modes and under suitable simplifications, qualitative aspects of the result do not undergo significant changes.

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways: namely, the light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite-volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.