Table of contents

This review is concerned with the motion of a point scalar charge, a point electric charge and a point mass in a specified background spacetime. In each of these three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone, the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular behaviour: the field diverges at the position of the particle. But Detweiler and Whiting have given a prescription to unambiguously isolate the field's singular part; their singular field obeys the same wave equation as the original field and it can be shown not to exert a force on the particle. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors and some of its applications. It continues with a thorough discussion of Green's functions in curved spacetime. It concludes with a detailed derivation of each of the three equations of motion.

We study the question of whether the linearization of the Kodama state around classical de Sitter spacetime is normalizable in the inner product of the theory of linearized gravitons on de Sitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann–Lemaître–Robertson–Walker (FLRW) models. We discuss 'vacuum bubbles' and closed–open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

We examine in the context of general relativity the dynamics of a spatially flat Robertson–Walker universe filled with a classical minimally coupled scalar field ϕ of exponential potential V(ϕ) ∼ exp(−μϕ) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for Ω_ϕ(w_ϕ) or q(w_ϕ), providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system for any value of μ, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints Ω_m0 ≈ 0.25 − 0.3, −1 ⩽ w_ϕ0 ⩽ −0.6, provides, independently of initial conditions and other parameters, the necessary condition , while the less conservative constraint −1 ⩽ w_ϕ ⩽ −0.93 gives . Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_ϕ ≈ −1, the general relation Ω_ϕ(w_ϕ) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (w_ϕ, Ω_ϕ) or (w_ϕ, q) is also derived.

We present the results of quality factor measurements for rod samples made of fused silica. To decrease the dissipation, we annealed our samples. The highest quality factor that we observed was Q = (2.03 ± 0.01) × 10⁸ for a mode at 384 Hz. This is the highest published value of Q in fused silica measured to date.

The massless field perturbations of the accelerating Minkowski and Schwarzschild spacetimes are studied. The results are extended to the propagation of the Proca field in Rindler spacetime. We examine critically the possibility of existence of a general spin–acceleration coupling in complete analogy with the well-known spin–rotation coupling. We argue that such a direct coupling between spin and linear acceleration does not exist.

We propose a state in loop quantum gravity theory with zero cosmological constant such that it could be associated with the flat spacetime vacuum solution. This state is constructed by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum general relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin-foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad representation, by defining the corresponding spin network functional integrals as SU(2) quantum group state sums.

We investigate the binding energy in two classes of polytropic perfect fluids. A general-relativistic bound from below is derived in the case of a static compact body, having the same form as in the Newtonian limit. It is shown that the positivity of the binding energy implies that the (properly defined) average speed of sound is smaller than the escape velocity. A necessary condition for the negative binding energy, stating that the maximal speed of sound is close to the escape velocity, is found in a class of fluids.

In this paper we report some results on the expectation values of a set of observables introduced for three-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev–Viro model. Instead of giving a formal description of the observables, we just formulate the paper by examples. This means that we just show how an idea works with particular cases and give a way to compute 'expectation values' in general by a topological procedure.

A class of Stephani cosmological models as a prototype of a non-homogeneous universe is considered. The non-homogeneity can lead to accelerated evolution, which is now observed from the SNe Ia data. Three samples of type Ia supernovae obtained by Perlmutter et al, Tonry et al and Knop et al are taken into account. Different statistical methods (best fits as well as maximum likelihood method) to obtain estimation for the model parameters are used. The Stephani model is considered as an alternative to the ΛCDM model in the explanation of the present acceleration of the universe. The model explains the acceleration of the universe at the same level of accuracy as the ΛCDM model (χ² statistics are comparable). From the best fit analysis it follows that the Stephani model is characterized by a higher value of density parameter Ω_m0 than the ΛCDM model. It is also shown that the model is consistent with the location of CMB peaks.

This paper proposes to study quasi-normal modes due to massive scalar fields. We, in particular, investigate the dependence of quasi-normal mode (QNM) frequencies on the field mass. From this research, we find that there are quasi-normal modes with arbitrarily long life when the field mass has specific values. It is also found that QNM may disappear when the field mass exceeds these values.

We find explicit solutions of type IIB string theory on corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of super Yang–Mills.

An adaptive mesh refinement scheme is implemented in a distributed environment using message passing interface to find solutions to the nonlinear sigma model. In a previous work, I studied the behaviour similar to black hole critical phenomena at the threshold for singularity formation in this flat-space model. The present study is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.