Table of contents

We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example, we give the gauge-invariant definition of the second-order curvature perturbation on uniform density hypersurfaces. Using only the energy conservation equation, we show that this curvature perturbation is conserved at second order on large scales for adiabatic perturbations.

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar–Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.

We show that a singularity can occur at a finite future time in an expanding Friedmann universe even when ρ > 0 and ρ + 3p > 0. Explicit examples are constructed and a simple condition is given which can be used to eliminate behaviour of this sort if it is judged to be unphysical.

Einstein's general theory of relativity predicts that an initially plane wavefront will curve because of gravity. This effect can now be measured using very long baseline interferometry (VLBI). A wavefront from a distant point source will curve as it passes the gravitational field of the Sun. We describe an idealized experiment to directly measure this curvature, using four VLBI stations on the Earth, separated by intercontinental distances. Expressed as a time delay, the size of the effect is a few hundred picoseconds and may be measurable with present technology.

The inflationary attractor properties of the canonical scalar field and Born–Infeld field are investigated in the Randall–Sundrum II scenario with a Gauss–Bonnet term in the bulk action. We find that the inflationary attractor property will always hold for both the canonical and Born–Infeld fields for any allowed non-negative Gauss–Bonnet coupling. We also briefly discuss the possibility of explaining the suppressed lower multiples and running a scalar spectral index simultaneously in the scenario of Gauss–Bonnet brane inflation.

We present and describe an exact solution of Einstein's equations which represents a snapping cosmic string in a vacuum background with a cosmological constant Λ. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of Λ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson–Trautman waves. It is also derived as a limit of the C-metric with Λ, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.

To every axi-symmetric isolated horizon we associate two sets of numbers, M_n and J_n with n = 0, 1, 2, ..., representing its mass and angular momentum multipoles. They provide a diffeomorphism invariant characterization of the horizon geometry. Physically, they can be thought of as the 'source multipoles' of black holes in equilibrium. These structures have a variety of potential applications ranging from equations of motion of black holes and numerical relativity to quantum gravity.

Gauge fields of mixed symmetry, corresponding to arbitrary representations of the local Lorentz group of the background spacetime, arise as massive modes in compactifications of superstring theories. We describe bosonic gauge field theories on constant curvature spaces whose fields are in irreducible representations of the general linear group corresponding to Young tableaux with two columns. The gauge-invariant actions for such fields are given and generally require the use of auxiliary fields and additional mass-like terms. We examine these theories in various (partially) massless regimes in which each of the mass-like parameters vanishes. We also make some comments about how the structure extends for gauge fields corresponding to arbitrary Young tableaux.

The Hawking radiation temperature and the entropy of a radiating rotating charged black hole are calculated by employing the method of tortoise coordinate transformation and the improved brick-wall model. A new tortoise coordinate transformation is introduced which simplifies the cut-off factor and more satisfying results are obtained. The results show that the temperature of the event horizon depends on time and angle, and the entropy of a non-stationary black hole is exactly proportional to its horizon area as in the case of a stationary black hole.

Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be 'predictive', in the sense that once some a priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a 'retrodictive' approach might usefully take observational data concerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk and snap—the second, third and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak, and are likely to remain weak for the foreseeable future.

It is shown that the field equations derived from an effective interaction Hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states) are Lorentz invariant. To derive this result, which is in agreement with the observational evidence, we use the geometrical properties of the electromagnetic field.

Recently, a scale invariant theory was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace—the space of all Riemannian 3-metrics modulo diffeomorphisms—to conformal superspace—the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. However, despite numerous attractive features, the theory suffers from at least one major problem: the volume of the universe is no longer a dynamical variable. In attempting to resolve this problem a new theory is found which has several surprising and attractive features from both quantization and cosmological perspectives. Furthermore, it is an extremely restrictive theory and thus may provide testable predictions quickly and easily. One particularly interesting feature of the theory is the resolution of the cosmological constant problem.

We consider the possibility that the UV completeness of a fundamental theory is achieved by a modification of propagators at large momenta. We assume that general covariance is preserved at all energies, and focus on the coupling of a scalar field to the background geometry as an example. Naively, one expects that the gravitational interaction, like Yukawa interactions, will be regularized by a propagator which decays to zero sufficiently fast above some cut-off scale, but we show that in order to avoid the ultraviolet divergence, the propagator should approach a nonzero constant. This incompatibility between the regularizations of gravitational and Yukawa interactions suggests that a symmetry of the particle spectrum is needed for a UV-complete fundamental theory.

Classically, the dynamics of a scalar field in a non-globally hyperbolic spacetime is ill-posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second-order operator acting on a Hilbert space defined on static slices. The present work extends this result by giving a similar prescription for defining dynamics in stationary spacetimes obeying certain mild assumptions. The prescription is defined in terms of a first-order operator acting on a different Hilbert space from that used in the static prescription. It preserves the important properties of the earlier prescription: the formal solution agrees with the Cauchy evolution within the domain of dependence, and smooth data of compact support always give rise to smooth solutions. In the static case, the first-order formalism agrees with the second-order formalism (using specifically the Friedrichs extension). Applications to field quantization are also discussed.

We consider a dynamical braneworld in a six-dimensional spacetime containing a singularity. Using the Israel conditions we study the motion of a 4-brane embedded in this setup. We analyse the brane behaviour when its position is perturbed about a fixed point and solve the full nonlinear dynamics in several possible scenarios. We also investigate possible gravitational shortcuts and calculate the delay between graviton and photon signals and the ratio of the corresponding subtended horizons.

We consider charged black holes within dilaton gravity with exponential-linear dependence of action coefficients on dilaton and minimal coupling to quantum scalar fields. This includes, in particular, CGHS and RST black holes in the uncharged limit. For non-extremal configuration quantum correction to the total mass, Hawking temperature, electric potential and metric are found explicitly and shown to obey the first generalized law. We also demonstrate that quantum-corrected extremal black holes in these theories do exist and correspond to the classically forbidden region of parameters in the sense that the total mass M_tot < Q (Q is a charge). We show that in the limit T_H → 0 (where T_H is the Hawking temperature) the mass and geometry of the non-extremal configuration go smoothly to those of the extremal one, except from the narrow near-horizon region. In the vicinity of the horizon the quantum-corrected geometry (however small quantum the coupling parameter κ would be) of a non-extremal configuration does not tend to the quantum-corrected extremal one but to the special branch of solutions with the constant dilaton (2D analogue of the Bertotti–Robinson metric) instead. Meanwhile, if κ = 0 exactly, the near-extremal configuration tends to the extremal one. We also consider the dilaton theory which corresponds classically to the spherically symmetrical reduction from the 4D case and show that for the quantum-corrected extremal black hole M_tot > Q.

In this work, we study the magnitude–redshift relation of a non-standard cosmological model. The model under consideration was first investigated within a special case of metric-affine gravity (MAG) and was recently recovered via different approaches by two other groups. Apart from the usual cosmological parameters for pressureless matter Ω_m, cosmological constant/dark energy Ω_λ and radiation Ω_r a new density parameter Ω_ψ emerges. The field equations of the model reduce to a system which is effectively given by the usual Friedmann equations of general relativity, supplied by a correction to the energy density and pressure in the form of Ω_ψ, which is related to the non-Riemannian structure of the underlying spacetime. We search for the best-fit parameters using recent SN Ia data sets and constrain the possible contribution of a new dark-energy-like component at low redshifts, thereby putting an upper limit on the presence of non-Riemannian quantities in the late stages of the universe. In addition, the impact of placing the data in redshift bins of variable size is studied. The numerical results of this work also apply to several anisotropic cosmological models which, on the level of the field equations, exhibit a similar scaling behaviour of the density parameters like our non-Riemannian model.

The exact double-Kerr solution of Kramer and Neugebauer is analysed by expanding it in powers of the masses m₁, m₂. For general values of the parameters the solution contains NUT sources and therefore is not flat at spatial infinity. These do not occur (or can be removed) in two special cases: (I) if a₁/m₁ = a₂/m₂, where a₁, a₂ are the angular momenta per unit mass; (II) if a₁ + a₂ = 0. In case (I) there is present, in addition to the two spinning objects, a massless spinning rod of finite length. The spacetime in this case contains closed timelike curves (CTC) even though the sources are realistic and lie in a compact region. We conclude that, in the absence of an explanation of CTC, general relativity does not give a satisfactory account of this physical system.

N = (1, 0) supergravity in six dimensions admits AdS₃ × S³ as a vacuum solution. We extend our recent results presented in Lü et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang–Mills–Chern–Simons supergravity in D = 3, up to quartic fermion terms, by S³ group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang–Mills kinetic terms as well as topological Chern–Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS₃ as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.

Holographic considerations are used in the scrutiny of a special class of braneworld cosmologies. Inherent to this class, the brane typically bounces, at a finite size, as a consequence of a charged black hole in the bulk. Whereas a prior treatment Medved A J M (2003 J. High Energy Phys. JHEP05(2003)008 (Preprint hep-th/0301010)) emphasized a brane that is void of standard-model matter, the analysis is now extended to include an intrinsic (radiation-dominated) matter source. An interesting feature of this generalized model is that a bounce is no longer guaranteed but, rather, depends on the initial conditions. Ultimately, we demonstrate that compliance with an appropriate holographic bound is a sufficient pre-requisite for a bounce to occur.

A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. The results are then confirmed using the so-called dwell time definition of quantum tunnelling. I conclude with some remarks about the strong equivalence principle in quantum mechanics.