Table of contents

The celebrated area–entropy formula for black holes has provided the most important clue in the search for the elusive theory of quantum gravity. We explore the possibility that the (linear) area–entropy relation acquires some smaller corrections. Using the Boltzmann–Einstein formula, we rule out the possibility for a power-law correction and provide severe constraints on the coefficient of a possible log-area correction. We argue that a non-zero logarithmic correction to the area–entropy relation would also imply a modification of the area–mass relation for quantum black holes.

We study the cosmological dynamics of an effective theory for a strongly coupled scalar field in the moduli space of supersymmetric Yang–Mills theory recently proposed by Silverstein and Tong, called 'D-cceleration'. We discuss various energy conditions in this theory. Then we prove the inflationary attractor property using the Hamilton–Jacobi method and study the phase portrait as well as the cosmological evolution of the scalar field.

Astrophysical sources of high frequency gravitational radiation are considered in association with a new interest in the very sensitive HFGW receivers required for the laboratory GW Hertz experiment. Special attention is paid to the phenomenon of primordial black-hole evaporation. It acts as a black body to all kinds of radiation, including gravitons, and, therefore, emits an equilibrium spectrum of gravitons during its evaporation. A limit on the density of high frequency gravitons in the universe is obtained, and the possibility of detecting them is briefly discussed.

Recent studies of the detectability of the cosmic topology of nearly flat universes have often concentrated on the range of values of Ω₀ given by current observations. Here we study the consequences of taking a range of bounds satisfying |Ω₀ − 1| ≪ 1, which include those expected from future observations such as the Planck mission, as well as those predicted by inflationary models. We show that in this limit, a generic detectable non-flat manifold is locally indistinguishable from either a cylindrical or toroidal manifold, irrespective of its global shape, with the former being more likely. Importantly, this is compatible with some recent indications of the alignment of the quadrupole and octupole moments, based on the analysis of the first year WMAP data. It also implies that in this limit an observer would not be able to distinguish topologically whether the universe is spherical, hyperbolic or flat. By severely restricting the expected topological signatures of detectable isometries, our results provide an effective theoretical framework for interpreting cosmological observations, and can be used to confine the parameter spaces which realistic search strategies, such as the 'circles in the sky' method, need to concentrate on.

The well-known 'displace, cut and reflect' method used to generate discs from given solutions of Einstein field equations is applied to the superposition of two extreme Reissner–Nordström black holes to construct discs made of charged dust and also non-axisymmetric planar distributions of charged dust on the z = 0 plane. They are symmetric with respect to two or one coordinate axes, depending on whether the black holes have equal or unequal masses, respectively. For these non-axisymmetric distributions of matter we also study the effective potential for geodesic motion of neutral test particles.

Optical activity of electromagnetic waves in a string inspired Kalb–Ramond cosmological background is studied in the presence of an extra spacetime dimension. The Kalb–Ramond-electromagnetic coupling, which originates from the gauge anomaly cancelling Chern–Simons term in a string inspired model, is explicitly calculated following the Randall–Sundrum braneworld conjecture. It is shown that the Randall–Sundrum scenario leads to an enormous enhancement of the optical rotation of a plane polarized electromagnetic wave propagating on the visible brane. The absence of any experimental support in favour of such a large rotation in astrophysical experiments on distant galactic radio waves indicates an apparent conflict between the Randall–Sundrum braneworld scenario and the presence of the Kalb–Ramond antisymmetric tensor field in the background spacetime.

We study the evolution of Bianchi-I spacetimes filled with a global unidirectional electromagnetic field F_μν interacting with a massless scalar dilatonic field according to the law Ψ(ϕ)F^μνF_μν where Ψ(ϕ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models that become isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All three features are confirmed for exact solutions found for the case usually considered, Ψ = e^2λϕ, λ = const. In particular, isotropizing models are found for . In the special case |λ| = 1, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric. In the two appendices, we discuss and compare four different isotropization criteria for arbitrary Bianchi-I spacetimes and present their regularity conditions.

We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. We show that in the canonical ensemble, the results for all statistical quantities for any spectrum can be reproduced by a heuristic picture of Bekenstein up to second order. For one of these spectra, the equally spaced spectrum, in light of a proposed connection of the black-hole area spectrum to the quasinormal mode spectrum and following Preprint hep-th/0304135, we present explicit calculations to argue that this spectrum is completely consistent with this connection. This follows without requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3). We also show that independent of the area spectrum, the degeneracy of the area observable is bounded by CAexp(A/4), where A is measured in Planck units and C is a constant of order unity.

Each spacecraft in the Laser Interferometer Space Antenna (LISA) houses a proof mass which follows a geodesic through spacetime. Disturbances which change the proof mass position, momentum and/or acceleration will appear in the LISA data stream as additive quadratic functions. These data disturbances inhibit signal extraction and must be removed. In this paper we discuss the identification and fitting of monochromatic signals in the data set in the presence of data disturbances. We also present a preliminary analysis of the extent of science result limitations with respect to the frequency of data disturbances.

We consider the motion of charges around Schwarzschild black holes when a magnetic field is present; analysis is focused on the exact solution of Maxwell equations in Schwarzschild spacetime describing dipolar fields generated by current loops around the black hole. This solution deserves particular attention, since it is suggestive of a relation with toroidal currents in accretion discs; with reference to applications of this same field solution, we point out and discuss an existing physical incoherence in past studies, and give the necessary emendation. Critical comparison with previous results is made. The circular orbit characteristics are examined in detail; two sets of solutions are found, both allowing stable circular orbits close to the event horizon, well beyond the Schwarzschild static limit at r = 6M. The existence of potential traps for highly relativistic particles within this same limit is also worth noting, since these same trapped particles may represent an effective source of synchrotron radiation.

We investigate the entropy of black holes in Gauss–Bonnet and Lovelock gravity using the Noether charge approach, in which the entropy is given as the integral of a suitable (n − 2) form charge over the event horizon. We compare the results to those obtained in other approaches. We also comment on the appearance of negative entropies in some cases, and show that there is an additive ambiguity in the definition of the entropy which can be appropriately chosen to avoid this problem.

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of general relativity. When the variation of the energy is written in a covariant form, it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so-called covariant ADM correction term. When specific boundary conditions are analysed one sees that the Komar energy is related to the gravitational heat while the ADM correction term plays the role of the Helmholtz free energy. These properties allow one to establish, inside a classical geometric framework, a formal analogy between gravitation and the laws governing the evolution of a thermodynamical system. The analogy applies to stationary spacetimes admitting multiple causal horizons as well as to AdS Taub-bolt solutions.

We study interaction of rotating higher-dimensional black holes with a brane in spacetimes with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can lose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher-dimensional black holes interacting with branes. The characteristic time when a rotating black hole with gravitational radius r₀ reaches this final stationary state is T ∼ r^p−1₀/(Gσ), where G is the higher-dimensional gravitational coupling constant, σ is the brane tension and p is the number of extra dimensions.

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel–Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

The evolution of the extra dimension is investigated in the context of braneworld cosmology. New cosmological solutions are found. In particular, solutions in the form of waves travelling along the extra dimension are identified.

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behaviour. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities.

We study the stretched membrane of a black hole as consisting of a perfect fluid. We find that the pressure of this fluid is negative and the specific heat is also negative. A surprising result is that if we are to assume the fluid to be composed of some quanta, then the dispersion relation of the fundamental quantum is E = m²/k, with m at the scale of the Planck mass. There are two possible interpretations of this dispersion relation. One is the noncommutative spacetime on the stretched membrane and the other is that the fundamental quanta are microscopic black holes.

The Efroimsky perturbation scheme for consistent treatment of gravitational waves and their influence on the background is summarized and compared with the classical Isaacson high-frequency approach. We demonstrate that the Efroimsky method in its present form is not compatible with the Isaacson limit of high-frequency gravitational waves, and we propose its natural generalization to resolve this drawback.

The Newman–Tamburino spherical metrics are investigated using the homothety formalism of the author's previous work (2002 Class. Quantum Grav.19 259) and shown to always admit a homothety. The analysis also reveals that these metrics always admit a Killing vector, correcting a claim by Collinson and French (1967 J. Math. Phys.8 701). The limit form of the cylindrical Newman–Tamburino metric is also shown to admit a homothety.

I construct a field theory on an evolving fuzzy 2-sphere, which is based on the idea of the evolving non-commutative worlds of the previous paper [1]. The equations of motion are similar to the one that can be obtained by dropping the time-derivative term of the equation derived sometime ago by Banks, Peskin and Susskind for pure-into-mixed-state evolutions. The equations do not contain an explicit time, and therefore follow the spirit of the Wheeler–DeWitt equation. The basic properties of the field theory, such as action, gauge invariance and charge and momentum conservation, are studied. The continuum limit of the scalar field theory shows that the background geometry of the corresponding continuum theory is given by ds² = −dt² + t dΩ², which saturates locally the cosmic holographic principle.

When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically acceptable value at late epochs. We outline implications of this for cosmology and galaxy formation.