Table of contents

One of the predictions of quantum gravity phenomenology is that, in situations where Planck-scale physics and the notion of a quantum spacetime are relevant, field propagation will be described by a modified set of laws. Descriptions of the underlying mechanism differ from model to model, but a general feature is that electromagnetic waves will have non-trivial dispersion relations. A physical phenomenon that offers the possibility of experimentally testing these ideas in the foreseeable future is the propagation of high-energy gamma rays from GRBs at cosmological distances. With the observation of non-standard dispersion relations within experimental reach, it is thus important to find out whether there are competing effects that could either mask or be mistaken for this one. In this letter, we consider possible effects from standard physics, due to electromagnetic interactions, classical as well as quantum, and coupling to classical geometry. Our results indicate that, for currently observed gamma-ray energies and estimates of cosmological parameter values, those effects are much smaller than the quantum gravity one if the latter is first order in the energy; some corrections are comparable in magnitude to the second-order quantum gravity ones, but they have a very different energy dependence.

This paper discusses the motivation and general design elements of a new fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, ∝G². The laser astrometric test of relativity (LATOR) mission uses laser interferometry between two micro-spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (100 m) multi-channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangle's three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy.

LATOR will not only improve the value of the parametrized post-Newtonian (PPN) parameter γ to unprecedented levels of accuracy of 1 part in 10⁸, it will also reach the ability to measure effects of the next post-Newtonian order (∝G²) of light deflection resulting from gravity's intrinsic nonlinearity. The solar quadrupole moment parameter, J₂, will be measured with high precision, as well as a variety of other relativistic effects including Lense–Thirring precession. LATOR will lead to very robust advances in the tests of fundamental physics: this mission could discover a violation or extension of general relativity, or reveal the presence of an additional long range interaction in the physical law. There are no analogues to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments.

Motivated by several pieces of evidence, in order to show that extremal black holes cannot be obtained as limits of non-extremal black holes, in this paper we calculate explicitly quasinormal modes for the Bañados, Teitelboim and Zanelli (BTZ) extremal black hole and show that the imaginary part of the frequency is zero. We obtain exact result for the scalar and fermionic perturbations. We also showed that the frequency is bounded from below for the existence of the normal modes (non-dissipative modes).

We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analysed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In particular, we demonstrate that the characteristic envelope singularity of the rotated wave fronts is a (non-scalar) curvature singularity, although all scalar invariants of the Riemann tensor vanish there.

We obtain global spacetime weighted-L² (Morawetz) and L⁴ (Strichartz) estimates for a massless chargeless spherically symmetric scalar field propagating on a super-extremal (overcharged) Reissner–Nordström background. To do this we first discuss the well-posedness of the Cauchy problem for scalar fields on non-globally hyperbolic manifolds, review the role played by the Friedrichs extension and go over the construction of the function spaces involved. We then show how to transform this problem to one about the wave equation on the Minkowski space with a singular potential, and prove that the potential thus obtained satisfies the various conditions needed in order for the estimates to hold.

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein–Yang–Mills theory, are shown to be -supersymmetric solutions of a wide variety of N = 1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang–Mills coupled to an axion σ and dilaton ϕ recently obtained as the reduction to four dimensions of the six-dimensional Salam–Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang–Mills connection on a self-dual metric and solving a Poisson equation for e^ϕ. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve of supersymmetry.

The ultrarelativistic limit of two-dimensional dilaton gravity is presented and its associated (anti-)self-dual energy–momentum tensor is derived. It is localized on a null line, although the line element remains twice differentiable. Relations to the Aichelburg–Sexl spacetime and constant dilaton vacua are pointed out. Geodesics are found to be smooth for minimally coupled test particles but non-smooth—with a finite jump in the acceleration—for test particles coupled non-minimally to the dilaton. Quantization on boosted backgrounds is discussed; no anomalous trace of the energy–momentum tensor arises and the 1-loop flux component can be adjusted to be equal to the classical flux of the shock wave.

A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in n − 4 spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers–Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property.

We consider a generalization of the DGP model, by adding a second brane with localized curvature, and allowing for a bulk cosmological constant and brane tensions. We study radion and graviton fluctuations in detail, enabling us to check for ghosts and tachyons. By tuning our parameters accordingly, we find bigravity models that are free from ghosts and tachyons. These models will lead to large distance modifications of gravity that could be observable in the near future.

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this paper, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac–Born–Infeld action. Topology change of the brane universe can be realized by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.

We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology, which are asymptotically dS, AdS or flat. For a negative cosmological constant these solutions are NUT charged generalizations of the topological black-hole solutions in higher dimensions. We also point out the existence of such NUT charged spacetimes in odd dimensions and explicitly construct such spaces in five and seven dimensions. The existence of such spacetimes with non-trivial topology is closely related to the existence of the cosmological constant. Finally, we discuss the global structure of such solutions and possible applications in string theory.

We present simulations of causal dynamical wavefunction collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalizing the fundamental field can overcome its noisiness and argue that this coarse grained renormalized field will show interesting structure if the state vector does on the coarse grained scale. We speculate on the implications for quantum gravity.

In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis—given in paper II—where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations.

We construct matter-coupled N = 2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector, tensor and hypermultiplets. By allowing off-diagonal vector–tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi–Yau manifolds with fluxes.

We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a two-fluid source. We write the equations as a two-dimensional dynamical system and analyse the qualitative, asymptotic behaviour of the models. We examine the possibility that in certain theories the Weyl 1-form may give rise to a late accelerated expansion of the universe and conclude that such behaviour is not met as a generic feature of the simplest cosmologies.

In this paper, we calculate the gravitational-wave power-spectra corresponding to different types of transitions between the inflationary regime and the radiation era. We study four cases, where inflation is followed by a stiff-matter phase, or by a dust-dominated phase, or by a combination of the two, before the universe enters the radiation era. Use is made of differential equations for the Bogoliubov coefficients, allowing us to model all the transitions between the different eras as continuous. New features appear, for frequencies above 10⁻⁵ rad s⁻¹, in an otherwise flat part of the spectrum.