Table of contents

Two fundamental tests of general relativity are achieved using over three decades of lunar laser ranging (LLR) data—confirming the equality of the Sun's acceleration rate of the Earth and Moon to about a part in 10¹³ precision, and finding no time variation in the strength of Newton's G to precision of a part in 10¹²per year. LLR is an ongoing mission, and these tests of physical theory should remain at the frontier of precision for time to come. The contribution of each individual LLR measurement to the precision of Ġ determination varies strongly through the lunar motion's monthly cycle and from month to month. A worth function which quantifies this variation is derived and illustrated: it can be employed by observers who have scheduling discretions in order to more rapidly improve the estimation precision for the scientific parameter Ġ.

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c²_s > 1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilize an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.

It is shown that there are no vacuum spacetimes (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a congruence of freely falling observers.

We introduce the brane–bulk interaction to discuss a limitation of the cosmological Cardy–Verlinde formula which is useful for the holographic description of brane cosmology. In the presence of the brane–bulk interaction, we cannot find the entropy representation of the first Friedmann equation (the cosmological Cardy–Verlinde formula). In the absence of the interaction, the cosmological Cardy–Verlinde formula is established even for the time-dependent charged AdS background. Hence, if there exists a dynamic exchange of energy between the brane and the bulk (that is, if ^t_y ≠ 0), we cannot achieve the cosmological holographic principle on the brane.

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this paper is to analyse the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in a paper by Wainwright and Hsu, and in a previous paper we analysed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces, and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine. Finally, we give asymptotic expansions for general Bianchi VII₀ metrics.

We study nonsingular cosmological scenarios in a general D-dimensional string effective action of the dilaton–modulus–axion system in the presence of the matter source. In the standard dilatonic Brans–Dicke parameter (ω = −1) with radiation, we analytically obtain singularity-free bouncing solutions where the universe starts out in a state with a finite curvature and evolves towards the weakly coupled regime. We apply this analytic method to the string-gas cosmology including the massive state in addition to the leading massless state (radiation), with and without the axion. We numerically find bouncing solutions which asymptotically approach an almost radiation dominant universe with a decreasing curvature irrespective of the presence of the axion, implying that inclusion of the matter source is crucial for the existence of such solutions for ω = −1. In the theories with ω ≠ −1, it is possible to obtain complete regular bouncing solutions with a finite dilaton and curvature in both past and future asymptotics for the general dimension, D. We also discuss the case where dilatonic higher-order corrections are involved to the tree-level effective action and demonstrate that the presence of axion/modulus fields and the matter source does not significantly affect the dynamics of the dilaton-driven inflation and the subsequent graceful exit.

Recent astrophysical observations suggest that the value of fine structure constant α = e²/c may be slowly increasing with time. This may be due to an increase of e or a decrease of c, or both. In this paper, we argue from model-independent considerations that this variation should be considered adiabatic. Then, we examine in detail the consequences of such an adiabatic variation in the context of a specific model of quantized charged black holes. We find that the second law of black-hole thermodynamics is obeyed, regardless of the origin of the variation, and that interesting constraints arise on the charge and mass of black holes. Finally, we estimate the work done on a black hole of mass M due to the proposed α variation.

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 < ω < c/|β|^1/2. This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin.

A plethora of models of the universe have been proposed in recent years claiming that the present universe is accelerating, being driven by some hypothetical source with negative pressure collectively known as dark energy, which do not appear to resemble any known form of matter tested in the laboratory. These models are motivated by the high-redshift supernovae (SN) Ia observations. Though low-density models, without dark energy, also appear to fit the SN Ia data reasonably well, however, they are ruled out by the cosmic microwave background (CMB) observations.

In this paper, we present a warped brane model with an additional surface term of brane curvature scalar in the action. This results in shifting the dynamical curvature of the model from its geometrical counterpart, which creates profound consequences. Even for Λ = 0, the low-energy decelerating model successfully explains the observed locations of the peaks in the angular power spectrum of CMB. This model also fits the high-redshift SN Ia observations, taken together with the recently observed SN 1997ff at z ≈ 1.7, very well. Additionally, it also fits the data on the angular size and redshift of the compact radio sources very well.

Using a gauge-invariant formalism we derive and solve the perturbed cosmological equations for the BSBM theory of varying fine structure 'constant'. We calculate the time evolution of inhomogeneous perturbations of the fine structure constant, δα/α on small and large scales with respect to the Hubble radius. In a radiation-dominated universe, small inhomogeneities in α will decrease on large scales but on scales smaller than the Hubble radius they will undergo stable oscillations. In a dust-dominated universe small inhomogeneous perturbations in α will become constant on large scales and on small scales they will increase as t^2/3, and δα/α will track δρ_m/ρ_m. If the expansion accelerates, as in the case of a Λ or quintessence-dominated phase, inhomogeneities in α will decrease on both large and small scales. The amplitude of perturbations in α will be much smaller than that of matter or radiation perturbations. We also present a numerical study of the nonlinear evolution of spherical inhomogeneities in radiation and dust universes by means of a comparison between the evolution of flat and closed Friedmann models with time-varying α. Various limitations of these simple models are also discussed.

In this paper we analyse in the Wilson loop context the parallel transport of vectors and spinors around a closed loop in the background spacetime of a rotating black string in order to classify its global properties. We also examine particular closed orbits in this spacetime and verify the Mandelstam relations.

The complete on-shell action of topological Einstein–Maxwell gravity in four dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N = 2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The local vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.

Kaigorodov spaces arise, after spherical compactification, as near-horizon limits of M2, M5 and D3-branes with a particular pp-wave propagating in a worldvolume direction. We show that the uncompactified near-horizon configurations K × S are solutions of D = 11 or D = 10 IIB supergravity which correspond to perturbed versions of their AdS × S analogues. We derive the Penrose–Güven limits of the Kaigorodov space and the total spaces and analyse their symmetries. An Inönü–Wigner contraction of the Lie algebra is shown to occur, although there is a symmetry enhancement. We compare the results to the maximally supersymmetric CW spaces found as limits of AdS × S spacetimes: the initial gravitational perturbation on the brane and its near-horizon geometry remains after taking non-trivial Penrose limits, but seems to decouple. One particular limit yields a time-dependent homogeneous plane-wave background whose string theory is solvable, while in the other cases we find inhomogeneous backgrounds.

We study geodesic motion of pseudo-classical spinning particles in the hot NUT–Reissner–Nordström space. We investigate the generalized Killing equations for spinning spaces and derive the constants of motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.

The Jackiw–Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on d dimensional flat spacetime. In terms of this interpretation of the model as a consistent string theory, it is discussed as to how the presence of a cosmological constant leads one to consider additional constraints on the parameters of the theory, even though the conformal anomaly is independent of the cosmological constant. The constraints agree with the necessary conditions required to ensure that the tachyon field turns out to be a primary prelogarithmic operator within the context of the worldsheet conformal field theory. Thus, the linearized tachyon field equation allows one to impose the diagonal condition for the interaction term. We analyse the neutralization of the Liouville mode induced by the coupling to the Jackiw–Teitelboim Lagrangian. The standard free field prescription leads one to obtain explicit expressions for three-point functions for the case of vanishing cosmological constant in terms of a product of Shapiro–Virasoro integrals; this fact is a consequence of the mentioned neutralization effect.

In this paper we will study some aspects of dS/CFT correspondence. We will focus on the relation between Witten's non-standard de Sitter inner product and correlators in the holographic dual conformal field theory. We will argue that from the definition of Witten's inner product and conjecture that the Hilbert space of initial states of a massive scalar field on ⁻ in de Sitter space corresponds to the Hilbert space of states of Euclidean CFT on ⁻, we can obtain CFT correlators in any vacuum state.

In this paper, we examine a generic theory of (1 + 1)-dimensional gravity with coupling to a scalar field. Special attention is paid to a class of models that have a power-law form of dilaton potential and can admit black-hole solutions. The study focuses on the formulation of a Lorentzian partition function. Extending a four-dimensional treatment by Makela and Repo, we incorporate the principles of Hamiltonian thermodynamics (as well as black-hole spectroscopy) and find that the partition function can be expressed in a calculable form. We then go on to extract the black-hole entropy, including the leading-order quantum correction. As anticipated, this correction can be expressed as the logarithm of the classical entropy. Interestingly, the prefactor for this logarithmic correction disagrees, in both magnitude and sign, with the findings from a prior study (on the same model). We comment on this discrepancy and provide a possible rationalization.

A new 2N-soliton solution is constructed for the electric/magnetic sector of the four-dimensional dilaton-Maxwell gravity with arbitrary value of coupling in the static and axisymmetric case. This solution possesses an infinitesimal limit of the current algebra form and preserves the asymptotic flatness property being applied to the asymptotically flat background.

The spacetime homogeneous Gödel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The results obtained are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have an infinite number of matter collineations in the degenerate case, i.e. det(T_ab) = 0, and do not admit proper matter collineations in the non-degenerate case, i.e. det(T_ab) ≠ 0. The degenerate case has the new constraints on the parameters m and w which characterize the causality features of the Gödel-type spacetimes.

In this paper we derive the low-energy effective action of type IIB theory compactified on half-flat manifolds and show that this precisely coincides with the low-energy effective action of type IIA theory compactified on a Calabi–Yau manifold in the presence of NS three-form fluxes. In this way we provide a further check of the recently formulated conjecture that half-flat manifolds appear as mirror partners of Calabi–Yau manifolds when NS fluxes are turned on.

In the formulation of (2 + 1)-dimensional gravity as a Chern–Simons gauge theory, the phase space is the moduli space of flat Poincaré group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincaré transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms.

We use the analytic continuation procedure proposed in our earlier works to study the thermodynamics of black holes in 2 + 1 dimensions. A general black hole in 2 + 1 dimensions has g handles hidden behind h horizons. The result of the analytic continuation of a black-hole spacetime is a hyperbolic 3-manifold having the topology of a handlebody. The boundary of this handlebody is a compact Riemann surface of genus G = 2g + h − 1. Conformal moduli of this surface encode in a simple way the physical characteristics of the black hole. The moduli space of black holes of a given type (g, h) is then the Schottky space at genus G. The (logarithm of the) thermodynamic partition function of the hole is the Kähler potential for the Weil–Peterson metric on the Schottky space. The Bekenstein bound on the black-hole entropy leads us to conjecture a new strong bound on this Kähler potential.

Relativistic astrometry has recently become an active field of research owing to new observational technologies which allow for accuracies of a microarcsecond. To assure this accuracy in data analysis, one has to perform ray tracing in a general relativistic framework including terms of the order of (v/c)³ in the weak field treatment of Einstein equations applied to the solar system. Basic to the solution of a ray tracing problem are the boundary conditions that one has to fix from the observational data. In this paper we solve this problem to (v/c)³ in a fully analytical way.

It has been proposed by Bekenstein and others that the horizon area of a black hole conforms, upon quantization, to a discrete and uniformly spaced spectrum. In this paper, we consider the area spectrum for the highly non-trivial case of a rotating (Kerr) black-hole solution. Following a prior work by Barvinsky, Das and Kunstatter, we are able to express the area spectrum in terms of an integer-valued quantum number and an angular-momentum operator. (The procedure employs a periodicity condition that can be viewed as a conjectural, although well-motivated input.) Moreover, by using an analogy between the Kerr black hole and a quantum rotator, we are able to quantize the angular-momentum sector. We find the area spectrum to be A_n,Jcl = 8πℏ(n + J_cl + 1/2), where n and J_cl are both integers. The quantum number J_cl is related to but distinct from the eigenvalue j of the angular momentum of the black hole. Actually, it represents the 'classical' angular momentum and, for J_cl ≫ 1, J_cl ≈ j.

Let = ₀ × ² be a pp-wave-type spacetime endowed with the metric ⟨·, ·⟩_z = ⟨·, ·⟩_x + 2du dv + H(x, u) du², where (₀, ⟨·, ·⟩_x) is any Riemannian manifold and H(x, u) is an arbitrary function. We show that the behaviour of H(x, u) at spatial infinity determines the causality of , say: (a) if −H(x, u) behaves subquadratically (i.e, essentially −H(x, u) ⩽ R₁(u)|x|²⁻ for some > 0 and large distance |x| to a fixed point) and the spatial part (₀, ⟨·, ·⟩_x) is complete, then the spacetime is globally hyperbolic, (b) if −H(x, u) grows at most quadratically (i.e, −H(x, u) ⩽ R₁(u)|x|² for large |x|) then it is strongly causal and (c) is always causal, but there are non-distinguishing examples (and thus, not strongly causal), even when −H(x, u) ⩽ R₁(u)|x|²⁺, for small > 0.

Therefore, the classical model ₀ = ², H(x, u) = ∑_{i, j}h_ij(u)x_ix_j(≢ 0), which is known to be strongly causal but not globally hyperbolic, lies in the critical quadratic situation with complete ₀. This must be taken into account for realistic applications. In fact, we argue that −H will be subquadratic (and the spacetime globally hyperbolic) if is asymptotically flat. The relation of these results with the notion of astigmatic conjugacy and the existence of conjugate points is also discussed.

We calculate one-loop scattering amplitudes for gravitons and two-forms in dimensions greater than four. The string-based Kawai–Lewellen–Tye relationships allow gravitons and two-forms to be treated in a unified manner. We use the results to determine the ultraviolet infinities present in these amplitudes and show how these determine the renormalized one-loop action in six and eight dimensions.

We show that every second-order ODE defines a four-parameter family of projective connections on its two-dimensional solution space. In a special case of ODEs, for which a certain point transformation invariant vanishes, we find that this family of connections always has a preferred representative. This preferred representative turns out to be identical to the projective connection described in Cartan's classic paper (Cartan E 1924 Bull. Soc. Math. France52 205–41, 1955 Oeuvres III1 825–62).

We compute the production of particles from the gravitational field of an expanding mass shell. Contrary to the situation of Hawking radiation and the production of cosmological perturbations during cosmological inflation, the example of an expanding mass shell has no horizon and no singularity. We apply the method of 'ray-tracing', first introduced by Hawking, and calculate the energy spectrum of the produced particles. The result depends on three parameters: the expansion velocity of the mass shell, its radius and its mass. Contrary to the situation of a collapsing mass shell, the energy spectrum is non-thermal. Invoking time reversal we reproduce Hawking's thermal spectrum in a certain limit.

I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary spacetime dimensions. I prove that when the spacetime manifold admits a metric of constant curvature, the propagator is not affected by terms with higher derivatives. More generally, certain Lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have been expected. In quantum gravity, the metric of constant curvature is an extremal, but not a minimum, of the complete action. Nonetheless, it appears to be the right perturbative vacuum, at least when the curvature is negative, suggesting that the quantum vacuum has a negative asymptotically constant curvature. The results of this paper give also a set of rules for a more economical use of effective quantum field theories and suggest that it might be possible to give mathematical sense to theories with infinitely many couplings at high energies, to search for physical predictions.

In regard to the initial-boundary-value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein–Christoffel formulation of the Einstein equations in the case of spherical symmetry.

We define a level for a large class of Lorentzian Kac–Moody algebras. Using this we find the representation content of very extended A_D−3 and E₈ (i.e., E₁₁) at low levels in terms of A_D−1 and A₁₀ representations, respectively. The results are consistent with the conjectured very extended A₈ and E₁₁ symmetries of gravity and maximal supergravity theories given respectively in preprints hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.

The properties of 5D gravitational flux tubes are considered. With the cross section and fifth dimension in the Planck region, such tubes can be considered as stringlike objects, namely Δ-strings. A model of attachment of Δ-string to a spacetime is offered. It is shown that the attachment point is a model of an electric charge for an observer living in the spacetime. The magnetic charges are forbidden in this model.

The absorption cross section for scattering of fermions off an extreme BTZ black hole is calculated. It is shown that, as in the case of scalar particles, an extreme BTZ black hole exhibits a vanishing absorption cross section, which is consistent with the vanishing entropy of such an object. Additionally, we give a general argument to prove that the particle flux near the horizon is zero. Finally, we show that the reciprocal space introduced previously in [1] gives rise to the same result and, therefore, it could be considered as the space where the scattering process takes place in an AdS spacetime.

We demonstrate that Plebański's first heavenly equation decouples in infinitely many ways into a triple of commuting (1 + 1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of one variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.

Stationary extended frames in general relativity are considered. The requirement of stationarity allows one to treat the spacetime as a principal fibre bundle over the one-dimensional group of time translations. Over this bundle a connection form establishes the simultaneity between neighbouring events accordingly with the Einstein synchronization convention. The mathematics involved is that of gauge theories where a gauge choice is interpreted as a global simultaneity convention. Then simultaneity in non-stationary frames is investigated: it turns out to be described by a gauge theory in a fibre bundle without structure group, the curvature being given by the Frölicher–Nijenhuis bracket of the connection. The Bianchi identity of this gauge theory is a differential relation between the vorticity field and the acceleration field. In order for the simultaneity connection to be principal, a necessary and sufficient condition on the 4-velocity of the observers is given.

We study massless Duffin–Kemmer–Petiau (DKP) fields in the context of Einstein–Cartan gravitation theory, interacting via minimal coupling procedure. In the case of an identically vanishing torsion (Riemannian spacetimes) we show that there exist local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. On the other hand, similarly to what happens with the Maxwell theory, a non-vanishing torsion, in general, breaks the usual U(1) local gauge symmetry of the electromagnetic field or, from a different point of view, imposes conditions on the torsion.