Table of contents

We show that the maximally supersymmetric pp-wave of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS × S solutions. In addition, we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS × S background is either Minkowski space or a maximally supersymmetric pp-wave.

We show how to derive systematically new forms of the BRST transformations for a generic gauge fixed action. They arise after a symmetry of the gauge fixed action is found in the sector involving the Lagrange multiplier and its canonical momentum.

The dynamical system constituted by two spherically symmetric thin shells and their own gravitational field is studied. The shells can be distinguished from each other, and they can intersect. At each intersection, they exchange energy on the Dray, 't Hooft and Redmount formula. There are bound states: if the shells intersect, one, or both, external shells can be bound in the field of internal shells. The space of all solutions to classical dynamical equations has six components; each has the trivial topology but a non-trivial boundary. Points within each component are labelled by four parameters. Three of the parameters determine the geometry of the corresponding solution spacetime and shell trajectories and the fourth describes the position of the system with respect to an observer frame. An account of symmetries associated with spacetime diffeomorphisms is given. The group is generated by an infinitesimal time shift, an infinitesimal dilatation and a time reversal.

The study of the two shell system started in our first paper, 'Pair of null gravitating shells I', is continued. An action functional for a single shell given by Louko, Whiting and Friedman is generalized to give appropriate equations of motion for two and, in fact, any number of spherically symmetric null shells, including the cases when the shells intersect. In order to find the symplectic structure for the space of solutions described in paper I, the pull back to the constraint surface of the Liouville form determined by the action is transformed into new variables. They consist of Dirac observables, embeddings and embedding momenta (the so-called Kuchar decomposition). The calculation includes the integration of a set of coupled partial differential equations. A general method of solving the equations is worked out.

The study of the two-shell system started in 'pair of null gravitating shells I and II' is continued. The pull back of the Liouville form to the constraint surface, which contains complete information about the Poisson brackets of Dirac observables, is computed in the singular double-null Eddington–Finkelstein (DNEF) gauge. The resulting formula shows that the variables conjugate to the Schwarzschild masses of the intershell spacetimes are simple combinations of the values of the DNEF coordinates on these spacetimes at the shells. The formula is valid for any number of in- and outgoing shells. After applying it to the two-shell system, the symplectic form is calculated for each component of the physical phase space; regular coordinates are found, defining it as a symplectic manifold. The symplectic transformation between the initial and final values of observables for the shell-crossing case is given.

We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if and only if there are future-pointing radial null geodesics emerging from the singularity. (ii) Limits of various spacetime invariants and other useful quantities (relating to Thorne's point–cigar–barrel–pancake classification and to isotropy/entropy measures) are studied in the approach to the singularity. (iii) The topology of the singularity is studied from the point of view of ideal boundary structure. In each case, the different nature of the visible and censored region of the singularity is emphasized.

Bousso's covariant entropy bound is put to the test in the context of a non-singular cosmological solution of general relativity found by Bekenstein. Although the model complies with every assumption made in Bousso's original conjecture, the entropy bound is violated due to the occurrence of negative energy density associated with the interaction of some the matter components in the model. We demonstrate how this property allows for the test model to 'elude' a proof of Bousso's conjecture which was given recently by Flanagan, Marolf and Wald. This corroborates the view that the covariant entropy bound should be applied only to stable systems for which every matter component carries positive energy density.

In this paper, we study some interesting properties of a spherically symmetric oscillating soliton star made of a real time-dependent scalar field which is called an oscillaton. The known final configuration of an oscillaton consists of a stationary stage in which the scalar field and the metric coefficients oscillate in time if the scalar potential is quadratic. The differential equations that arise in the simplest approximation, that of coherent scalar oscillations, are presented for a quadratic scalar potential. This allows us to take a closer look at the interesting properties of these oscillating objects. The leading terms of the solutions considering quartic and cosh scalar potentials are worked in the so-called stationary limit procedure. This procedure reveals the form in which oscillatons and boson stars may be related and useful information about oscillatons is obtained from the known results of boson stars. Oscillatons could compete with boson stars as interesting astrophysical objects, since they would be predicted by scalar field dark matter models.

A general recipe proposed elsewhere to define, via the Noether theorem, the variation of energy for a natural field theory is applied to Einstein–Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural bundles. The Einstein–Maxwell theory then turns out to be natural rather than gauge-natural. As a consequence of this assumption, a correction term like that used by Regge and Teitelboim is needed to define the variation of energy, as well as for the pure electromagnetic part of the Einstein–Maxwell Lagrangian. Integrability conditions for the variational equation which defines the variation of energy are analysed in relation to boundary conditions on physical data. As an application the first law of thermodynamics for rigidly rotating horizons is obtained.

It is shown that in a semiclassical model of the universe the out-of-equilibrium (Landau) and phenomenological entropies grow with the 'usual' evolutions a ∼ t^α, α < 2, breaking the time symmetry of the evolution equations.

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild spacetime. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation as far as these coordinates are concerned.

By using O(7,7) transformations, to deform D6-branes, we obtain half-supersymmetric bound state solutions of type IIA supergravity, containing D6, D4, D2, D0, F1-branes and waves. We lift the solutions to M-theory which gives half-supersymmetric M-theory bound states, e.g. KK6–M5–M5–M5– M2–M2–M2–MW. We also take near-horizon limits for the type IIA solutions, which give supergravity duals of seven-dimensional non-commutative open string theory (with spacetime and space–space non-commutativity), non-commutative Yang–Mills theory (with space–space and light-like non-commutativity) and an open D4-brane theory.

We report on progress made in the construction of higher-derivative superinvariants for type-II theories in ten dimensions. The string amplitude calculations required for this analysis exhibit interesting features which have received little attention in the literature so far. We discuss two examples from a forthcoming publication: the construction of the (H_NS)²R³ terms and the fermionic completion of the R⁴ terms. We show that a correct answer requires very careful treatment of the chiral splitting theorem, implies unexpected new relations between fermionic correlators, and most interestingly, necessitates the use of world-sheet gravitino zero modes in the string vertex operators. In addition we compare the relation of our results to the predictions of the linear scalar superfield of the type-IIB theory.

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects, the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where spacetime is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) classical behaviour in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behaviour representing quantum Euclidean space.

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy E, the axial component of the angular momentum, L_z, and Carter's constant Q. These parameters are obtained by solving the Hamilton–Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies ω_r, ω_θ and ω_ϕ associated with the radial, polar and azimuthal components of orbital motion, respectively. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this paper, it is shown that the fundamental frequencies are geometric invariants and explicit formulae in terms of quadratures are derived. The numerical evaluation of these formulae in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters, such as the semi-latus rectum p, the eccentricity e or the inclination parameter θ₋ are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulae.