Abstract:
We develop a careful definition of energy for nonsupersymmetric warped product asymptotically $AdS_d \times M_q$ solutions which include a nonzero p-form. In the case of an electric p-form extending along all the AdS directions, and in particular in the case of self-dual fields like those used in the Freund-Rubin construction, the Hamiltonian is well defined only if a particular asymptotic gauge for the p-form is used. Rather surprisingly, asymptotically this gauge is time dependent, despite the fact the field and metric are not. We then consider a freely orbifolded $AdS_5 \times S_5$ and demonstrate that the standard boundary conditions allow states of arbitrarily negative energy. The states consist of time symmetric initial data describing bubbles that are regular up to singularities due to smeared D3-branes. We discuss the evolution of this data and point out that if the usual boundary conditions are enforced such bubbles may never reach infinity.

Abstract:
We argue that the recent measurement of the neutrino velocity to be higher than the velocity of light could be due to violation of Lorentz invariance by the muon neutrinos. This result need not undermine special-relativistic foundational notions of causality.

Abstract:
Treating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the critical behaviour of charged AdS black holes. We complete the analogy of this system with the liquid-gas system and study its critical point, which occurs at the point of divergence of specific heat at constant pressure. We calculate the critical exponents and show that they coincide with those of the Van der Waals system.

Abstract:
We extend the problem of $(1+1)$ circular dilaton gravity to include charged particles. We examine the two (charged) particle case in detail and find an exact equilibrium solution. We then extend this to $N-$particles and obtain a solution for this case as well. This class of solutions corresponds to $N$-particles of the same mass, spaced evenly around the circle with charges chosen so that the electric field satisfies $E^{2}=$constant. We discuss the relation of these solutions to the previous uncharged equilibrium solutions and examine the behavior when the number of particles is large. We comment on the challenges in further generalizing the solutions we obtain.

Abstract:
Inflation has the potential to seed the galactic magnetic fields observed today. However, there is an obstacle to the amplification of the quantum fluctuations of the electromagnetic field during inflation: namely the conformal invariance of electromagnetic theory on a conformally flat underlying geometry. As the existence of a preferred minimal length breaks the conformal invariance of the background geometry, it is plausible that this effect could generate some electromagnetic field amplification. We show that this scenario is equivalent to endowing the photon with a large negative mass during inflation. This effective mass is negligibly small in a radiation and matter dominated universe. Depending on the value of the free parameter of the theory, we show that the seed required by the dynamo mechanism can be generated. We also show that this mechanism can produce the requisite galactic magnetic field without resorting to a dynamo mechanism.

Abstract:
Black hole radiation of gravitinos is investigated as the classically forbidden tunneling of spin-3/2 fermions through an event horizon. We show that all four spin states of the gravitino yield the same emission temperature, and retrieve the Unruh temperature in a Rindler spacetime as well as the Hawking temperature for a Kerr-Newman charged rotating black hole.

Abstract:
We construct new charged solutions of the Einstein-Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher dimensional Reissner-Nordstr\"{o}m spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.

Abstract:
We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. We also find the the multiple nut parameter extension of the inhomogeneous Einstein metrics on complex line bundles found recently by Lu, Page and Pope. We also provide a more general form of the Eguchi-Hanson solitons found by Clarkson and Mann. We discuss the global structure of such solutions and possible applications in string theory.

Abstract:
We investigate the pair creation of noncommutative black holes in a background with positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild deSitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive mass spacetimes admit one cosmological horizon and two, one or no black hole horizons, while negative mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the non-singular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the deSitter background is quantum mechanically stable according to experience. However positive mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the universe, Planck size black holes production would have been largely disfavoured. We also find a potential instability for production of negative-mass solitons.

Abstract:
We consider the behaviour of bipartite and tripartite non-locality between fermionic entangled states shared by observers, one of whom uniformly accelerates. We find that while fermionic entanglement persists for arbitrarily large acceleration, the Bell/CHSH inequalities cannot be violated for sufficiently large but finite acceleration. However the Svetlichny inequality, which is a measure of genuine tripartite non-locality, can be violated for any finite value of the acceleration.