Axially symmetric gravitational fields

The present thesis consists of three parts. In the first part we give a brief historical outline of the most important results that have been obtained in the theory of axially symmetric gravitational fields. Parts II and III are devoted to two contributions by the writer to this branch of the general theory of relativity. A bibliography of papers dealing with the subject is given at the end. This bibliography has been arranged in chronological order, and references to it are made by quoting the authors name followed by the year of publication

A rotating cylinder in an asymptotically locally anti-de Sitter background

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.Comment: To appear in Classical and Quantum Gravit

Closed timelike curves in asymmetrically warped brane universes

In asymmetrically warped spacetimes different warp factors are assigned to space and to time. We discuss causality properties of these warped brane universes and argue that scenarios with two extra dimensions may allow for timelike curves which can be closed via paths in the extra-dimensional bulk. In particular, necessary and sufficient conditions on the metric for the existence of closed timelike curves are presented. We find a six-dimensional warped metric which satisfies the CTC conditions, and where the null, weak and dominant energy conditions are satisfied on the brane (although only the former remains satisfied in the bulk). Such scenarios are interesting, since they open the possibility of experimentally testing the chronology protection conjecture by manipulating on our brane initial conditions of gravitons or hypothetical gauge-singlet fermions (sterile neutrinos) which then propagate in the extra dimensions.Comment: 24 pages, 2 figures; major corrections: CTC metric generalized from 5D to 6D, the new 6D metric satisfies the conclusions attributed (incorrectly) to the 5D metric in v

Can a circulating light beam produce a time machine?

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC's occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett's solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.Comment: 5 pages, RevTe

Self-gravitating clouds of generalized Chaplygin and modified anti-Chaplygin Gases

The Chaplygin gas has been proposed as a possible dark energy, dark matter candidate. As a working fluid in a Friedmann-Robertson-Walker universe, it exhibits early behavior reminiscent of dark matter, but at later times is more akin to a cosmological constant. In any such universe, however, one can expect local perturbations to form. Here we obtain the general equations for a self-gravitating relativistic Chaplygin gas. We solve these equations and obtain the mass-radius relationship for such structures, showing that only in the phantom regime is the mass-radius relationship large enough to be a serious candidate for highly compact massive objects at the galaxy core. In addition, we study the cosmology of a modified anti-Chaplygin gas. A self-gravitating cloud of this matter is an exact solution to Einstein's equations.Comment: 16 page

Centrifugal force induced by relativistically rotating spheroids and cylinders

Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect to axes that do not rotate as seen from infinity experiences a centrifugal force. Although the spacetime there is Minkowskian out to the inner cylinder nevertheless that space has been induced to rotate, so relative to the local inertial frame the particle is traversing a circular orbit.Comment: 12 pages, 2 figure

An exterior for the G\"{o}del spacetime

We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $\Lambda$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solutions. There is a considerable similarity between the spacetimes investigated here and those of van Stockum referring to an infinite cylinder of rotating dust matched to vacuum, with $\Lambda=0$.Comment: 11 pages, LaTeX 2.09, no figures. Submitted to Classical and Quantum Gravit

Closed timelike curves via post-selection: theory and experimental demonstration

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. CTCs appear in many solutions of Einstein's field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum field theory. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we explore an alternative quantum formulation of CTCs and show that it is physically inequivalent to Deutsch's. Because it is based on combining quantum teleportation with post-selection, the predictions/retrodictions of our theory are experimentally testable: we report the results of an experiment demonstrating our theory's resolution of the well-known `grandfather paradox.Comment: 5 pages, 4 figure

Causality-Violating Higgs Singlets at the LHC

We construct a simple class of compactified five-dimensional metrics which admits closed timelike curves (CTCs), and derive the resulting CTCs as analytic solutions to the geodesic equations of motion. The associated Einstein tensor satisfies all the null, weak, strong and dominant energy conditions. In particular, no negative-energy "tachyonic" matter is required. In extra-dimensional models where gauge charges are bound to our brane, it is the Kaluza-Klein (KK) modes of gauge-singlets that may travel through the CTCs. From our brane point of view, many of these KK modes would appear to travel backward in time. We give a simple model in which time-traveling Higgs singlets can be produced by the LHC, either from decay of the Standard Model (SM) Higgs or through mixing with the SM Higgs. The signature of these time-traveling singlets is a secondary decay vertex pre-appearing before the primary vertex which produced them. The two vertices are correlated by momentum conservation. We demonstrate that pre-appearing vertices in the Higgs singlet-doublet mixing model may well be observable at the LHC.Comment: 55 pages, 5 figures, v4: Version updated to include in single manuscript the contents of Erratum [Phys. Rev. D 88, 069901(E) (2013)], Reply [Phys. Rev. D 88, 068702 (2013)], Comment [Phys. Rev. D 88, 068701 (2013), arXiv:1302.1711], and original published article [Phys. Rev. D 87, 045004 (2013), arXiv:1103.1373]. Positive conclusions remain unchange

Studies Of The Over-Rotating BMPV Solution

We study unphysical features of the BMPV black hole and how each can be resolved using the enhancon mechanism. We begin by reviewing how the enhancon mechanism resolves a class of repulson singularities which arise in the BMPV geometry when D--branes are wrapped on K3. In the process, we show that the interior of an enhancon shell can be a time machine due to non-vanishing rotation. We link the resolution of the time machine to the recently proposed resolution of the BMPV naked singularity / "over-rotating" geometry through the expansion of strings in the presence of RR flux. We extend the analysis to include a general class of BMPV black hole configurations, showing that any attempt to "over-rotate" a causally sound BMPV black hole will be thwarted by the resolution mechanism. We study how it may be possible to lower the entropy of a black hole due to the non-zero rotation. This process is prevented from occurring through the creation of a family of resolving shells. The second law of thermodynamics is thereby enforced in the rotating geometry - even when there is no risk of creating a naked singularity or closed time-like curves