Towards a closed differential aging formula in special relativity

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the analogous and more natural problem for a Fermi-Walker decomposition being still open.Comment: Latex2e, 6 pages, 1 figure, uses psfrag. Contribution to the Proceedings of The Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain September 4-8, 200

Causally simple inextendible spacetimes are hole-free

It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to causal continuity. Physically, it means that if there is some partial Cauchy hypersurface which, for some reason, does not fully develop its influence, then there is some discontinuity in the causal relation.Comment: Revtex4, 9 pages. v2: minor correction

Nonadiabatic creation of macroscopic superpositions with strongly correlated 1D bosons on a ring trap

We consider a strongly interacting quasi-one dimensional Bose gas on a tight ring trap subjected to a localized barrier potential. We explore the possibility to form a macroscopic superposition of a rotating and a nonrotating state under nonequilibrium conditions, achieved by a sudden quench of the barrier velocity. Using an exact solution for the dynamical evolution in the impenetrable-boson (Tonks-Girardeau) limit, we find an expression for the many-body wavefunction corresponding to a superposition state. The superposition is formed when the barrier velocity is tuned close to multiples of integer or half-integer number of Coriolis flux quanta. As a consequence of the strong interactions, we find that (i) the state of the system can be mapped onto a macroscopic superposition of two Fermi spheres, rather than two macroscopically occupied single-particle states as in a weakly interacting gas, and (ii) the barrier velocity should be larger than the sound velocity to better discriminate the two components of the superposition.Comment: 5 pages, 3 figures, revised introduction and new Fig3, final version to appear in PR

The causal ladder and the strength of K-causality. I

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The causal hierarchy of spacetime is built from chronology up to K-causality and new characterizations of the distinction and strong causality properties are obtained. The closure of the causal future is not transitive, as a consequence its repeated composition leads to an infinite causal subladder between strong causality and K-causality - the A-causality subladder. A spacetime example is given which proves that K-causality differs from infinite A-causality.Comment: 16 pages, one figure. Old title: ``On the relationship between K-causality and infinite A-causality''. Some typos fixed; small change in the proof of lemma 4.

Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Static Observers in Curved Spaces and Non-inertial Frames in Minkowski Spacetime

Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy-momentum tensor of the source is analyzed.Comment: 28 pages, 4 figures

Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page