On the causal properties of warped product spacetimes

It is shown that the warped product spacetime P=M *_f H, where H is a complete Riemannian manifold, and the original spacetime M share necessarily the same causality properties, the only exceptions being the properties of causal continuity and causal simplicity which present some subtleties. For instance, it is shown that if diamH=+\infty, the direct product spacetime P=M*H is causally simple if and only if (M,g) is causally simple, the Lorentzian distance on M is continuous and any two causally related events at finite distance are connected by a maximizing geodesic. Similar conditions are found for the causal continuity property. Some new results concerning the behavior of the Lorentzian distance on distinguishing, causally continuous, and causally simple spacetimes are obtained. Finally, a formula which gives the Lorentzian distance on the direct product in terms of the distances on the two factors (M,g) and (H,h) is obtained.Comment: 22 pages, 2 figures, uses the package psfra

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

Non-imprisonment conditions on spacetime

The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proved that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a result the non-imprisonment conditions can be included in the causal ladder of spacetimes. Finally, totally imprisoned causal curves are studied in detail, and results concerning the existence and properties of minimal invariant sets are obtained.Comment: 12 pages, 2 figures. v2: improved results on totally imprisoned curves, a figure changed, some misprints fixe

Multiply Warped Products with Non-Smooth Metrics

In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the curvature of a multiply warped product with $C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$, $f_2$ for the multiply warped products of the form $M=(0,\ 2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page

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

ESR Spectrum of the 9‐Molybdomanganate(IV) Ion in Dilute Single Crystal

The ESR spectrum of a single crystal of (NH4)6[NI(IV)O6Mo9O26]⋅8H2O containing 1% (NH4)6‐[Mn(IV)O6Mo9O26]⋅8H2O has been investigated. This is the first ESR report on quadrivalent manganese in a chemically well‐characterized environment. The site symmetry is D3D3, and anisotropic gg values, hyperfine splittings, and zero‐field splitting values were obtained by fitting the spectrum with an axial spin Hamiltonian.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71351/2/JCPSA6-50-9-3647-1.pd

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented.Comment: 20 pages, minor corrections, references adde

Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies

Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincar\ue9 duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincar\ue9 duality for the new cohomology groups