General Relativistic Thermoelectric Effects in Superconductors

We discuss the general-relativisticcontributions which occur in the electromagneticproperties of a superconductor with a heat flow. Theappearance of a general-relativistic contribution to themagnetic flux through a superconducting thermoelectricbimetallic circuit is shown. The response of theJosephson junctions to a heat flow is investigated inthe general-relativistic framework. Somegravitothermoelectric effects which are observable in thesuperconducting state in the Earth's gravitational fieldare considered.     

Letter: Classical and Quantum Evolution of Non-Isentropic Hot Singular Layers in Finite-Temperature General Relativity

The spherically symmetric layer of matter isconsidered within the frame-works of general relativity.We perform a generalization of the already known theoryfor the case of nonconstant surface entropy and finite temperature. We also propose theminisuperspace model to determine the behavior of thetemperature field and perform the Wheeler-DeWittquantization.     

Finslerian Spaces Possessing Local Relativistic Symmetry

It is shown that the problem of a possibleviolation of the Lorentz transformations at Lorentzfactors > 5 × 10¹⁰,indicated by the situation which has developed in thephysics of ultra-high energy cosmic rays (the absence of the GZKcutoff), has a nontrivial solution. Its essence consistsin the discovery of the so-called generalized Lorentztransformations which seem to correctly link the inertial reference frames at any values of. Like the usual Lorentz transformations, thegeneralized ones are linear, possess group propertiesand lead to the Einstein law of addition of3-velocities. However, their geometric meaning turns out tobe different: they serve as relativistic symmetrytransformations of a flat anisotropic Finslerian eventspace rather than of Minkowski space. Consideration is given to two types of Finsler spaces whichgeneralize locally isotropic Riemannian space-time ofrelativity theory, e.g. Finsler spaces with a partiallyand entirely broken local 3D isotropy. The investigation advances arguments for the correspondinggeneralization of the theory of fundamental interactionsand for a specific search for physical effects due tolocal anisotropy of space-time.     

A Class of Anisotropic (Finsler-)Space-time Geometries

A particular Finsler-metric proposed in [1, 2]and describing a geometry with a preferred nulldirection is characterized as belonging to a subclasscontained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to theirgroup of isometries. These turn out to be isomorphic tosubgroups of the Poincare (Lorentz-) group complemented by the generator of a dilatation.The arising Finsler geometries may be used for theconstruction of relativistic theories testing theisotropy of space. It is shown that the Finsler space with the only preferred null direction is the anisotropic space closest to isotropic Minkowski-spaceof the full class discussed.     

Finding Collineations of Kimura Metrics

Kimura investigated static spherically symmetric metrics and found several to have quadratic first integrals. We use REDUCE and the package Dimsym to seek collineations for these metrics. For one metric we find that three proper projective collineations exist, two of which are associated with the two irreducible quadratic first integrals found by Kimura. The third projective collineation is found to have a reducible quadratic first integral. We also find that this metric admits two conformal motions and that the resulting reducible conformal Killing tensors also lead to Kimura's quadratic integrals. We demonstrate that when a Killing tensor is known for a metric we can seek an associated collineation by solving first order equations that give the Killing tensor in terms of the collineation rather than the second order determining equations for collineations. We report less interesting results for other Kimura metrics.     

Third Rank Killing Tensors in General Relativity. The (1 + 1)-dimensional Case

Third rank Killing tensors in (1 +1)-dimensional geometries are investigated andclassified. It is found that a necessary and sufficientcondition for such a geometry to admit a third rankKilling tensor can always be formulated as a quadratic PDE, oforder three or lower, in a Kahler type potential for themetric. This is in contrast to the case of first andsecond rank Killing tensors for which the integrability condition is a linear PDE. The motivation for studying higher rank Killing tensors in (1 +1)-geometries, is the fact that exact solutions of theEinstein equations are often associated with a first orsecond rank Killing tensor symmetry in the geodesicflow formulation of the dynamics. This is in particulartrue for the many models of interest for which thisformulation is (1 + 1)-dimensional, where just one additional constant of motion suffices forcomplete integrability. We show that new exact solutionscan be found by classifying geometries admitting higherrank Killing tensors.     

Modified No-hair Conjecture and the Limiting Process

It is argued that the Schwarzschild black hole solution follows as a unique limit of the Brans-Dicke Class I solutions, provided the correct iterated limit is taken. Such a uniqueness is essential for the validity of a recent version of the no-hair conjecture. A non-trivial modification to this version is proposed in order to exclude Brans-Dicke Class IV solutions which appear to represent scalar hair black holes in general.