Comparing metrics at large: harmonic vs quo-harmonic coordinates

To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of time-like congruences and corresponding adapted coordinates: the harmonic and quo-harmonic classes. Besides the intrinsic definition and some of their intrinsic properties and differences we consider with some detail their differences at the level of the linearized approximation of the field equations. The hard part of this paper is an explicit and general determination of the harmonic and quo-harmonic coordinates adapted to the stationary character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to order five of their asymptotic expansions. It also contains some relevant remarks on such problems as defining the multipoles of vacuum solutions or matching interior and exterior solutions.Comment: 27 pages, no figure

Ambipolar Nernst effect in NbSe2_2

The first study of Nernst effect in NbSe$_2$ reveals a large quasi-particle contribution with a magnitude comparable and a sign opposite to the vortex signal. Comparing the effect of the Charge Density Wave(CDW) transition on Hall and Nernst coefficients, we argue that this large Nernst signal originates from the thermally-induced counterflow of electrons and holes and indicates a drastic change in the electron scattering rate in the CDW state. The results provide new input for the debate on the origin of the anomalous Nernst signal in high-T$_c$ cuprates.Comment: 5 pages including 4 figure

Conserved Matter Superenergy Currents for Hypersurface Orthogonal Killing Vectors

We show that for hypersurface orthogonal Killing vectors, the corresponding Chevreton superenergy currents will be conserved and proportional to the Killing vectors. This holds for four-dimensional Einstein-Maxwell spacetimes with an electromagnetic field that is sourcefree and inherits the symmetry of the spacetime. A similar result also holds for the trace of the Chevreton tensor. The corresponding Bel currents have previously been proven to be conserved and our result can be seen as giving further support to the concept of conserved mixed superenergy currents. The analogous case for a scalar field has also previously been proven to give conserved currents and we show, for completeness, that these currents also are proportional to the Killing vectors.Comment: 13 page

Evidence for a new magnetic field scale in CeCoIn5

The Nernst coefficient of CeCoIn5 displays a distinct anomaly at H_K ~ 23 T. This feature is reminiscent of what is observed at 7.8 T in CeRu2Si2, a well-established case of metamagnetic transition. New frequencies are observed in de Haas-van Alphen oscillations when the field exceeds 23 T, which may indicate a modification of the Fermi surface at this field.Comment: submitted to Physical Review Letter

Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case when we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein-Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.Comment: 15 page

Cosmology in the Solar System: Pioneer effect is not cosmological

Does the Solar System and, more generally, a gravitationally bound system follow the cosmic expansion law ? Is there a cosmological influence on the dynamics or optics in such systems ? The general relativity theory provides an unique and unambiguous answer, as a solution of Einstein equations with a local source in addition to the cosmic fluid, and obeying the correct (cosmological) limiting conditions. This solution has no analytic expression. A Taylor development of its metric allows a complete treatment of dynamics and optics in gravitationally bound systems, up to the size of galaxy clusters, taking into account both local and cosmological effects. In the solar System, this provides an estimation of the (non zero) cosmological influence on the Pioneer probe: it fails to account for the " Pioneer effect " by about 10 orders of magnitude. We criticize contradictory claims on this topic

The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy

We calculate the instantaneous proper radial acceleration of test particles (as measured by a locally defined Lorentzian observer) in a Weyl spacetime, close to the horizon. As expected from the Israel theorem, there appear some bifurcations with respect to the spherically symmetric case (Schwarzschild), which are explained in terms of the behaviour of the superenergy, bringing out the physical relevance of this quantity in the study of general relativistic systems.Comment: 14 pages, Latex. 4 figures. New references added. Typos corrected. To appear in Int. J. Theor. Phy

The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on closed form, we settle with giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a $C$-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally $C$-spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12

Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec. 3.2.3 in the Supplement making connection to the post-Newtonian approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled) Supplement; references updated. The Supplement is provided in ancillary file. Matches the final published versio

Dynamical laws of superenergy in General Relativity

The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in General Relativity has remained obscure and no interpretation has achieved wide acceptance. In principle, they cannot represent {\em energy} and the term {\em superenergy} has been coined for the hypothetical physical magnitude lying behind them. In this work we try to shed light on the true physical meaning of {\em superenergy} by following the same procedure which enables us to give an interpretation of the electromagnetic energy. This procedure consists in performing an orthogonal splitting of the Bel and Bel-Robinson tensors and analysing the different parts resulting from the splitting. In the electromagnetic case such splitting gives rise to the electromagnetic {\em energy density}, the Poynting vector and the electromagnetic stress tensor, each of them having a precise physical interpretation which is deduced from the {\em dynamical laws} of electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel and Bel-Robinson tensors is more complex but, as expected, similarities with electromagnetism are present. Also the covariant divergence of the Bel tensor is analogous to the covariant divergence of the electromagnetic energy-momentum tensor and the orthogonal splitting of the former is found. The ensuing {\em equations} are to the superenergy what the Poynting theorem is to electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more acknowledgments added. To appear in Classical and Quantum Gravit