Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

Class of Einstein--Maxwell Dilatons

Three different classes of static solutions of the Einstein--Maxwell equations non--minimally coupled to a dilaton field are presented. The solutions are given in general in terms of two arbitrary harmonic functions and involve among others an arbitrary parameter which determines their applicability as charged black holes, dilaton black holes or strings. Most of the known solutions are contained as special cases and can be non--trivially generalized in different ways.Comment: Published in Physical Review D, R310 (1995

Non-collinear magnetic structures: a possible cause for current induced switching

Current induced switching in Co/Cu/Co trilayers is described in terms of ab-initio determined magnetic twisting energies and corresponding sheet resistances. In viewing the twisting energy as an energy flux the characteristic time thereof is evaluated by means of the Landau-Lifshitz-Gilbert equation using ab-initio parameters. The obtained switching times are in very good agreement with available experimental data. In terms of the calculated currents, scalar quantities since a classical Ohm's law is applied, critical currents needed to switch magnetic configurations from parallel to antiparallel and vice versa can unambiguously be defined. It is found that the magnetoresistance viewed as a function of the current is essentially determined by the twisting energy as a function of the relative angle between the orientations of the magnetization in the magnetic slabs, which in turn can also explain in particular cases the fact that after having switched off the current the system remains in the switched magnetic configuration. For all ab-initio type calculations the fully relativistic Screened Korringa-Kohn-Rostoker method and the corresponding Kubo-Greenwood equation in the context of density functional theory are applied.Comment: 20 pages, 4 tables and 15 figures, submitted to PR

Gravitational fields as generalized string models

We show that Einstein's main equations for stationary axisymmetric fields in vacuum are equivalent to the motion equations for bosonic strings moving on a special nonflat background. This new representation is based on the analysis of generalized harmonic maps in which the metric of the target space explicitly depends on the parametrization of the base space. It is shown that this representation is valid for any gravitational field which possesses two commuting Killing vector fields. We introduce the concept of dimensional extension which allows us to consider this type of gravitational fields as strings embedded in D-dimensional nonflat backgrounds, even in the limiting case where the Killing vector fields are hypersurface orthogonal.Comment: latex, 25 page

Autonomic Nervous System characterization in hyperbaric environments considering respiratory component and non-linear analysis of Heart Rate Variability

Objectives: an evaluation of Principal Dynamic Mode (PDM) and Orthogonal Subspace Projection (OSP) methods to characterize the Autonomic Nervous System (ANS) response in three different hyperbaric environments was performed. Methods: ECG signals were recorded in two different stages (baseline and immersion) in three different hyperbaric environments: (a) inside a hyperbaric chamber, (b) in a controlled sea immersion, (c) in a real reservoir immersion. Time-domain parameters were extracted from the RR series of the ECG. From the Heart Rate Variability signal (HRV), classic Power Spectral Density (PSD), PDM (a non-linear analysis of HRV which is able to separate sympathetic and parasympathetic activities) and OSP (an analysis of HRV which is able to extract the respiratory component) methods were used to assess the ANS response. Results: PDM and OSP parameters follows the same trend when compared to the PSD ones for the hyperbaric chamber dataset. Comparing the three hyperbaric scenarios, significant differences were found: i) heart rate decreased and RMSSD increased in the hyperbaric chamber and the controlled dive, but they had the opposite behavior during the uncontrolled dive; ii) power in the OSP respiratory component was lower than power in the OSP residual component in cases a and c; iii) PDM and OSP methods showed a significant increase in sympathetic activity during both dives, but parasympathetic activity increased only during the uncontrolled dive. Conclusions: PDM and OSP methods could be used as an alternative measurement of ANS response instead of the PSD method. OSP results indicate that most of the variation in the heart rate variability cannot be described by changes in the respiration, so changes in ANS response can be assigned to other factors. Time-domain parameters reflect vagal activation in the hyperbaric chamber and in the controlled dive because of the effect of pressure. In the uncontrolled dive, sympathetic activity seems to be dominant, due to the effects of other factors such as physical activity, the challenging environment, and the influence of breathing through the scuba mask during immersion. In sum, a careful description of the changes in all the possible factors that could affect the ANS response between baseline and immersion stages in hyperbaric environments is needed for better interpretation of the results

Geometrothermodynamics

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy

Generating Gowdy cosmological models

Using the analogy with stationary axisymmetric solutions, we present a method to generate new analytic cosmological solutions of Einstein's equation belonging to the class of $T^3$ Gowdy cosmological models. We show that the solutions can be generated from their data at the initial singularity and present the formal general solution for arbitrary initial data. We exemplify the method by constructing the Kantowski-Sachs cosmological model and a generalization of it that corresponds to an unpolarized $T^3$ Gowdy model.Comment: Latex, 15 pages, no figure

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio

Dynamic exchange coupling and Gilbert damping in magnetic multilayers

We theoretically study dynamic properties of thin ferromagnetic films in contact with normal metals. Moving magnetizations cause a flow of spins into adjacent conductors, which relax by spin flip, scatter back into the ferromagnet, or are absorbed by another ferromagnet. Relaxation of spins outside the moving magnetization enhances the overall damping of the magnetization dynamics in accordance with the Gilbert phenomenology. Transfer of spins between different ferromagnets by these nonequilibrium spin currents leads to a long-ranged dynamic exchange interaction and novel collective excitation modes. Our predictions agree well with recent ferromagnetic-resonance experiments on ultrathin magnetic films.Comment: 15 pages, 3 figures, for MMM'02 proceeding

On the Thermodynamics of Simple Non-Isentropic Perfect Fluids in General Relativity

We examine the consistency of the thermodynamics of irrotational and non-isentropic perfect fluids complying with matter conservation by looking at the integrability conditions of the Gibbs-Duhem relation. We show that the latter is always integrable for fluids of the following types: (a) static, (b) isentropic (admits a barotropic equation of state), (c) the source of a spacetime for which $r\ge 2$, where $r$ is the dimension of the orbit of the isometry group. This consistency scheme is tested also in two large classes of known exact solutions for which $r< 2$, in general: perfect fluid Szekeres solutions (classes I and II). In none of these cases, the Gibbs-Duhem relation is integrable, in general, though specific particular cases of Szekeres class II (all complying with $r<2$) are identified for which the integrability of this relation can be achieved. We show that Szekeres class I solutions satisfy the integrability conditions only in two trivial cases, namely the spherically symmetric limiting case and the Friedman-Roberson-Walker (FRW) cosmology. Explicit forms of the state variables and equations of state linking them are given explicitly and discussed in relation to the FRW limits of the solutions. We show that fixing free parameters in these solutions by a formal identification with FRW parameters leads, in all cases examined, to unphysical temperature evolution laws, quite unrelated to those of their FRW limiting cosmologies.Comment: 29 pages, Plain.Te