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Hernando Quevedo

Publications and source records attributed to Hernando Quevedo.

At least 163 records · Page 9Linked to original sources
arXiv2008

Geometrothermodynamics of asymptotically anti - de Sitter black holes

We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as true curvature singularities. We interpret this as a further indication that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

hep-th↗
arXiv2008

Towards the topological quantization of classical mechanics

We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis' formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be associated with a principal fiber bundle. As an application of topological quantization we derive expressions for the topological spectra of some simple mechanical systems and show that they reproduce the discrete behavior of the corresponding canonical spectra.

math-ph↗
arXiv2007

The geometry of thermodynamics

We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre invariant metric, which is given in terms of the fundamental equation of the corresponding thermodynamic system, and analyze its geometric properties in the case of the van der Waals gas, and black holes. We conclude that the geometry of this particular metric reproduces the thermodynamic behavior of the van der Waals gas, and the Reissner-Nordström black hole, but it is not adequate for the thermodynamic description of Kerr black holes.

math-ph↗
arXiv2007

Topological spectrum of classical configurations

For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a principle fiber bundle that contains all the physical and geometric information of the configuration. The topological spectrum follows from the investigation of the corresponding topological invariants. Examples are given which illustrate the procedure and the significance of the topological spectrum as a discretization relationship among the parameters that determine the physical meaning of classical configurations.

math-ph↗
arXiv2007

Geometrothermodynamics of black holes

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold's and Ruppeiner's thermodynamic metrics for black holes. For the Reissner-Nordström black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.

gr-qc↗
arXiv2007

Entropy and anisotropy

We address the problem of defining the concept of entropy for anisotropic cosmological models. In particular, we analyze for the Bianchi I and V models the entropy which follows from postulating the validity of the laws of standard thermodynamics in cosmology. Moreover, we analyze the Cardy-Verlinde construction of entropy and show that it cannot be associated with the one following from relativistic thermodynamics.

gr-qc↗
arXiv2006

Topological quantization of the harmonic oscillator

We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which can be assigned to any configuration of classical mechanics, when formulated according to Maupertuis formalism.

math-ph↗
arXiv2006

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.

physics.chem-ph↗
arXiv2006

Time paradox in Quantum Gravity

The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in quantum field theories which consider the Minkowski metric as the background spacetime. We discuss the problems which this non-dynamical concept of time causes in general relativity that is characterized by a dynamical spacetime.

gr-qc↗
arXiv2005

On the local Lorentz invariance in N=1 supergravity

We discuss the local Lorentz invariance in the context of N=1 supergravity and show that a previous attempt to find explicit solutions to the Lorentz constraint in terms of $γ-$matrices is not correct. We improve that solution by using a different representation of the Lorentz operators in terms of the generators of the rotation group, and show its compatibility with the matrix representation of the fermionic field. We find the most general wave functional that satisfies the Lorentz constraint in this representation.

gr-qc↗
arXiv2005

Pioneer's Anomaly and the Solar Quadrupole Moment

The trajectories of test particles moving in the gravitational field of a non-spherically symmetric mass distribution become affected by the presence of multipole moments. In the case of hyperbolic trajectories, the quadrupole moment of an oblate mass induces a displacement of the trajectory towards the mass source, an effect that can be interpreted as an additional acceleration directed towards the source. Although this additional acceleration is not constant, we perform a general relativistic analysis in order to evaluate the possibility of explaining Pioneer's anomalous acceleration by means of the observed Solar quadrupole moment, within the range of accuracy of the observed anomalous acceleration. We conclude that the Solar quadrupole moment generates an acceleration which is of the same order of magnitude of Pioneer's constant acceleration only at distances of a few astronomical units.

gr-qc↗
arXiv2005

Gowdy $T^3$ Cosmological Models in N=1 Supergravity

We investigate the canonical quantization of supergravity N=1 in the case of a midisuperspace described by Gowdy $T^3$ cosmological models. The quantum constraints are analyzed and the wave function of the universe is derived explicitly. Unlike the minisuperspace case, we show the existence of physical states in midisuperspace models. The analysis of the wave function of the universe leads to the conclusion that the classical curvature singularity present in the evolution of Gowdy models is removed at the quantum level due to the presence of the Rarita-Schwinger field.

gr-qc↗
arXiv2005

The field-to-particle transition problem

We formulate in an intuitive manner several conceptual aspects of the field-to-particle transition problem which intends to extract physical properties of elementary particles from specific field configurations. We discuss the possibility of using the conceptual basis of the holographic principle and the mathematical fundaments of nonlinear sigma models for the field-to-particle transition. It is shown that certain classical gravitational configurations in vacuum may contain physical parameters with discrete values, and that they behave under rotations as particle-like objects.

gr-qc↗
arXiv2004

Acausality in Gowdy spacetimes

We present a parametrization of $T^3$ and $S^1\times S^2$ Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.

gr-qc↗
arXiv2004

Regular non-twisting S-branes

We construct a family of time and angular dependent, regular S-brane solutions which corresponds to a simple analytical continuation of the Zipoy-Voorhees 4-dimensional vacuum spacetime. The solutions are asymptotically flat and turn out to be free of singularities without requiring a twist in space. They can be considered as the simplest non-singular generalization of the singular S0-brane solution. We analyze the properties of a representative of this family of solutions and show that it resembles to some extent the asymptotic properties of the regular Kerr S-brane. The R-symmetry corresponds, however, to the general Lorentzian symmetry. Several generalizations of this regular solution are derived which include a charged S-brane and an additional dilatonic field.

hep-th↗
arXiv2004

Time and "angular" dependent backgrounds from stationary axisymmetric solutions

Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \times S^2$ Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized $S$-branes depending not only on time but also on an ``angular'' variable.

gr-qc↗
arXiv2004

Topological quantization of gravitational fields

We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordström and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships.

math-ph↗