arXiv subjects

Hernando Quevedo

Publications and source records attributed to Hernando Quevedo.

At least 91 records · Page 5Linked to original sources

arXiv2019

Charged Taub-NUT solution in Lovelock gravity with generalized Wheeler polynomials

Wheeler's approach to finding exact solutions in Lovelock gravity has been predominantly applied to static spacetimes. This has led to a Birkhoff's theorem for arbitrary base manifolds in dimensions higher than four. In this work, we generalize the method and apply it to a stationary metric. Using this perspective, we present a Taub-NUT solution in eight-dimensional Lovelock gravity coupled to Maxwell fields. We use the first-order formalism to integrate the equations of motion in the torsion-free sector. The Maxwell field is presented explicitly with general integration constants, while the background metric is given implicitly in terms of a cubic algebraic equation for the metric function. We display precisely how the NUT parameter generalizes Wheeler polynomials in a highly nontrivial manner.

gr-qc↗

arXiv2019

Extended Thermodynamics of Self-Gravitating Skyrmions

A modification of the hedgehog ansatz has recently led to novel exact black hole solutions with selfgravitating SU(2) Skyrme fields. Considering a negative cosmological constant the black holes are not asymptotically anti-de Sitter (AdS) but rather asymptote to an AdS version of Barriola--Vilenkin spacetime. We examine the thermodynamics of the system interpreting the cosmological constant as a bulk pressure. We use the standard counterterm method to obtain a finite Euclidean action. For a given coupling of the matter action, the system behaves as does a charged AdS black hole in the fixed charged ensemble. We find that in the limit case when the Skyrme model becomes a nonlinear sigma model the system exhibits a first order phase transition of Hawking--Page type. The universality class of these Einstein--Skyrme black holes is that of van der Waals.

gr-qc↗

arXiv2019

On the physical significance of geometrothermodynamic metrics

In geometrothermodynamics (GTD), to study the geometric properties of the equilibrium space three thermodynamic metrics have been proposed so far. These metrics are obtained by using the condition of Legendre invariance and can be computed explicitly once a thermodynamic potential is specified as the fundamental equation. We use the remaining diffeomorphism invariance in the phase and equilibrium spaces to show that the components of the GTD-metrics can be interpreted as the second moment of the fluctuation of a new thermodynamic potential. This result establishes a direct connection between GTD and fluctuation theory. In this way, the diffeomorphism invariance of GTD allows us to introduce new thermodynamic coordinates and new thermodynamic potentials, which are not related by means of Legendre transformations to the fundamental thermodynamic potentials.

math-ph↗

arXiv2019

Modified Chaplygin Gas Cosmology from Geometrothermodynamics

The modified Chaplygin gas (MCG) cosmological model is derived by using the geometrothermodynamics (GTD) formalism. We show that the MCG corresponds to a system with internal thermodynamic interaction and describes the current accelerated expansion of the universe. Moreover, we also show that the MCG can be interpreted as a unified model for dark energy and dark matter that is perfectly consistent with the current SNe observations and CMB anisotropy measurements.

gr-qc↗

arXiv2019

$C^3$ matching for asymptotically flat spacetimes

We propose a criterion for finding the minimum distance at which an interior solution of Einstein's equations can be matched with an exterior asymptotically flat solution. It is based upon the analysis of the eigenvalues of the Riemann curvature tensor and their first derivatives, implying $C^3$ differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the $C^3$ matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.

gr-qc↗

arXiv2018

Quasi-homogeneous black hole thermodynamics

Although the fundamental equations of ordinary thermodynamic systems are known to correspond to first-degree homogeneous functions, in the case of non-ordinary systems like black holes the corresponding fundamental equations are not homogeneous. We present several arguments, indicating that black holes should be described by means of quasi-homogeneous functions of degree different from one. In particular, we show that imposing the first-degree condition leads to contradictory results in thermodynamics and geometrothermodynamics of black holes. As a consequence, we show that in generalized gravity theories the coupling constants like the cosmological constant, the Born-Infeld parameter or the Gauss-Bonnet constant must be considered as thermodynamic variables.

gr-qc↗

arXiv2018

Statistical origin of Legendre invariant metrics

Legendre invariant metrics have been introduced in Geometrothermodynamics to take into account the important fact that the thermodynamic properties of physical systems do not depend on the choice of thermodynamic potential from a geometric perspective. In this work, we show that these metrics also have a statistical origin which can be expressed in terms of the average and variance of the differential of the microscopic entropy. To show this, we use a particular reparametrization of the coordinates of the corresponding thermodynamic phase space.

cond-mat.stat-mech↗

arXiv2018

Kinematic and statistical inconsistencies of Ho$\check{\textrm{r}}$ava-Lifshitz cosmology

We investigate the validity of a \emph{minimal} cosmological model derived from the renormalizable Ho$\check{\textrm{r}}$ava action at low redshift scales by using different cosmological and statistical tests. Assuming pure attractive gravity, i.e., $λ>1/3$ in the Ho$\check{\textrm{r}}$ava action, we compare the Union 2.1 supernova type Ia data with the kinematics following from a model-independent approach. The two approaches, although compatible, lead to explicit cosmographic constraints on the free parameters of the Ho$\check{\textrm{r}}$ava action, which turn out to be in strong disagreement with the $Λ$CDM, $w$CDM and Chevallier-Polarski-Linder scenarios. To show this, we use standard diagnostic tools of regression models, namely the Akaike and the Bayesian Information Criteria. Using such model-independent statistical methods, we show that Ho$\check{\textrm{r}}$ava-Lifshitz cosmology differs from the standard dark energy scenarios, \emph{independently} of the number of free parameters involved in the model. Since this result is valid at small redshift domains, it indicates the presence of inconsistencies in the minimal version of Ho$\check{\textrm{r}}$ava-Lifshitz cosmology even at the level of background cosmology.

gr-qc↗

arXiv2018

Chern Index of Taub-Bolt instantons in Einstein-Born-Infeld gravity

Partition functions can be calculated by saddle point approximations whenever regular solutions exist, as they dominate the path integral. We examine a regular Taub-Bolt dyon of Einstein-Born-Infeld theory which has electric and magnetic flux proportional to each other. Magnetic flux is found to be essentially a winding number and the electric flux turns out to be indexed by it.

hep-th↗

arXiv2018

Nonvalidity of I-Love-Q Relations for Hot White Dwarf Stars

The equilibrium configurations of uniformly rotating white dwarfs at finite temperatures are investigated, exploiting the Chandrasekhar equation of state for different isothermal cores. The Hartle-Thorne formalism is applied to construct white dwarf configurations in the framework of Newtonian physics. The equations of structure are considered in the slow rotation approximation and all basic parameters of rotating hot white dwarfs are computed to test the so-called moment of inertia, tidal Love number and quadrupole moment ($I$-Love-$Q$) relations. It is shown that even within the same equation of state the $I$-Love-$Q$ relations are not universal for white dwarfs at finite temperatures.

astro-ph.SR↗

arXiv2018

An effective model for inflation from geometrothermodynamics: a detailed analysis of thermodynamics and cosmological perturbations

Inflationary models usually assume the existence of scalar fields or other exotic gravitational sources. We investigate an alternative approach in which the entire Universe is considered as a thermodynamic system described by geometrothermodynamics. A particular van der Waals like fundamental equation is used to construct an effective inflationary model which is consistent with the main physical requirements, such as the number of e-foldings and the times for the onset and end of inflation, predicting in this way a volume of approximately $10^{-84}$ m$^3$ at the onset of inflation. The phase transition structure and thermodynamic behavior of the system are consistent with the expected properties of an inflationary scenario. Cosmological perturbations of the model are shown to be in agreement with the corresponding primordial power spectrum providing the seeds for the creation of large-scale structure.

gr-qc↗

arXiv2018

Non-extensive statistical mechanics of a self-gravitating gas

The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the generalized statistics of Tsallis and analyze the statistical and thermodynamical implications for a self-gravitating gas, obtaining analytical and convergent expressions for the equation of state and specific heat in the canonical as well as microcanonical ensembles. Although our results are comparable in both ensembles, it turns out that only in the canonical case the thermodynamic quantities depend explicitly on the non-extensivity parameter, indicating that the question of ensemble equivalence for Tsallis statistics must be further reviewed.

cond-mat.stat-mech↗

arXiv2018

Nonperturbative quantization à la Heisenberg and thermodynamics of monopole configurations

For field theories in which no small parameter is available, we propose a definition of nonperturbative quantum states in terms of the complete set of Green functions, based upon the utilization of Heisenberg's quantization procedure. We apply this method to obtain the energy spectra of a quantum monopole and of a flux tube. The partition function and thermodynamic quantities for one quantum monopole are evaluated numerically. A dilute gas of noninteracting quantum monopoles is considered, for which the partition function and thermodynamic quantities are evaluated as well. All the obtained statistical and thermodynamic functions contain quantum corrections associated with the internal structure of the quantum monopole.

hep-th↗

arXiv2017

Topological Quantum Numbers of Dyonic Fields over Taub-Bolt

We study the global structure of dyonic fields on a Taub-Bolt background, and compare our results with similar fields over Taub-NUT and Schwarzschild spaces. It is shown that the electric and magnetic charges are quantized and lead to a classification of dyonic Taub-Bolt configurations. The quantization condition for the magnetic charge is similar to that of Dirac's monopole.

gr-qc↗

arXiv2017

Can spacetime curvature be used in future navigation systems?

We argue that the curvature generated by a gravitational field can be used to calculate the corresponding metric which determines the trajectories of freely falling test particles. To this end, we present a method to compute the metric from a given curvature tensor. We use Petrov's classification to handle the structure and properties of the curvature tensor, and Cartan's structure equations in an orthonormal tetrad to investigate the differential equations that relate the curvature with the metric. The second structure equation is integrated to obtain the explicit expression for the connection $1-$form from which the components of the orthonormal tetrad are obtained by using the first structure equation. This opens the possibility of using the curvature of astrophysical objects like the Earth to determine the position of freely falling satellites that are used in modern navigation systems.

gr-qc↗

arXiv2017

Comparison of Vacuum Static Quadrupolar Metrics

We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analyzing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the $q-$metric, a variant of the Zipoy-Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter.

gr-qc↗

arXiv2017

Homogeneity and thermodynamic identities in geometrothermodynamics

We propose a classification of thermodynamic systems in terms of the homogeneity properties of their fundamental equations. Ordinary systems correspond to homogeneous functions and non-ordinary systems are given by generalized homogeneous functions. This affects the explicit form of the Gibbs-Duhem relation and Euler's identity. We show that these generalized relations can be implemented in the formalism of black hole geometrothermodynamics in order to completely fix the arbitrariness present in Legendre invariant metrics.

gr-qc↗

arXiv2016

Geometrothermodynamic model for the evolution of the Universe

Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic interaction, and show it to be equivalent to the standard $Λ$CDM paradigm. The second step includes thermodynamic interaction and produces a model consistent with the main features of inflation. With the proposed fundamental equation we are thus able to describe all the known epochs in the evolution of our Universe, starting from the inflationary phase.

gr-qc↗