arXiv subjects

Francisco Nettel

Publications and source records attributed to Francisco Nettel.

At least 19 recordsLinked to original sources

arXiv2025

Gravitational wave polarization modes and the kinematical tensors in general relativity and beyond

Relations between the kinematical tensors (the expansion, the shear, and the vorticity) and the polarization modes of gravitational waves are studied within the context of metric theories of gravity by considering freely falling test particles. After analyzing exact relations, we consider slowly moving particles under the influence of a weak gravitational field. Linearized plane waves of theories representative of those determined by a general second-order Lagrangian, including General Relativity, are shown to exemplify the following interconnections: between the transverse components of the shear and the transverse tensor polarization mode; between the expansion, and both the transverse scalar and the longitudinal polarization modes; and between the longitudinal-transverse components of both the shear and the vorticity, and the vector polarization mode. These relations, from the theoretical point of view, offer a novel insight into the interpretation of the polarization modes in terms of the kinematical tensors. Additionally, the inclusion of the kinematical tensors in the study of gravitational waves might provide a new outlook on their phenomenology.

gr-qc↗

arXiv2024

GKLS Vector Field Dynamics for Gaussian States

We construct the vector field associated to the GKLS generator for systems described by Gaussian states. This vector field is defined on the dual space of the algebra of operators, restricted to operators quadratic in position and momentum. It is shown that the GKLS dynamics accepts a decomposition principle, that is, this vector field can be decomposed in three parts, a conservative Hamiltonian component, a gradient-like, and a Choi-Kraus or jump vector field. The two last terms are considered a "perturbation" associated with dissipation. Examples are presented for a harmonic oscillator with different dissipation terms.

quant-ph↗

arXiv2022

Darker and brighter branes: Suppression and enhancement of photon production in a strongly coupled magnetized plasma

We extend our holographic analysis of the emission of photons by a strongly coupled plasma subject to a very intense external magnetic field. We previously showed that in a particular model, any photon produced by the plasma had to be in its only polarization state parallel to the reaction plane. In this paper we consider a construction that relaxes a formerly imposed constraint, permitting the emission of photons with either out-plane or in-plane polarization. This constitutes a completion of our former study because the fully back-reacted equations decouple for these two polarization states in such a manner that those involving the in-plane are identical to the ones we explored previously. In view of the above, part of the details concerning the calculations and of the numerical results for the differential rate of emitted photons that we present here correspond exactly to those omitted in our preceding letter. One of our main results is that the production of photons is increased by the introduction of a non-vanishing magnetic field with an intensity up to a value $B_{\vartheta}$, above which the effect is reversed and said production becomes lower than the $B=0$ case. The characteristic intensity $B_{\vartheta}$ depends on the propagation direction and tends to zero as the photon momentum becomes aligned with the magnetic field. Additionally, we also show that the magnetic field has the effect of increasing the value of the elliptic flow, providing a possible explanation for the excess measured in collision experiments. The holographic model is constructed using an effective five-dimensional action that includes a scalar field in addition to the constant magnetic field.

hep-th↗

arXiv2021

Emission of linearly polarized photons in a strongly coupled magnetized plasma from the gauge/gravity correspondence

We use holographic methods to show that photons emitted by a strongly coupled plasma subject to a magnetic field are linearly polarized regardless of their four-momentum, except when they propagate along the field direction. The gravitational dual is constructed using a 5D truncation of 10-dimensional type IIB supergravity, and includes a scalar field in addition to the constant magnetic one. In terms of the geometry of the collision experiment that we model, our statement is that any photon produced there has to be in its only polarization state parallel to the reaction plane.

hep-th↗

arXiv2020

Reparametrizations and metric structures in thermodynamic phase space

We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase space are related to thermodynamic equilibrium and statistical fluctuations in the Boltzmann-Gibbs statistical mechanics. The physical motivation for this analysis rests upon the possibility of having, instead of a direct control of the intensive parameters determining the state of the corresponding physical reservoirs, the control of a set of differentiable functions of the original variables. Likewise, we consider a set of differentiable functions of the extensive variables accounting for the possibility of not having direct access to the original variables. We find that the effect of reparametrizations on the thermodynamic phase space can be codified, in geometrical terms, in its contact and Riemannian structures. In particular, we single out a rank-two tensor that enters in the definition of the metric which geometrically comprises the information about such reparametrizations. We notice that even if these geometric structures are modified by the reparametrizations, the metric structure on the thermodynamic space of equilibrium states is preserved.

math-ph↗

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

The zeroth law in quasi-homogeneous thermodynamics and black holes

Motivated by black holes thermodynamics, we consider the zeroth law of thermodynamics for systems whose entropy is a quasi-homogeneous function of the extensive variables. We show that the generalized Gibbs-Duhem identity and the Maxwell construction for phase coexistence based on the standard zeroth law are incompatible in this case. We argue that the generalized Gibbs-Duhem identity suggests a revision of the zeroth law which in turns permits to reconsider Maxwell's construction in analogy with the standard case. The physical feasibility of our proposal is considered in the particular case of black holes.

gr-qc↗

arXiv2017

Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.

gr-qc↗

arXiv2017

Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case

In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [arXiv:gr-qc/0611024] that Finsler geometry can provide some generalization of Riemannian geometry which may allow to account for non-trivial (Planckian) structure of relativistic particles' configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of Finsler geometry. We take into account the general strategy of analysis of modifications of dispersion relations in curved spacetimes proposed in [arXiv:1507.02056], generalizing to the de Sitter case the results obtained in [arXiv:1407.8143], for deformed relativistic particle kinematics in flat spacetime using Finsler formalism.

gr-qc↗

arXiv2016

UV dimensional reduction to two from group valued momenta

We describe a new model of deformed relativistic kinematics based on the group manifold $U(1) \times SU(2)$ as a four-momentum space. We discuss the action of the Lorentz group on such space and and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by {\it two} energy scales $λ$ and $κ$. A relevant feature of the model is that it exhibits a running spectral dimension $d_s$ with the characteristic short distance reduction to $d_s =2$ found in most quantum gravity scenarios.

hep-th↗

arXiv2016

Deformed phase spaces with group valued momenta

We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the $n$-dimensional generalization of the $κ$-deformed momentum space and the $SL(2, \mathbb{R})$ momentum space in three space-time dimensions. We discuss classical momentum observables associated to multi-particle systems and argue that these combine according the usual four-vector addition despite the non-abelian group structure of momentum space.

hep-th↗

arXiv2015

Topological quantization of gravitational fields as generalized harmonic maps

We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to the Einstein field equations as generalized strings, where the base space for the generalized harmonic map is a two-dimensional manifold. The results obtained here point to an incompatibility of the classical description of the gravitational field and its symmetries with a discretization of the parameters that enter in its description.

math-ph↗

arXiv2014

Thermodynamic curvature and ensemble nonequivalence

In this work we consider thermodynamic geometries defined as Hessians of different potentials and derive some useful formulae that show their complementary role in the description of thermodynamic systems with two degrees of freedom that show ensemble nonequivalence. From the expressions derived for the metrics, we can obtain the curvature scalars in a very simple and compact form. We explain here the reason why each curvature scalar diverges over the line of divergence of one of the specific heats. This application is of special interest in the study of changes of stability in black holes as defined by Davies. From these results we are able to prove on a general footing a conjecture first formulated by Liu, Lü, Luo and Shao stating that different Hessian metrics can correspond to different behaviors in the various ensembles. We study the case of two thermodynamic dimensions. Moreover, comparing our result with the more standard turning point method developed by Poincaré, we obtain that the divergence of the scalar curvature of the Hessian metric of one potential exactly matches the change of stability in the corresponding ensemble.

math-ph↗

arXiv2014

Brighter Branes, enhancement of photon production by strong magnetic fields in the gauge/gravity correspondence

We use the gauge/gravity correspondence to calculate the rate of photon production in a strongly coupled N=4 plasma in the presence of an intense magnetic field. We start by constructing a family of back reacted geometries that include the black D3-brane solution, as a smooth limiting case for B=0, and extends to backgrounds with an arbitrarily large constant magnetic field. This family provides the gravitational dual of a field theory in the presence of a very strong magnetic field which intensity can be fixed as desired and allows us to study its effect on the photon production of a quark-gluon plasma. The inclusion of perturbations in the electromagnetic field on these backgrounds is consistent only if the metric is perturbed as well, so we use methods developed to treat operator mixing to manage these general perturbations. Our results show a clear enhancement of photon production with a significant anisotropy, which, in qualitative agreement with the experiments of heavy ion collisions, is particularly noticeable for low P.

hep-th↗

arXiv2013

The conformal metric structure of Geometrothermodynamics

We present a thorough analysis on the invariance of the most widely used metrics in the Geometrothermodynamics (GTD) programme. We centre our attention in the invariance of the curvature of the space of equilibrium states under a change of fundamental representation. Assuming that the systems under consideration can be described by a fundamental relation which is a homogeneous function of a definite order, we demonstrate that such invariance is only compatible with total Legendre transformations in the present form of the programme. We give the explicit form of a metric which is invariant under total Legendre transformations and whose induced metric produces a curvature which is independent of the fundamental representation. Finally, we study a generic system with two degrees of freedom and whose fundamental relation is homogeneous of order one.

math-ph↗

arXiv2012

Topological quantization of the free massive bosonic field

We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric representation of this physical system. We take as a concrete example the case of free massive bosonic fields in two dimensions represented by the minimal embedding of a two dimensional surface into a pp-wave spacetime. We use this geometric representation to construct the fiber bundle corresponding to some specific field configurations and then find their topological spectra, defined in terms of the Euler invariant. We discuss the results for some particular configurations and their consequences for the energy of the system.

math-ph↗

arXiv2011

Topological discretization of bosonic strings

We apply the method of topological quantization to obtain the bosonic string topological spectrum propagating on a flat background. We define the classical configuration of the system, and construct the corresponding principal fiber bundle (pfb) that uniquely represents it. The topological spectrum is defined through the characteristic class of the pfb. We find explicit expressions for the topological spectrum for particular configurations of the bosonic strings on a Minkowski background and show that they lead to a discretization of the total energy of the system.

math-ph↗

arXiv2008

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.

math-ph↗