Cesar S. Lopez-Monsalvo

Cesar S. Lopez-Monsalvo
Metropolitan Autonomous University | UAM · Departamento de Ciencias Básicas

Dr
Working on applications of contact geometry in material science and gravity.

About

46
Publications
4,068
Reads
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371
Citations
Citations since 2016
21 Research Items
251 Citations
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2016201720182019202020212022010203040
Introduction
At the moment we are joining efforts in building a set of applications of contact geometry in mathematical physics at the various boundaries of multidisciplinary research, in particular, gravity, electrodynamics, material science and geometric control theory.
Additional affiliations
September 2015 - present
Metropolitan Autonomous University
Position
  • Conacyt research Fellow
September 2011 - present
Universidad Nacional Autónoma de México
Position
  • PostDoc Position
November 2007 - April 2011
University of Southampton
Position
  • PhD
Education
October 2007 - May 2011
University of Southampton
Field of study
  • General Relativity
October 2006 - September 2007
Imperial College London
Field of study
  • Quantum Fields and Fundamental Forces
August 1999 - June 2004

Publications

Publications (46)
Article
In this work we analyze several aspects of the application of contact geometry to thermodynamics. We first investigate the role of gauge transformations and Legendre symmetries in thermodynamics, with respect to both the contact and the metric structures. Then we present a novel mathematical characterization of first order phase transitions as equi...
Article
Full-text available
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bon...
Preprint
Full-text available
In this manuscript we provide a fully geometric formulation for the constitutive relations and their corresponding induced electromagnetic fields in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general differential form language. Here, we c...
Article
In this work we show that a Legendre transformation is nothing but a mere change of contact polarization from the point of view of contact geometry. Then, we construct a set of Riemannian and pseudo-Riemannian metrics on a contact manifold by introducing almost contact and para-contact structures and we analyze their isometries. We show that it is...
Article
Full-text available
The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in part...
Article
In this work, we show that the orthogonality between rays and fronts of light propagation in a medium is expressed in terms of a suitable metric contact structure of the optical medium without boundaries. Moreover, we show that considering interfaces (modeled as boundaries), orthogonality is no longer fulfilled, leading to optical aberrations and,...
Preprint
Full-text available
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
Preprint
In this work, we use the fact that kinematics of light propagation in a non-dispersive medium associated with a bi-metric spacetime is expressed by means of a 1-parameter family of contact transformations. We present a general technique to find such transformations and explore some explicit examples for Minkowski and anti-deSitter spacetimes geomet...
Article
Full-text available
A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to...
Preprint
Full-text available
In this work, we use the geometric equivalence between Fermat's and Huygens' principles to show that the kinematics of light propagation in a non-dispersive medium associated with a bi-metric spacetime is expressed by means of a 1-parameter family of contact transformations. We present a general technique to find such transformations and explore so...
Article
Full-text available
We show that the three-dimensional Thurston geometries are vacuum solutions to the 3D new massive gravity equations of motion. We analyze their Lorentzian counterparts as well.
Preprint
A central problem in General Relativity is obtaining a solution to describe the source's interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by Newman-Janis to gene...
Preprint
Full-text available
We present a concise definition of an electromagnetic curve on a Riemannian manifold and illustrate the explicit case of the motion of a charged particle on the unit sphere under the influence of a uniform magnetic field.
Preprint
Full-text available
We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of motion. We analyze their Lorentzian counterparts as well.
Preprint
Full-text available
A class of three dimensional contact manifolds is shown to describe certain types of superconductors. Specializing to a particular para-Sasakian metric on the three-sphere shows it to be a vacuum solution of three-dimensional massive gravity. The geometry is Lorentzian and the manifold enjoys local isometry given by the Heisenberg algebra. The back...
Article
Full-text available
In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general language of differential forms. Then,...
Preprint
In this work we show that a Legendre transformation is nothing but a mere change of symplectic polarization from the point of view of contact geometry. Then, we construct a set of Riemannian and pseudo-Riemannian metrics on a contact manifold by introducing almost contact and para-contact structures and we analyze their isometries. We show that it...
Article
Full-text available
In this work, it is shown that it is possible to operate a wind energy conversion system (WECS) based on a doubly fed induction generator while operating in a different mode than maximum power tracking. Here, using the recent results on the steady state solution of the torque balance transcendental equation, analytical expressions for all the state...
Article
When a wind energy conversion system (WECS) based on a doubly fed induction generator is operating in a different mode than maximum power tracking, there exist two different modes of operation. Here, it is shown that such modes satisfy the torque balance condition between the WECS and the electric network, which is described by a transcendental equ...
Article
Full-text available
The desire to understand physiological mechanisms of neuronal systems has led to the introduction of engineering concepts to explain how the brain works. The synchronization of neurons is a central topic in understanding the behavior of living organisms in neurosciences and has been addressed using concepts from control engineering. We introduce a...
Article
Full-text available
In this work 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. Besides, we argue that the generalized Gi...
Article
Full-text available
The aim of the present manuscript is to present a novel proposal in Geometric Control Theory inspired in the principles of General Relativity and energy-shaping control.
Article
In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols...
Article
Full-text available
We present a relativistic model describing a thin disk system composed of two fluids. The system is surrounded by a halo in the presence of a non-trivial electromagnetic field. We show that the model is compatible with the variational multi-fluid thermodynamics formalism, allowing us to determine all the thermodynamic variables associated with the...
Article
Full-text available
In this work we consider conformal gauge transformations of the geometric structure of thermodynamic fluctuation theory. In particular, we show that the Thermodynamic Phase Space is naturally endowed with a non-integrable connection, defined by all those processes that annihilate the Gibbs 1-form, i.e. reversible processes. Therefore the geometry o...
Article
Full-text available
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bon...
Article
Full-text available
In this work we tie concepts derived from statistical mechanics, information theory and contact Riemannian geometry within a single consistent formalism for thermodynamic fluctuation theory. We derive the concrete relations characterizing the geometry of the Thermodynamic Phase Space stemming from the relative entropy and the Fisher-Rao information...
Article
Full-text available
The work within the Geometrothermodynamics programme rests upon the metric structure for the thermodynamic phase-space. Such structure exhibits discrete Legendre symmetry. In this work, we study the class of metrics which are invariant along the infinitesimal generators of Legendre transformations. We solve the Legendre-Killing equation for a $K$-c...
Conference Paper
Full-text available
Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the pr...
Article
Full-text available
The thermodynamics of Maxwell-Dilaton (dirty) black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for...
Article
Full-text available
In this work we give a characterisation of first order phase transitions as equilibrium processes on the thermodynamic phase space for which the Legendre symmetry is broken. Furthermore, we consider generalised theories of thermodynamics, where the potential is a homogeneous function of any order $\beta$ and we propose a (contact) Hamiltonian formu...
Article
In this work we employ a recently devised metric within the Geometrothermodynamics program to study ordinary thermodynamic systems. The new feature of this metric is that, in addition to Legendre symmetry, it exhibits invariance under a change of representation. This metric was derived in a previous work by the authors while addressing the problem...
Article
Full-text available
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 re...
Article
Full-text available
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial...
Article
Full-text available
We present an exact, axially symmetric, static, vacuum solution for $f(R)$ gravity in Weyl's canonical coordinates. We obtain a general explicit expression for the dependence of $df(R)/dR$ upon the $r$ and $z$ coordinates and then the corresponding explicit form of $f(R)$, which must be consistent with the field equations. We analyze in detail the...
Article
Full-text available
We comment on the conclusions found by Larra\~naga and Mojica regarding the consistency of the Geoemtrothermodynamics programme to describe the critical behaviour of a Gibbons-Maeda-Garfinkle-Horowitz-Strominger charged black hole. We argue that making the appropriate choice of metric for the thermodynamic phase space and, most importantly, conside...
Article
Full-text available
This thesis deals with the dynamics of irreversible processes within the context of the general theory of relativity. In particular, we address the problem of the 'infinite' speed of propagation of thermal disturbances in a dissipative fluid. The present work builds on the multi-fluid variational approach to relativistic dissipation, pioneered by C...
Article
Full-text available
This paper revisits the problem of heat conduction in relativistic fluids, associated with issues concerning both stability and causality. It has long been known that the problem requires information involving second order deviations from thermal equilibrium. Basically, any consistent first-order theory needs to remain cognizant of its higher-order...
Article
Full-text available
The non-equilibrium thermodynamics of relativistic systems have a rich phenomenology. The simplest phenomenon in the class of dissipative processes is that of heat. This letter presents a brief summary of the efforts made to tackle the problem of relativistic heat conduction. In particular, we focus on the multi-fluid approach to relativistic dissi...
Article
Full-text available
We study the (local) propagation of plane waves in a relativistic, non- dissipative, two-fluid system, allowing for a relative velocity in the “background” configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow—either across an interface or when two or more fluids interpenetrate—and...
Article
Full-text available
We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy caus...
Article
Full-text available
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the we...
Article
Full-text available
We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $\lambda=\alpha R_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields (\alpha = 4 \pi^2 / \ln(2)) and a to...

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Projects

Projects (3)
Project
To obtain applications of contact geometric techniques in material science and its intertwining with gravitational theory and optics.
Project
Understanding the general mathematical features of contact Hamiltonian systems, together with their applications to physics (classical and quantum), control theory and science in general.
Project
We study relativistic models describing a disk surrounded by a halo in the presence of an electromagnetic field. The models are obtained by solving the Einstein-Maxwell equations using a distributional approach for the energy-momentum tensor.