# Cesar S. Lopez-MonsalvoMetropolitan Autonomous University | UAM · Departamento de Ciencias Básicas

Cesar S. Lopez-Monsalvo

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

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

September 2011 - present

November 2007 - April 2011

Education

October 2007 - May 2011

October 2006 - September 2007

August 1999 - June 2004

## Publications

Publications (46)

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...

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...

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...

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...

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...

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,...

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.

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...

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...

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...

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.

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...

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.

We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of motion. We analyze their Lorentzian counterparts as well.

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...

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,...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

## Projects

Projects (3)

To obtain applications of contact geometric techniques in material science and its intertwining with gravitational theory and optics.

Understanding the general mathematical features of contact Hamiltonian systems, together with their applications to physics (classical and quantum), control theory and science in general.

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.