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Enrique Álvarez

Publications and source records attributed to Enrique Álvarez.

At least 19 recordsLinked to original sources
arXiv2025

Some aspects of QFT in non-inertial frames

Some aspects of quantum field theory in a general (i.e. non inertial) frame of Minkowski spacetime are studied. Conditions for the presence of horizons as well as for the modification of the definition of positive energy solutions are examined. The standard wisdom is confirmed that none of these phenomena is generic. This corroborates that in the general case there is no natural way to define positive frequencies, which is the standard road to define particles. In that sense, (as well as in others) non inertial frames are similar to curved spacetimes.

hep-th↗
arXiv2024

Some consequences of the Kerr-Schild gauge

Generalized Kerr-Schild nilpotent deformations of an arbitrary background spacetime $\overline{g}_{\m\n}(x)$ are considered. Those are of the form $\overline{g}_{\m\n}+l_\m l_\n$ with $l^2=0$. The relationship between the Ricci tensor of the background metric and the Ricci tensor of the deformed metric is found exactly. It consists of two terms, one is essentially the Fierz-Pauli operator, and the other is new. When the background is flat, the Kerr-Schild family is recovered. Novel examples for more general backgrounds (even including some simple sources) are discussed.

gr-qc↗
arXiv2024

The origin of the cosmological constant

It is well-known that in unimodular gravity the cosmological constant is not sourced by a constant energy density, but rather appears as some sort of integration constant. In this work we try to flesh this out by studying in some detail a couple of examples, one from cosmology and the other from gravitational collapse.

hep-th↗
arXiv2024

Superposition of gravitational fields

Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.

gr-qc↗
arXiv2023

The quantum dynamics of Lagrange multipliers

When implementing a non-linear constraint in quantum field theory by means of a Lagrange multiplier, $ł(x)$, it is often the case that quantum dynamics induce quadratic and even higher order terms in $ł(x)$, which then does not enforce the constraint anymore. This is illustrated in the case of Unimodular Gravity, where the constraint is that the metric tensor has to be unimodular ($g(x)\equiv \det\,g_{\m\n}(x)=-1$).

hep-th↗
arXiv2023

A Primer on Unimodular Gravity

This chapter provides an introduction to Unimodular Gravity both at the classical and quantum level, discussing the rôle it might play in the partial solution of the Cosmological Constant problem. The main objective of this work is to serve as a conceptual introduction to Unimodular gravity without disregarding computational detail. In that sense, techniques used at the research level are presented and applied in detail.

gr-qc↗
arXiv2023

Variations on the Goroff-Sagnotti operator

The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of motion, assuming it to be spherically symmetric, not necessarily static. Even in the non-spherically symmetric case, we present a necessary condition for an algebraically generic spacetime to solve the corresponding equations of motion. Some examples of an application of said condition are explicitly worked out.

gr-qc↗
arXiv2023

The fate of horizons under quantum corrections

We have studied a lagrangian in which the Einstein-Hilbert term is deformed by the Weyl cube operator, which is the lowest-dimension operator that is non-vanishing on shell and appears as a two-loop counterterm. There is a tension between the Schwarzschild de Sitter (SdS) spacetime and this operator, which we study in some detail.

hep-th↗
arXiv2022

Orbital instability of periodic waves for scalar viscous balance laws

The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital (nonlinear) instability in appropriate periodic Sobolev spaces. The analysis is based on the well-posedness theory, the smoothness of the data-solution map, and an abstract result of instability of equilibria under nonlinear iterations. The resulting instability criterion is applied to two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a local Hopf bifurcation around a critical value of the velocity. The second family comprises arbitrarily large period waves which arise from a homoclinic (global) bifurcation and tend to a limiting traveling pulse when their fundamental period tends to infinity. In the case of both families, the criterion is applied to conclude their orbital instability under the flow of the nonlinear viscous balance law in periodic Sobolev spaces with same period as the fundamental period of the wave.

math.AP↗
arXiv2022

Divergences of the scalar sector of quadratic gravity

The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties are analyzed.

hep-th↗
arXiv2021

Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source

A hyperbolic model for diffusion, nonlinear transport (or advection) and production of a scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwell type expressing non-Fickian diffusion by means of a relaxation time relation. The production or source term is assumed to be of logistic type. This paper studies the existence and spectral stability properties of spatially periodic traveling wave solutions to this system. It is shown that a family of subcharacteristic periodic waves emerges from a local Hopf bifurcation around a critical value of the wave speed. These waves have bounded fundamental period and small-amplitude. In addition, it is shown that these waves are spectrally unstable as solutions to the hyperbolic system. For that purpose, it is proved that the Floquet spectrum of the linearized operator around a wave can be approximated by a linear operator whose point spectrum intersects the unstable half plane of complex numbers with positive real part.

math.AP↗
arXiv2021

Some comments on the Hamiltonian for Unimodular Gravity

Several alternative formulations of the first order approach to unimodular gravity are presented. There is always a particular one such that it is {\em classically} equivalent to the second order formulation; this we call {\em educated}. It is often at variance with the {\em naive} approach, in which the lagrangian is taken as given exactly by the same expression as in the second order formulation; only the number and character of the independent variables changes. Namely, typically some of the momenta are now considered as coordinates. The ensuing Hamiltonians are thereby discussed and their physical differences pointed out.

gr-qc↗
arXiv2016

Conformal Dilaton Gravity: Classical Noninvariance Gives Rise To Quantum Invariance

When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory has been determined using only conformal invariance . Those finite counterterms do not have any inverse power of any mass scale in front of them (precisely because of conformal invariance) and then they are not negligible in the low energy deep infrared limit. The general form of the ensuing modifications to the scalar field equation of motion has been determined and some physical consequences extracted.

hep-th↗
arXiv2015

Quantum Corrections to Unimodular Gravity

The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.

hep-th↗
arXiv2015

First Order formulation of Unimodular Gravity

First order lagrangians for the Weyl invariant formulation of Unimodular Gravity are proposed. Several alternatives are examined; in some of them first and second order are equivalent in a certain gauge only.

hep-th↗
arXiv2015

Some Cosmological Consequences of Weyl Invariance

We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of $N$ conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime metric is assumed, the Ward identity for conformal invariance guarantees that the gravitational equations hold whenever the scalar fields EM do so. It follows that any scale factor can solve the theory provided a non-trivial profile for a dilaton field. In particular, accelerated expansion is a natural solution to the full set of equations.

hep-th↗
arXiv2013

No Conformal Anomaly in Unimodular Gravity

The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor enjoys unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is consistent as well.

hep-th↗