Searcharxiv⌕ Search

arXiv subjects

Eduardo J. S. Villaseñor

Publications and source records attributed to Eduardo J. S. Villaseñor.

At least 19 recordsLinked to original sources
arXiv2026

From Holst to Carroll Gravity, a Hamiltonian point of view

The Carrollian regime of gravity provides a useful ultrarelativistic framework for studying asymptotically flat spacetimes, horizon dynamics, and condensed matter systems. In this paper, we present a comprehensive Hamiltonian analysis of the most general Carroll-invariant Lagrangian that can be derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.

gr-qc↗
arXiv2026

Husain-Kuchař model as the Carrollian limit of the Holst term

We show how the Husain-Kuchař model can be understood as a Carrollian limit of the Holst term in the context of background-independent field theories described in terms of coframes and spin connections. We also discuss the footprint of the Carrollian symmetry in the Hamiltonian formulation of the Husain-Kuchař action.

gr-qc↗
arXiv2025

Hidden diffeos in the Hamiltonian formulation of a background independent field theory

We analyze from a geometric perspective the Hamiltonian formulation of a recent modification of the Husain-Kuchař model where, while preserving the connection as a dynamical variable, the other field is restricted to be the exterior covariant derivative of a Lie algebra-valued function. We prove that 3-dimensional diffeomorphisms can be accommodated among the local gauge transformations of the model in addition to the internal gauge symmetries.

gr-qc↗
arXiv2024

Dynamical time and Ashtekar variables for the Husain-Kuchař model

The relation between the Husain-Kuchař model and some extensions thereof that incorporate a dynamical time variable is explored. To this end, we rely on the geometric approach to the Hamiltonian dynamics of singular (constrained) systems provided by the Gotay-Nester-Hinds method (GNH). We also use recent results regarding the derivation of the Ashtekar formulation for Euclidean general relativity without using the time gauge. The insights provided by the geometric approach followed in the paper shed light on several issues related to the dynamics of general relativity and the role of time.

gr-qc↗
arXiv2024

Euclidean self-dual gravity: Ashtekar variables without gauge fixing

The Gotay-Nester-Hinds method is used in this paper to study the Hamiltonian formulation of the Euclidean self-dual action. This action can be used to arrive at the complex Ashtekar formulation of General Relativity or a real connection formulation for Euclidean General Relativity. The main result of the paper is a derivation of the Ashtekar formulation for Euclidean gravity without using any gauge fixing. It is interesting to compare this derivation with the one corresponding to the Holst action. In particular it is worth noting that no "tertiary" constraints appear in the case considered in the present paper.

gr-qc↗
arXiv2024

Spacetime symmetries and geometric diffusion

We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold $(M,g)$. Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric solutions of the relativistic diffusion equation. Additionally, we analyze the conservation laws associated with the presence of Killing vector fields on $(M,g)$ and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we present several relevant examples of symmetric spacetimes.

gr-qc↗
arXiv2022

Edge observables of the Maxwell-Chern-Simons theory

We analyze the Lagrangian and Hamiltonian formulations of the Maxwell-Chern-Simons theory defined on a manifold with boundary for two different sets of boundary equations derived from a variational principle. We pay special attention to the identification of the infinite chains of boundary constraints and their resolution. We identify edge observables and their algebra [which corresponds to the well-known $U(1)$ Kac-Moody algebra]. Without performing any gauge fixing, and using the Hodge-Morrey theorem, we solve the Hamilton equations whenever possible. In order to give explicit solutions, we consider the particular case in which the fields are defined on a $2$-disk. Finally, we study the Fock quantization of the system and discuss the quantum edge observables and states.

hep-th↗
arXiv2022

Consistent and non-consistent deformations of gravitational theories

We study the internally abelianized version of a range of gravitational theories, written in connection tetrad form, and study the possible interaction terms that can be added to them in a consistent way. We do this for 2+1 dimensional and 3+1 dimensional models. In the latter case we show that the Cartan-Palatini and Holst actions are not consistent deformations of their abelianized versions. We also show that the Husain-Kuchař and Euclidean self-dual actions are consistent deformations of their abelianized counterparts. This suggests that if the latter can be quantized, it could be possible to devise a perturbative scheme leading to the quantization of Euclidean general relativity along the lines put forward by Smolin in the early nineties.

gr-qc↗
arXiv2022

On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

We study a generalization of the Holst action where we admit nonmetricity and torsion in manifolds with timelike boundaries (both in the metric and tetrad formalism). We prove that its space of solutions is equal to the one of the Palatini action. Therefore, we conclude that the metric sector is in fact identical to GR, which is defined by the Einstein-Hilbert action. We further prove that, despite defining the same space of solutions, the Palatini and (the generalized) Holst Lagrangians are not cohomologically equal. Thus, the presymplectic structure and charges provided by the Covariant Phase Space method might differ. However, using the relative bicomplex framework, we show the covariant phase spaces of both theories are equivalent (and in fact equivalent to GR), as well as their charges, clarifying some open problems regarding dual charges and their equivalence in different formulations.

gr-qc↗
arXiv2021

Three roads to the geometric constraint formulation of gravitational theories with boundaries

The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester, Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we will use a concrete example as a test bed: an extension of the Pontryagin and Husain-Kuchař actions to four dimensional manifolds with boundary.

gr-qc↗
arXiv2021

Covariant phase space for gravity with boundaries: metric vs tetrad formulations

We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting problem that we solve here by using the cohomological approach provided by the relative bicomplex framework. This setting provides a clean and ambiguity-free way to describe the solution spaces and associated symplectic structures. We also compute several relevant charges in both schemes and show that they are equivalent, as expected.

gr-qc↗
arXiv2021

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological approach provided by the relative bicomplex framework. Finally, we discuss some of the physical implications derived from this equivalence in the context of singularity identification through curvature invariants.

gr-qc↗
arXiv2021

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.

gr-qc↗
arXiv2021

Concise symplectic formulation for tetrad gravity

We discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and the time gauge.

gr-qc↗
arXiv2020

Geometric formulation of the Covariant Phase Space methods with boundaries

We analyze in full-detail the geometric structure of the covariant phase space (CPS) of any local field theory defined over a space-time with boundary. To this end, we introduce a new frame: the "relative bicomplex framework". It is the result of merging an extended version of the "relative framework" (initially developed in the context of algebraic topology by R.~Bott and L.W.~Tu in the 1980s to deal with boundaries) and the variational bicomplex framework (the differential geometric arena for the variational calculus). The relative bicomplex framework is the natural one to deal with field theories with boundary contributions, including corner contributions. In fact, we prove a formal equivalence between the relative version of a theory with boundary and the non-relative version of the same theory with no boundary. With these tools at hand, we endow the space of solutions of the theory with a (pre)symplectic structure canonically associated with the action and which, in general, has boundary contributions. We also study the symmetries of the theory and construct, for a large group of them, their Noether currents, and charges. Moreover, we completely characterize the arbitrariness (or lack thereof for fiber bundles with contractible fibers) of these constructions. This clarifies many misconceptions about the role of the boundary terms in the CPS description of a field theory. Finally, we provide what we call the CPS-algorithm to construct the aforementioned (pre)symplectic structure and apply it to some relevant examples.

math-ph↗
arXiv2019

On the asymptotics of the rescaled Appell polynomials

We introduce a new representation for the rescaled Appell polynomials and use it to obtain asymptotic expansions to arbitrary order. This representation consists of a finite sum and an integral over a universal contour (i.e. independent of the particular polynomials considered within the Appell family). We illustrate our method by studying the zero attractors for rescaled Appell polynomials. We also discuss the asymptotics to arbitrary order of the rescaled Bernoulli polynomials.

math.CA↗