arXiv subjects

Maria-Jose Guzman

Publications and source records attributed to Maria-Jose Guzman.

9 recordsLinked to original sources

arXiv2023

The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity

General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold's connection. They lead, respectively, to the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we focus on STEGR and present its differences with the conventional, curvature-based GR. We exhibit the 3+1 decomposition of the STEGR Lagrangian in the coincident gauge and present the Hamiltonian, the Hamiltonian and momenta constraints, and Hamilton's equations. For a particular case of spherical symmetry, we explicitly show the differences in the Hamiltonian and the Hamiltonian constraint between GR and STEGR. We finally discuss the implications that these differences, which represent genuine different features between the two formulations of gravity, might encompass to numerical relativity.

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arXiv2023

Geometry and covariance of symmetric teleparallel theories of gravity

We present the geometric foundations and derivations of equations of motion for symmetric teleparallel theories of gravity in the coincident gauge and covariant frameworks. We discuss the theoretical challenges introduced by the auxiliary fields responsible for the covariantisation procedure. We elucidate a tetradic structure interpretation behind this covariant formulation. Regarding the effect of covariantisation at the level of the equations of motion, we explicitly show that the only physical change, in case of setting an arbitrary energy-momentum tensor to the right hand side, resides in the requirement of the fulfillment of the covariant conservation laws. Also, we have explicitly introduced the fundamental covariantly-conserved teleparallel tetrad for the symmetric teleparallel frameworks.

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arXiv2022

Hamilton's equations in the covariant teleparallel equivalent of general relativity

We present Hamilton's equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the Hamiltonian for TEGR obtained through the vector, antisymmetric, symmetric and trace-free, and trace irreducible decomposition of the phase space variables. We present the Hamiltonian for TEGR in the covariant formalism for the first time in the literature, by considering a spin connection depending on Lorentz matrices. We introduce the mathematical formalism necessary to compute Hamilton's equations in both Weitzenbock gauge and covariant formulation, where for the latter we must introduce new fields: Lorentz matrices and their associated momenta. We also derive explicit relations between the conjugate momenta of the tetrad and the conjugate momenta for the metric that are traditionally defined in GR, which are important to compare both formalisms.

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arXiv2022

Contemplating the fate of modified gravity

Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same time, available experimental evidence is limited for testing gravity as a force beyond the regimes in which the theory of general relativity has proven to be successful. This situation leads researchers to look for ``the simplest modification'' to general relativity in a certain class of models, which is enough to solve one or more problems. As a result, we are lost amid a variety of theories with no deeper guiding principle. We give a general review of existing approaches and discuss the current state of the art.

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arXiv2021

Lorentz symmetries and primary constraints in covariant teleparallel gravity

In this article we explore local Lorentz transformations in theories of gravity based on the teleparallel formalism. For the teleparallel equivalent of general relativity (TEGR), the spin connection plays no role in the equations of motion, and therefore it is possible to simply put it equal to zero with no change in physical quantities, and then the theory is formulated purely in terms of the tetrad field which can be freely chosen in any way. In nonlinear modifications of TEGR, this is a more intricate issue, and vanishing spin connection is then the Weitzenböck gauge choice which imposes restrictions on the choice of tetrad. This has led to considering the so-called covariant formulation of $f(T)$ gravity. We examine the primary constraints arising when passing to the Hamiltonian framework, and compute their algebra. We show that the problems of local Lorentz symmetry breaking still appear in this formulation, even if in a different disguise.

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arXiv2021

Approaches to spherically symmetric solutions in f(T) gravity

We study properties of static spherically symmetric solutions in $f(\mathbb T)$ gravity. Based on our previous work on generalising Bianchi identities for this kind of theories, we show how this search of solutions can be reduced to the study of two relatively simple equations. One of them does not depend on the function $f$ and therefore describes the properties of such solutions in any $f(\mathbb T)$ theory. Another equation is the radial one and, if a possible solution is chosen, it allows to find out which function $f$ is suitable for it. We use these equations to find exact and perturbative solutions for arbitrary and specific choices off.

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arXiv2021

Non-trivial Minkowski backgrounds in f(T) gravity

Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(T)$ gravity. We perform Lorentzian perturbations at first order around non-trivial backgrounds and show that some Lorentz modes can exhibit non-trivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities, however they can cast doubts onto even theoretical viability of these models.

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arXiv2021

Classification of primary constraints for new general relativity in the premetric approach

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients $c_i, i=1,2,3$ appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients $c_i$. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

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arXiv2020

Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics

Theories of $f(T)$ gravity are being actively confronted with cosmological observations, and are being studied for their potential to solve famous problems of cosmology. A necessary step is to extend these studies to astrophysical settings. However, to this end one must understand the structure of spherically symmetric solutions. We show that two different known approaches to these solutions are actually fully equivalent from the point of view of Lorentz-covariant formalism. Moreover, we explain Bianchi identities in $f(T)$ gravity and apply them to show that the corresponding equations are always compatible. It puts these efforts on much firmer grounds than before.

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