arXiv subjects

Carmen Ferrara

Publications and source records attributed to Carmen Ferrara.

6 recordsLinked to original sources

arXiv2026

Vacuum stability in Geometric Trinity of Gravity

The decay of a metastable (false) vacuum plays a crucial role in constraining Standard Model and beyond the Standard Model physics. In particular, it has been shown that gravity can have a significant impact on the calculation of the decay rate. In this context, it is natural to ask whether different but classically equivalent formulations of gravity lead to the same physical predictions. The aim of this paper is to analyze vacuum decay in teleparallel and symmetric teleparallel equivalent formulations of General Relativity (GR), namely TEGR and STEGR. Although these theories describe the same classical dynamics, it is of paramount importance to understand whether this equivalence persists also at the quantum level. In this respect, the analysis of vacuum stability may provide a particularly sensitive testing ground. The central question is whether the decay rate of a false vacuum computed within TEGR or STEGR coincides with the corresponding result obtained in GR. Our analysis shows that the tunneling exponent remains unchanged, offering a non-trivial example in which the equivalence between different formulations of gravity extends beyond classical dynamics.

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arXiv2026

Primary Constraints of Newer General Relativity

We study the primary constraint structure of Newer General Relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action is built from a scalar formed by quadratic combinations of the nonmetricity tensor, with arbitrary coefficients $c_i$ in the Lagrangian. We decompose the Lagrangian and compute the canonical momenta conjugate to the metric. We characterize the primary constraints arising from these momenta by identifying when the map between velocities and momenta becomes non-invertible, and organize the outcome through a fully nonlinear decomposition into scalar, vector and tensor sectors. Comparing with previous results in the literature, we recover five and three primary constraints associated with the tensor and vector sectors, respectively. We also identify a previously unreported degeneracy in the scalar sector, which yields either one or two scalar primary constraints depending on the conditions imposed on the parameters $c_i$. Finally, we obtain the primary constraints associated with the covariant formulation of symmetric teleparallel gravity.

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arXiv2025

Extended Geometric Trinity of Gravity

Extensions of equivalent representations of gravity are discussed in the metric-affine framework. First, we focus on: (i) General Relativity, based upon the metric tensor whose dynamics is given by the Ricci curvature scalar $R$; (ii) the Teleparallel Equivalent of General Relativity, based on tetrads and spin connection whose dynamics is given by the torsion scalar $T$; (iii) the Symmetric Teleparallel Equivalent of General Relativity, formulated with respect to both the metric tensor and the affine connection and characterized by the non-metric scalar $Q$ with the role of gravitational field. They represent the so-called Geometric Trinity of Gravity, because, even if based on different frameworks and different dynamical variables, such as curvature, torsion, and non-metricity, they express the same gravitational dynamics. Starting from this framework, we construct their extensions with the aim to study possible equivalence. We discuss the straightforward extension of General Relativity, the $f(R)$ gravity, where $f(R)$ is an arbitrary function of the Ricci scalar. With this paradigm in mind, we take into account $f(T)$ and $f(Q)$ extensions showing that they are not equivalent to $f(R)$. Dynamical equivalence is achieved if boundary terms are considered, that is $f(T-\tilde{B})$ and $f(Q-B)$ theories. The latter are the extensions of Teleparallel Equivalent of General Relativity and Symmetric Teleparallel of General Relativity, respectively. We obtain that $f(R)$, $f(T-\tilde{B})$, and $f(Q-B)$ form the Extended Geometric Trinity of Gravity. The aim is to show that also if dynamics are equivalent, foundations of theories of gravity can be very different.

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arXiv2024

The Equivalence Principle as a Noether Symmetry

The Equivalence Principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein Equivalence Principle and the Strong Equivalence Principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate.

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arXiv2023

The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity

In the framework of metric-affine gravity, we consider the role of the boundary term in Symmetric Teleparallel Gravity assuming $f(Q,B)$ models where $f$ is a smooth function of the non-metricity scalar $Q$ and the related boundary term $B$. Starting from a variational approach, we derive the field equations and compare them with respect to those of $f(Q)$ gravity in the limit of $B\to0$. It is possible to show that $f(Q,B)=f(Q-B)$ models are dynamically equivalent to $f(R)$ gravity as in the case of teleparallel $f(\tilde{B}-T)$ gravity (where $B\neq \tilde{B}$). Furtherrmore, conservation laws are derived. In this perspective, considering boundary terms in $ f(Q)$ gravity represents the last ingredient towards the Extended Geometric Trinity of Gravity, where $f(R)$, $f(T,\tilde{B})$, and $f(Q,B)$ can be dealt with under the same standard. We also compare and discuss about the Gibbons-Hawking-York boundary term of General Relativity and the boundary term $B$ in $f(Q,B)$ gravity.

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arXiv2022

Comparing Equivalent Gravities: common features and differences

We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe the so called {\it Geometric Trinity of Gravity}. Specifically, we consider General Relativity, constructed upon the metric tensor and based on the curvature $R$; Teleparallel Equivalent of General Relativity, formulated in terms of torsion $T$ and relying on tetrads and spin connection; Symmetric Teleparallel Equivalent of General Relativity, built up on non-metricity $Q$, constructed from metric tensor and affine connection. General Relativity is formulated as a geometric theory of gravity based on metric, whereas teleparallel approaches configure as gauge theories, where gauge choices permit not only to simplify calculations, but also to give deep insight into the basic concepts of gravitational field. In particular, we point out how foundation principles of General Relativity (i.e the Equivalence Principle and the General Covariance) can be seen from the teleparallel point of view. These theories are dynamically equivalent and this feature can be demonstrated under three different standards: (1) the variational method; (2) the field equations; (3) the solutions.

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