Related papers: Non-Vacuum Solutions in Cotton Theory

The framework of General Relativity (GR) has recently been expanded through the introduction of Cotton Gravity (CG), a theoretical extension proposed by J. Harada. This modified approach integrates the Cotton tensor into the gravitational…

The "Codazzi formulation", based on a Codazzi tensor, provides a more robust and straightforward theoretical framework for "Cotton Gravity" (CG) than its original formulation in terms of the Cotton tensor. Using this formulation we provide…

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as ''Cotton gravity'' (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but…

Cotton gravity was recently introduced as a higher derivative extension of General Relativity. The field equations of the theory involve the rank-3 Cotton tensor. Here we show that all solutions of the theory, including the black holes,…

We study black hole solutions in an extension of General Relativity (GR) with an explicit non-minimal coupling between matter and curvature. General black hole solutions satisfying the known energy conditions are derived including the ones…

We demonstrate that the non-vacuum field equations of Cotton gravity and Conformal Killing gravity admit a generalized class of Vaidya-type solutions. In particular, beyond the standard induced term associated with the matter source, the…

We address in this article the criticism in a recently submitted article by Clement and Noiucer (arXiv:2312.17662 [gr-qc]) on "Cotton Gravity" (CG), a gravity theory alternative to General Relativity. These authors claim that CG is "not…

It is shown that the Cotton tensor can describe the effects of gravity beyond general relativity. Any solution of the Einstein equations with or without the cosmological constant satisfies the field equations described by the Cotton tensor.…

The discrepancy between the observed value of the cosmological constant (CC) and its expected value from quantum field theoretical considerations motivates the search for a theory in which the CC is decoupled from the vacuum energy. In this…

Recently, as a generalization of general relativity, a gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That theory allows an additional contribution to the gravitational potential…

We consider a recently introduced extension of General Relativity dubbed as Cotton gravity (CG), based on the use of the Cotton tensor, to estimate the size of a new constant $\gamma$ appearing within a spherically symmetric, vacuum…

We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By…

We derive Friedman-Lemaitre-Robertson-Walker (FLRW) models as non-trivial solutions of "Cotton Gravity" (CG), a recently proposed gravity theory alternative to General Relativity (GR) based on the Cotton tensor. Using an equivalent…

It is well-known that the theory of Cotton gravity proposed by Harada is trivially solved by all isotropic and homogeneous cosmologies. We show that this under-determination is more general. More precisely, the degree of arbitrariness in…

Harada proposed a modified theory of gravity called Cotton gravity, and argued that it successfully explains the rotation curves of $84$ galaxies without the need of dark matter. In this work we use galaxy-galaxy lensing technique to test…

In this paper we present the general spherically symmetric static solution to the vacuum equations of Cotton gravity. The obtained metric solution reveals the presence of singularities at the photosphere of a spherical source, which…

The Friedmann equations of Cotton gravity provide a simple parametrization to reproduce, by tuning a single function, the Friedmann equations of several extensions of gravity, such as f(R), modified Gauss-Bonnet f(G), teleparallel f(T), and…

The Vector-Tensor (VT) theories of gravity are a class of alternative theories to General Relativity (GR) that are characterized by the presence of a dynamical vector field besides the metric. They are studied in attempts to understand…

It has recently been suggested that vacuum black holes of General Relativity (GR) can become spontaneously scalarised when appropriate non-minimal couplings to curvature invariants are considered. These models circumvent the standard black…

The present work has a double aim. On the one hand we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincar\'e Gauge Theory. On the other hand…