Related papers: Geodesic Deviation Equation in $\Lambda$CDM $f(T,\…
We study the geodesic deviation (GD) equation in a generalized version of the S\'{a}ez--Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy…
Gravity gradiometry within the framework of the general theory of relativity involves the measurement of the elements of the relativistic tidal matrix, which is theoretically obtained via the projection of the spacetime curvature tensor…
This paper is devoted to investigate the recently proposed modified Gauss-Bonnet $f(\mathcal{G},T)$ gravity, with $\mathcal{G}$, the Gauss-Bonnet term, coupled with ${T}$, the trace of energy-momentum tensor. We have used the Noether…
The aim of this paper is to introduce a new modified gravity theory named as $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy…
The $f(R,T)$ gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, $R$, and the trace of the stress-energy tensor, $T$; its field equations also depend on matter Lagrangian, $\mathcal{L}_{m}$. In the…
We propose an extension of the symmetric teleparallel gravity, in which the gravitational action $L$ is given by an arbitrary function $f$ of the nonmetricity $Q$ and of the trace of the matter energy-momentum tensor $T$, so that…
The search for the gravitational energy-momentum tensor is often qualified as an attempt of looking for ``the right answer to the wrong question''. This position does not seem convincing to us. We think that we have found the right answer…
We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this…
We present an analysis of an $f(T, \mathcal{T})$ extension of the Teleparallel Equivalent of General Relativity, where $T$ denotes the torsion and $\mathcal{T}$ the trace of the energy-momentum tensor. This extension includes non--minimal…
This article presents cosmological models that arise in a subclass of $f(R,T)=f(R)+f(T)$ gravity models, with different $f(R)$ functions and fixed $T$-dependence. That is, the gravitational lagrangian is considered as $f(R,T)=f(R)+\lambda…
In this work, we linearize the field equations of $f(R)$ gravity using the Starobinsky model, $R+R^2/(6m^2)$, and examine the modifications to General Relativity. We derive an equation for the trace, $T$, of the energy-momentum tensor,…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the…
We consider f(R,T) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory,…
By using the relativistic top theory, we derive a relativistic top deviation equation. This equation turns out to be a generalization of the geodesic deviation equation for a pair of nearby point particles. In fact, we show that when the…
We consider f(R,T) modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the…
A simple differential analysis of issue of the correspondence between notion of geodesics in gravitation theory of GTR and straights of inertial motion in the Minkowski space-time discovers that, conventional certification of the geodesics…
In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an…
The (4+1) dimensional conformally flat Eisenhart geometry is investigated in this work, stressing the contribution of the stress tensor generating its curvature. The energy-momentum tensor $T^{a}_{~b}$ is traceless and has only one nonzero…
We write the field equations of torsion gravity theories and the N\oe ther identity they obey directly in terms of metric and contorsion tensor components expressed with respect to natural coordinates, i.e. without using vierbien but…