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The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the…
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,…
We investigate the existence of static, spherically symmetric compact objects within the framework of symmetric teleparallel scalar-tensor gravity. This theory extends the Brans-Dicke and scalar-tensor models within the symmetric…
We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general…
Two tetrad spaces reproducing spherically symmetric spacetime are applied to the equations of motion of higher-order torsion theories. Assuming the existence of conformal Killing vector, two isotropic solutions are derived. We show that the…
We present a new Hamiltonian formulation of the Teleparallel Equivalent of General Relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on…
A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is…
In this work a tetrad theory of gravity, invariant under conformal transformations, is investigated. The action of the theory is similar to the action of Maxwell's electromagnetism. The role of the electromagnetic gauge potential is played…
This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General…
The main aim of this paper is to obtain a completely new relativistic non-singular model for static, spherically symmetric isotropic celestial compact stars in the $f(R, T)$ gravity scenario. In this regard, we have considered the isotropic…
This paper delves into the impact of extended symmetric teleparallel theory on anisotropic compact stellar structures. The explicit field equations were formulated by considering a minimum model of this extended gravity. Basically, the…
In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about…
The torsion models have stood out among the proposals for an alternative description of gravity. The simplest of them, the Teleparallel theory, is equivalent to General Relativity and there are many studies that seek to study its extension…
This paper explores stability of the Einstein universe against linear homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for…
Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can…
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
We consider the sector of Horndeski's gravity characterized by the coupling between the kinetic scalar field term and the Einstein tensor. We numerically construct neutron star configurations where the external geometry is identical to the…
In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling…