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Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established…
Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for $f(R)$ modified gravity for an appropriate choice of the function…
In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the…
We discuss the possibility of explaining observations usually related to the existence of dark matter by passing from the general relativity (GR) theory to a modified theory of gravity, the embedding theory proposed by Regge and Teitelboim.…
A solution to the dark matter problem is set forth in the framework of reductive semiclassical gravity, i.e., semiclassical gravity involving quantum state reduction. In that theory, the Einstein equation includes the energy-momentum tensor…
We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is…
In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
In order to test the Einstein gravitation theory (EGT) we compare their predictions with the measured results in the following phenomena: the perihelion advance of planets, deflection of light, radar echo delays around the Sun and an…
In this work, we present a review of Energy-Momentum Squared Gravity (EMSG) -- more specifically, $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ represents the Ricci scalar and $T_{\mu\nu}$ denotes the energy-momentum tensor. The inclusion…
An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the…
We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that…
We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first…
We explore the scalar field obtained under the conformal transformation of the spacetime metric $g_{\mu\nu}$ from the Jordan frame to the Einstein frame in $f(R)$ gravity. This scalar field is the result of the modification in the…
Gravastars have been considered as a feasible alternative to black holes in the past couple of decades. Stable models of gravastar have been studied in many of the alternative gravity theories besides standard General Relativity (GR). The…
Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level.…
Emergent modified gravity is a canonical theory based on general covariance where the spacetime is not fundamental, but rather an emergent object. This feature allows for modifications of the classical theory and can be used to model new…
An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially…
In this Note we show that Einstein's equations for gravity are generically invariant under 'disformations'. We also show that the particular subclass when this is not true yields the equations of motion of 'Mimetic Gravity'. Finally we give…
The role of space-time torsion in general relativity is reviewed in accordance with some recent results on the subject. It is shown that, according to the connection compatibility condition, the usual Riemannian volume element is not…