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In general relativity, the only dynamical field describing the gravitational interaction of matter, is the metric. It induces the causal structure of spacetime, governs the motion of physical bodies through its Levi-Civita connection, and…
It is more important than ever to push experimental tests of gravitational theory to the limits of existing technology in both range and sensitivity. This brief review focuses on spin-based tests of General Relativity and their implications…
The introduction of General Relativity (GR) in 1915 revolutionized our understanding of gravity, but over time, its limitations in explaining phenomena like dark energy, dark matter, and quantum gravity have motivated alternative theories.…
Chameleon and similar (symmetron and dilation) theories of gravity can exhibit new and interesting features on cosmological scales whilst screening the modifications on small scales thereby satisfying solar system tests of general…
We review different approaches to the Hamiltonian analysis of teleparallel theories of gravity. In particular the Hamiltonian analysis for $f(\mathbb{T})$ theories led to disputed results in the literature. The aim of this review is to…
Over the last few years, a set of new results from pulsar timing has introduced much tighter constraints on violations of the strong equivalence principle (SEP), either via a direct verification of the universality of free fall for a pulsar…
I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I…
This paper aims to discuss two issues that can have a significant impact on the foundations of the theory of gravitation: (1). The existence of relativity of space-time geometry with respect to the properties of used reference frame, which…
We explore the geometrical meaning of teleparallel geometries and the role of covariance in their definition. We argue that pure gauge connections are a necessary ingredient for describing geometry and gravity in terms of torsion and…
In this brief review, I summarize the new development on the correspondence between noncommuative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. I elucidate why a gauge theory in NC spacetime should…
Among the effects predicted by the General Theory of Relativity for the orbital motion of a test particle, the post-Newtonian gravitomagnetic Lense-Thirring effect is very interesting and, up to now, there is not yet an undisputable…
In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an…
We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski…
In several classes of modified gravity theories, extra degrees of freedom are not completely screened in the interiors of stellar and substellar objects. In such theories, the hydrostatic equilibrium condition inside these objects is…
In this work, the experiment is discussed on the verification of the principle of universality of gravitational interactions and some related problems of gravity theory and physics of elementary particles. The meaning of this proposal lies…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…
As we now know, there are indeed at least two major difficulties with General Relativity (GR). The first one is related with its incompatibility with quantum mechanics, in the absence of a widely accepted consistent theory that combines 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.…
This paper considers general relativistic (GR) effects in currently observed extrasolar planetary systems. Although GR corrections are small, they can compete with secular interactions in these systems and thereby play an important role.…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…