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We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
We study the interplay of general relativity, the equivalence principle, and high-precision experiments involving atomic transitions and g factor measurements. In particular, we derive a generalized Dirac Hamiltonian, which describes both…
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…
Due to its relatively large eccentricity and proximity to the Sun, Mercury's orbital motion provides one of the best solar-system tests of relativistic gravity. We emphasize the number of feasible relativistic gravity tests that can be…
An outstanding question in modern Physics is whether general relativity (GR) is a complete description of gravity among bodies at macroscopic scales. Currently, the best experiments supporting this hypothesis are based on high-precision…
We investigate qualitatively and quantitatively the impact of the general relativistic gravito-electromagnetic forces on hyperbolic orbits around a massive spinning body. The gravito-magnetic field, which is the cause of the well known…
We estimate the possible variations of the gravitational constant G in the framework of a generalized (Bergmann-Wagoner-Nordtvedt) scalar-tensor theory of gravity on the basis of the field equations, without using their special solutions.…
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and…
Einstein's general relativity, as the most successful theory of gravity, is one of the cornerstones of modern physics. However, the experimental tests for gravity in the high energy region are limited. The emerging gravitational-wave…
Gravitomagnetic effects originates from the rotation of the source of the gravitational field and from the rotational features of the observers' frame. In recent years, gravitomagnetism has been tested by means of its impact on the…
We have recently proposed an "Ultra-Strong" version of the Equivalence Principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy…
We propose a novel method for testing gravity models using seismic data from Earth. By imposing observational constraints on Earth's moment of inertia and mass, we rigorously limit the gravitational models' parameters within a $2\sigma$…
It is known that General Relativity ({\bf GR}) uses Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical space-time. $M_4$ means here a four-dimensional differentiable manifold endowed with Lorentzian metric $g$. The metric…
We consider the gravity assist maneuver, that is, a correction of spacecraft motion at its passing near a planet, as a tool for evaluating the Eddington post-Newtonian parameters $\beta$ and $\gamma$, characterizing vacuum spherically…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special…
In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space-time algebra for gravitation developed by Lasenby and Doran (Lasenby, A. N., Doran, C. J. L, and Gull, S.F.: Gravity, gauge theories…
In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined…
Einstein's theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
In this contribution we present two new proposals for measuring the general relativistic gravitomagnetic component of the gravitational field of the Earth. One proposal consists of the measurement of the difference of the rates of the…