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A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
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…
The dynamics of extended bodies endowed with multipolar structure up to the mass quadrupole moment is investigated in the Schwarzschild background according to the Dixon's model, extending previous works. The whole set of evolution…
We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the…
A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a…
Electromagnetic field produced by magnetic multipoles in hyperbolic motion is derived and compared with electromagnetic field produced by electric multipoles in hyperbolic motion. The resulting fields are related by duality symmetry.…
Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both…
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…
Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even…
Previous work established a universal form for the equation of motion of small bodies in theories of a metric and other tensor fields that have second-order field equations following from a covariant Lagrangian in four spacetime dimensions.…
An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation,…