Related papers: Fourth-post-Newtonian-exact approximation to Gener…
The Newtonian limit of the most general fourth order gravity is performed with metric approach in the Jordan frame with no gauge condition. The most general theory with fourth order differential equations is obtained by generalizing the…
Gibbons and Schiller have raised the physically interesting conjecture that forces in general relativity are bounded from above by the mathematically compact relation ${\cal F}\leq c^4/4G$. In the present compact paper we explicitly prove,…
We report on recent results obtained in the post-Newtonian framework for the modelling of the gravitational waves emitted by binary systems of spinning compact objects (black holes and/or neutron stars). These new results are obtained at…
We consider the classic problem of a compact fluid source that behaves non-relativistically and that radiates gravitational waves. The problem consists of determining the metric close to the source as well as far away from it. The…
This work systematically investigates the post-Newtonian behavior of general quadratic gravity in the weak-field regime. By extending the Einstein-Hilbert action to include quadratic curvature terms as $\mathcal{L}\propto R-\lambda C^2+\mu…
A general bimetric theory of gravitation is described as a linear in the second approximation. This is allowed due to the small experimental significance of the higher order terms. Solar System tests are satisfied. The theory allows black…
We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak…
We study the Nordstr\"om-Vlasov system which describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstr\"om scalar theory of gravitation. If the speed of light $c$ is considered as a…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
We find a plethora of new analytic black holes and globally regular horizonless spacetimes in three dimensions. The solutions involve a single real scalar field $\phi$ which always admits a magnetic-like expression proportional to the…
We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are…
We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This…
The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a…
We construct an analytical approximation for the numerical black hole metric of P. Kanti, et. al. [PRD54, 5049 (1996)] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a…
In this article I present a simple Newtonian heuristic for deriving a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames [the Einstein…
We define a new paradigm --- postrelativity --- based on the hypothesis of a preferred hidden Newtonian frame in relativistic theories. It leads to a modification of general relativity with ether interpretation, without topological…