Related papers: Multipolar equations of motion for extended test b…
We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a…
A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow…
Our previous work developed a framework for treating the motion of a small body in general relativity, based on a one-parameter-family of solutions to Einstein's equation. Here we give an analysis of the coordinate freedom allowed within…
The features of equatorial motion of an extended body in Kerr spacetime are investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body is assumed to stay at quasi-equilibrium and respond instantly to external…
We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…
We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…
Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
In the present paper we take a step towards the generalization of the post-Newtonian formalism to tensor-multi-scalar theories. These are theories where we have more than one scalar field being mediators of the gravitational interaction in…
The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills'…
There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation $\delta Q = T \delta S$. Our proof relies on extending previous arguments by using a more general definition of the Noether…
We study the Euclidean gravitational path integral computing the Renyi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle…
By extending the framework of the gravitational clock compass we show how a suitably prepared set of clocks can be used to extract information about the gravitational field in the context of General Relativity. Conceptual differences…
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…
The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime---that is, where one mass is significantly smaller than the other---in the full context of our contemporary theory of gravity,…
The geometry around a rotating massive body, which carries charge and electrical currents, could be described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). When a small body is…