Related papers: A Rigorous Derivation of Gravitational Self-force
In recent years, asymptotic approximation schemes have been developed to describe the motion of a small compact object through a vacuum background to any order in perturbation theory. The schemes are based on rigorous methods of matched…
We revisit the problem of the equations of motion of a system of $N$ self-interacting massive particles (without spins) in the first post-Minkowskian (1PM) approximation of general relativity. We write the equations of motion, gravitational…
The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$.…
The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object…
The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom'', which…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
We formulate a spherical harmonically decomposed 1+1 scheme to self-consistently evolve the trajectory of a point particle and its gravitational metric perturbation to a Schwarzschild background spacetime. Following the work of Moncrief, we…
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of…
Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in…
General relativity, treated as a low energy effective field theory, predicts quantum corrections to Newtons law of gravitation arising from loops of matter and graviton fields. While these corrections are negligible for the Standard Model…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of…
We propose a new metric perturbation scheme under a possible constraint of the gauge conditions in which we obtain a physically expected prediction of the orbital evolution caused by the MiSaTaQuWa self-force. In this new scheme of a metric…
In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. An extension of an earlier…
Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. It is known that the metric perturbation induced by a particle can be divided into two parts, the…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…