Related papers: Second Order Gravitational Self-Force
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum…
Non-gravitational forces play surprising and, sometimes, centrally important roles in shaping the motions and properties of small planetary bodies. In the solar system, the morphologies of comets, the delivery of meteorites and the shapes…
The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that…
Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the…
As we now know, there are indeed at least two major difficulties with General Relativity (GR). The first one is related with its incompatibility with quantum mechanics, in the absence of a widely accepted consistent theory that combines the…
We consider instability of the Friedmann world model to the second-order in perturbations. We present the perturbed set of equations up to the second-order in the Friedmann background world model with general spatial curvature and the…
In this paper, we consider a nonlinear second order equation modelling rocket motion in the gravitational field obstructed by the drag force. The proofs of the main results are based on topological fixed point approach.
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…
We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are…
When pressure is not negligible in comparison with energy density, the external gravitational field and the motion of particles in it are modified. For spherically symmetric body two effective mass parameters determine the external…
The cosmological background of gravitational waves can be tuned by the higher-order corrections to the gravitational Lagrangian. In particular, it can be shown that assuming $R^{1+\epsilon}$, where $\epsilon$ indicates a generic (eventually…
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in General Relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no…
A gravitational machine is defined as an arrangement of gravitating masses from which useful energy can be extracted. It is shown that such machines may exist if the masses are of normal astronomical size. A simple example of a…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…