Related papers: Nonlinear Dynamics in General Relativity
The gravitational force harbours a fundamental instability against collapse. In standard General Relativity without Quantum Mechanics, this implies the existence of black holes as natural, stable solutions of Einstein's equations. If one…
Up to now, Einstein's general theory of relativity has passed all experimental tests. But yet we know that it is not a fundamental theory and that it is incompatible with quantum theory. While several extended and improved gravitational…
The linearized Einstein theory in the approximately flat time-space is modified accounting for a massive graviton as a dark matter in the universe. On the basis of magnetic-type Maxwell- Proca -Vlasov equations, the interactions of the…
Is the graviton massless? This problem was addressed in the literature at a phenomenological level, using modified dispersion relations for gravitational waves, in linearized calculations around flat space. Here, we perform a detailed…
We consider the scattering of gravitational waves off a Schwarzschild black hole in $f(R)$ gravity. We show that the reflection and transmission coefficients for tensor waves are the same as in General Relativity. While the scalar waves,…
We investigate gravitational radiation in the linear approximation within the framework of the recent nonlocal generalization of Einstein's theory of gravitation. In this theory, nonlocality can simulate dark matter; in fact, in the…
We introduce a family of solutions of Einstein's gravity minimally coupled to an anisotropic fluid, describing asymptotically flat black holes with "hair" and a regular horizon. These spacetimes can describe the geometry of galaxies…
We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…
We study the plane (not necessarily monochromatic) gravitational waves at nonlinear quadratic order on a flat background in vacuum. We show that, in the harmonic gauge, the nonlinear waves are unstable. We argue that, at this order, this…
We numerically integrate the Einstein's equations for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with a spatial curvature perturbation and evolving primordial tensor perturbations using the Einstein…
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black holes. In this paper I discuss another,…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
The recently established formalism of a worldline quantum field theory, which describes the classical scattering of massive bodies in Einstein gravity, is generalized up to quadratic order in spin -- for a pair of Kerr black holes revealing…
The recently proposed formalism of extended Jordan-Brans-Dicke gravity makes it possible to calculate energy loss rate due to both gravitational wave and scalar field (giving the origin of dark energy) wave emission at merger of a black…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…