Related papers: Nonlinear Dynamics in General Relativity
The galactic `dark matter' effect is regarded as one of the major problems in fundamental physics. Here it is explained as a self-interaction dynamical effect of space itself, and so is not caused by an unknown form of matter. Because it…
The global attraction is established for all finite energy solutions to a model $\mathbf{U}(1)$-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that {\it each finite…
Largely motivated by the development of highly sensitive gravitational-wave detectors, our understanding of merging compact binaries and the gravitational waves they generate has improved dramatically in recent years. Breakthroughs in…
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 detection of gravitational waves has offered us the opportunity to explore the dynamical and strong-field regime of gravity. Because matched filtering is more sensitive to variations in the gravitational waveform phase than the…
We show how the concurrent implementation of the exact solutions of the Einstein equations, of the equations of motion of the test particles, and of the relativistic estimate of the emission of gravitational waves from test particles, can…
There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant $\Lambda$, however tiny. In particular, even the post-Newtonian quadrupole formula,…
In this work, we investigate the gravitational wave emission from the periodic orbital motion of a test particle around two specific types of black holes in Einstein-\AE{}ther theory, a modified gravity that locally breaks Lorentz symmetry…
We study stationary slowly rotating black holes, up to quadratic order in the spin angular momentum, in dynamical Chern-Simons gravity and shift symmetric Einstein scalar Gauss-Bonnet gravity, as models of string-inspired gravities. These…
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave…
General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or…
The violent collisions of black holes provide for excellent test-beds of Einstein's general relativity in the strong/dynamical gravity regime. We here demonstrate the resolving power one can gain upon the use of multi-band observations of…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
Gravitational decoupling allows to obtain new solutions of general relativity. In this paper, we obtain new solutions of the Einstein field equations which describe non-singular black holes. We consider Hayward and Bardeen regular black…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent…
Charged and/or rotating black holes in General Relativity feature Cauchy horizons, which indicate a breakdown of predictability in the theory. Focusing on spherically symmetric charged black holes, we remark that the inevitability of…
In this paper, we consider the propagation of waves in the space-time of a single black hole with a static Schwarzschild radius in the expanding universe, namely, the solutions of the linear and semilinear Klein-Gordon equations.
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for…
These notes give a concise introduction to General Relativity at the advanced undergraduate level, starting from the weak field limit and gravitational waves, then introducing curved manifolds and Riemannian geometry. The nonlinear…