Related papers: A formalism for analyzing vacuum spacetimes
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einsteins Field equations for vacuum, yields the Schwarzschild Metric as the unique solution,…
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories---a correspondence dubbed the…
The Newman-Penrose map, which is closely related to the classical double copy, associates certain exact solutions of Einstein's equations with self-dual solutions of the vacuum Maxwell equations. Here we initiate an extension of the…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein Gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin…
In this paper, we construct and study solutions of Einstein's equations in vacuum with a positive cosmological constant which can be considered as inhomogeneous generalizations of the Nariai cosmological model. Similar to this Nariai…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
We construct a Lie-Rinehart algebra over an infinitesimal extension of the space of initial value fields for Einstein's equations. The bracket relations in this algebra are precisely those of the constraints for the initial value problem.…
Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter"…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
This paper reviews the Einstein Cartan theory (ECT), the famous extension of general relativity (GR) in presence of spacetime torsion. The vacuum equations are derived step by step. Vielbein formulation is discussed for determining the…
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle…
A class of gauges for the Einstein vacuum equations is introduced, along with three symmetric hyperbolic systems. The first implies the local realizability of the gauge. The second is the dynamical subset of the field equations. The third…