Related papers: Initial Value Problem in General Relativity
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
The form of the initial value constraints in Ashtekar's hamiltonian formulation of general relativity is recalled, and the problem of solving them is compared with that in the traditional metric variables. It is shown how the general…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
In generally covariant metric gravity theories with tensor matter fields, the initial value constraint equations, unlike in general relativity, are in general not just the 0\mu-components of the metric field equation. This happens because…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical problem. Therefore, any additional structure in their…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…