Related papers: Initial Value Problem in General Relativity
We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN…
Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when…
In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined…
After a historical discussion of Einstein's 1907 principle of equivalence, a homogeneous gravitational field in Minkowski spacetime is constructed. It is pointed out that the reference frames in gravitational theory can be understood as…
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…
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore,…
The present work is a natural continuation of the previous paper arXiv:0911.5597. In this work, within the scope of the Generalized Uncertainty Principle, a model of the high energy deformation for a particular case of Einstein's equations…
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General…
General Relativity in dimension $n = p + q$ can be formulated as a gauge theory for the conformal group $SO(p+1,q+1)$, along with an additional field reducing the structure group down to the Poincar\'e group $ISO(p,q)$. In this paper, we…
Astrophysical black holes arise as exact solutions of the Einstein field equations. Therefore, any alternative, such as a gravastar, must satisfy the same level of mathematical rigor and internal consistency. A physically viable gravastar…
One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…