Related papers: Mixed Hyperbolic - Second-Order Parabolic Formulat…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the…
We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of…
We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the $3+1$-decomposition of spacetime, we…
Second-order formulations of the 3+1 Einstein equations obtained by eliminating the extrinsic curvature in terms of the time derivative of the metric are examined with the aim of establishing whether they are well posed, in cases of…
We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and F.…
Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being nonperturbatively renormalizable in the Weinberg sense. The present paper applies the…
We study the $1/c$ expansion of general relativity within a formulation that is compatible with both the Arnowitt-Deser-Misner and the Kol-Smolkin decompositions. The Einstein-Hilbert action takes a common form for those decompositions as…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
The Einstein-Hilbert worldspace action is used to investigate the dynamics of extended object. In the Robertson-Walker worldspace, this is seen to introduce a pressureless density which could contribute to dark matter. Such pressureless…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the ADM…