Related papers: A Penrose-Like Inequality for General Initial Data…
We study the initial value problem for a defocusing semi-linear wave equation with spatially growing nonlinearity. By employing Moser-Trudinger type inequalities and Strichartz estimates, we establish global well-posedness in the energy…
Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and…
For complete spin initial data sets with an asymptotically anti--de Sitter end, we introduce a charged energy--momentum defined as a linear functional arising from the Einstein--Maxwell constraints. Under a dominant energy condition adapted…
We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they…
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
Using Visser's semi-analytical model for the stress-energy tensor corresponding to the conformally coupled massless scalar field in the Unruh vacuum, we examine, by explicitly evaluating the relevant integrals over half-complete geodesics,…
Using the time evolution equations of (cosmological) General Relativity in the first order Fischer-Marsden form, we construct an integral that measures the amount of non-stationary energy on a given spacelike hypersurface in $D$ dimensions.…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…
We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-AdS system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the…
We consider initial data for extreme vacuum asymptotically flat black holes with $\mathbb{R} \times U(1)^2$ symmetry. Such geometries are critical points of a mass functional defined for a wide class of asymptotically flat, `$(t-\phi^i)$'…
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…
We derive the higher dimensional generalization of Penrose-Tod equation describing apparent horizons in Robinson-Trautman spacetimes. New results concerning the existence and uniqueness of its solutions in four dimensions are proven.…
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
Let a particle move in the flat space-time under the action of the electric potential. If it decays to two fragments, the energy of debris can be larger than the original energy and, moreover, the efficiency of such a process can be…
We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary, where the boundary is allowed to have a…
We conjecture a family of matrix quantum mechanical models that are holographically dual to discrete light-cone quantization of M-theory in pp-wave-like backgrounds. These backgrounds can be obtained from a Penrose limit of AdS$_4\times…
The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction…