Related papers: A Penrose-Like Inequality for General Initial Data…
Beginning from the standard Arnowitt-Deser-Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon…
We prove the equality case of the Penrose inequality in all dimensions for asymptotically flat hypersurfaces. It was recently proven by G. Lam that the Penrose inequality holds for asymptotically flat graphical hypersurfaces in Euclidean…
We prove a new geometric inequality that relates the Arnowitt-Deser-Misner mass of initial data to a quasilocal angular momentum of a marginally future trapped surface inner boundary. The inequality is expressed in terms of a 1-spinor,…
We give a simplified approach to Kunzinger & Saemann's theory of Lorentzian length spaces in the globally hyperbolic case; these provide a nonsmooth framework for general relativity. We close a gap in the regularly localizable setting, by…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations…
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse…
We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemari\'{e}-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the…
Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or non-equal masses (i.e. isometric or non-isometric horizons).…
In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain…
We consider the 2-d isentropic compressible Euler equations. It was shown in by E. Chiodaroli, C. De Lellis and O. Kreml that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak…
The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A…
Using the Newman-Penrose formalism we study the characteristic initial value problem in vacuum General Relativity. We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of…
We formulate spacetime inequalities applicable to quantum-corrected black holes to all orders of backreaction in semiclassical gravity. Namely, we propose refined versions of the quantum Penrose and reverse isoperimetric inequalities, valid…
As we know, from the Einstein equations the vanishing of the four-divergence of the (symmetric) energy-momentum tensor follows. This is the case because the fourdivergence of the Einstein tensor (which is also symmetric) vanishes…
Here we consider a scenario in which dark energy is associated with the apparent area of a surface in the early universe. In order to resemble the cosmological constant at late times, this hypothetical reference scale should maintain an…
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…
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…