Related papers: Penrose's singularity theorem and the Kerr space-t…
In this paper we extend our 2007 paper, Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions, arXiv:0710.5046 to include consideration of universal expansion, various implications of extendibility and…
We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy…
We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $\Lambda$, always reduces the efficiency of this…
We analyze Lorentzian spacetimes subject to curvature-dimension bounds using the Bakry-\'Emery-Ricci tensor. We extend the Hawking-Penrose type singularity theorem and the Lorentzian timelike splitting theorem to synthetic dimensions $N\le…
Building upon the work of Brendle, Marques and Neves on the construction of counterexamples to Min-Oo's conjecture, we exhibit deformations of the de Sitter-Schwarzschild space of dimension $n\geq 3$ satisfying the dominant energy condition…
Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking…
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…
To what extent are all astrophysical, dark, compact objects both black holes (BHs) and described by the Kerr geometry? We embark on the exercise of defying the universality of this remarkable idea, often called the "Kerr hypothesis". After…
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…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
Roger Penrose introduced the concept of the trapped surface: a spacelike hypersurface where the two null normals have negative expansion. The trapped surface along with the null convergence condition leads to null geodesic incompleteness.…
The Kerr geometry is believed to represent the exterior spacetime of astrophysical black holes. We here re-analyze the geometry of Kerr-like metrics (Kerr, Kerr-Newman, Kerr-de Sitter, and Kerr-anti de Sitter), paying particular attention…
It is shown that the Kerr-Newman solution, representing charged and rotating stationary black holes, admits analytic extension at the singularity. This extension is obtained by using new coordinates, in which the metric tensor becomes…
In this article, we examine the possibility that there exist special scalar-tensor theories of gravity with completely nonsingular FRW solutions. Our investigation in fact shows that while most probes living in such a Universe never see the…
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably.…
We apply our model of quantum gravity to a Kerr-AdS spacetime of dimension $2 m+1$, $m\ge2$, where all rotational parameters are equal, resulting in a wave equation in a quantum spacetime which has a sequence of solutions that can be…
In the first part of this thesis, Kerr-Schild metrics and extended Kerr-Schild metrics are analyzed in the context of higher dimensional general relativity. Employing the higher dimensional generalizations of the Newman-Penrose formalism…
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables…
The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide…
This paper studies the singularity structure of FLRW spacetimes without particle horizons at the $C^0$-level of the metric. We show that in the case of constant spatial curvature $K=+1$, and without any further assumptions on the scale…