Related papers: A counter-example to a recent version of the Penro…
Some features of the Schwarzschild and Kruskal metric are being discussed under the assumption that the Schwarzschild model can be explained geometrically.
We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal.…
We examine the linearized equations around extremal Kerr horizon and give some arguments towards stability of the horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry.
An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric…
Arising from admissible extended scale-critical short-pulse initial data, we show that 3+1 dimensional Einstein vacuum equations admit dynamical Kerr black hole formation solutions. Our hyperbolic arguments combine the scale-critical…
Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture of general reltivity.
We generalize the formulation of horizon symmetries presented in previous literature to include diffeomorphisms that can shift the location of the horizon. In the context of the AdS/CFT duality, we show that horizon symmetries can be…
We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the…
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity…
We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing…
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…
For an asymptotically flat initial data, the Penrose inequality gives a lower bound of the Arnowitt-Deser-Misner total mass of a spacetime in terms of the area of certain surfaces representing black holes. This is a deep and beautiful…
We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces. We prove a Laplacian comparison theorem for Alexandrov spaces under…
We establish the spacetime Penrose inequality in spherical symmetry in spacetime dimensions $n+1\geq3$ with charge and cosmological constant from the initial data perspective. We also show that this result extends to the Gauss-Bonnet theory…
In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16\pi}$. An important special case of this…
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We derive a relative version of the slicing Bennequin inequalities for cobordant Legendrian knots, and review a few proofs of the result.
This paper investigates the global dynamics of the apparent horizon. We present an approach to establish its existence and its long-term behaviors. Our apparent horizon is constructed by solving the marginally outer trapped surface (MOTS)…
We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for a class of hypersurfaces in certain locally hyperbolic manifolds. As an application we derive an optimal Penrose inequality for asymptotically…