Related papers: A Penrose-type inequality for static spacetimes
Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the…
We establish a Penrose-type inequality with angular momenta for four dimensional, biaxially symmetric, maximal, asymptotically flat initial data sets $(M,g,k)$ for the Einstein equations with fixed angular momenta and horizon inner boundary…
We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding…
The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike…
We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime.…
We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing…
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces. Our new definition based only on distance properties allows us also to deal with discrete spaces.…
We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within (mainly) a…
In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres…
Building on previous works of H. L. Bray, of P. Miao, and of S. Almaraz, E. Barbosa, and L. L. de Lima, we develop a doubling procedure for asymptotically flat half-spaces $(M,g)$ with horizon boundary $\Sigma\subset M$ and mass…
In the Einstein gravity, it is well-known that strictly stationary and vacuum regular spacetime should be the Minkowski spacetime. In the Einstein-Gauss-Bonnet theory, we shall show the similar statement, that is, strictly static(no event…
We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contraction property. The remarkable class of examples of spacetimes…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…
In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds $(M^{n}, g)$ with boundary and with dimension $ n < 8$ that was establishedby McCormick. First, we show that any asymptotically flat static…
In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for…
Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci…
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…
The famous Minkowski inequality provides a sharp lower bound for the mixed volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of powers of the volumes of the individual bodies $K$ and $M$. The special case where $K$…
We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards…