相关论文: Geometry of three manifolds and existence of Black…

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…

On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First we establish integral inequalities for functions defined solely on the boundary and apply them to…

The horizon area and curvature of three-charge BPS black strings are studied in the D-brane ensemble for the stationary black string. The charge distributions along the string are used to translate the classical expressions for the horizon…

In this paper we describe a model of a four-dimensional spherically symmetric black hole in a limiting curvature theory of gravity. In this theory the Einstein-Hilbert action is modified by adding to the action terms providing inequality…

A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary…

Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We…

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and with nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For…

The influence of the Maxwell field on a static, asymptotically flat and spherically-symmetric Gauss-Bonnet black hole is considered. Numerical computations suggest that if the charge increases beyond a critical value, the inner determinant…

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…

Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also…

In this note, we prove that for a complete noncompact three dimensional Riemannian manifold with bounded sectional curvature, if it has uniformly positive scalar curvature, then there is a uniform lower bound on the injectivity radius.

We study how the geometry of the large extra dimensions may affect field theory results on a three-brane. More specifically, we compare cross sections for graviton emission from a brane when the internal space is a N-torus and a N-sphere…

In the context of Born-Infeld gravity theories we report the existence of a regular black hole interior representing a spherically symmetric vacuum solution of the theory. It reduces to the Schwarzschild interior metric in the weak field…

Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, curvature singularities, and asymptotic infinity. These structures are usually identified by…

Motivated by capturing putative quantum effects at the horizon scale, we model the black hole horizon as a membrane with fluctuations following a Gaussian profile. By extending the membrane paradigm at the semiclassical level, we show that…

This paper is about positive scalar curvature on a compact manifold $X$ with non-empty boundary $\partial X$. In some cases, we completely answer the question of when $X$ has a positive scalar curvature metric which is a product metric near…

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with boundary cannot have a metric of positive $m$-intermediate…

We study the dynamics of colliding domain walls including self-gravity. The initial data is set up by applying a BPS domain wall in five-dimensional supergravity, and we evolve the system determining the final outcome of collisions. After a…

We develop and significantly generalize the effective worldvolume theory for higher-dimensional black holes recently proposed by the authors. The theory, which regards the black hole as a black brane curved into a submanifold of a…

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area…