相关论文: Remarks on the stability operator for MOTS

We prove that a marginally outer trapped surface (MOTS) can form as a result of Einsteinian evolution in pure vacuum spacetime starting from regular initial data free of MOTSs due to pure boundary effects. We adapt a Cauchy-double-null…

Let $(\tilde{\Sigma},h_{ab},K_{ab})$ be an initial data set and let $x^a$ be a symmetry vector of $\tilde{\Sigma}$. Consider a MOTS $\mathcal{S}$ in $\tilde{\Sigma}$ and let the symmetry vector be decomposable along the unit normal to…

In this paper we survey some recent advances in the analysis of marginally outer trapped surfaces (MOTS). We begin with a systematic review of results by Schoen and Yau on Jang's equation and its relationship with MOTS. We then explain…

Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the associated new line…

There are notable similarities between the marginally outer trapped surfaces (MOTSs) present in the interior of a binary black hole merger and those present in the interior of the Schwarzschild black hole. Here we study the existence and…

We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for…

We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a…

The aim of this work is to present an initial data version of Hawking's theorem on the topology of back hole spacetimes in the context of manifolds with boundary. More precisely, we generalize the results of G. J. Galloway and R. Schoen…

We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass $|a| \ll M$. We prove that each eigenvalue depends analytically on $a$ (in a neighbourhood of $a=0$), and compute its first…

We study the causal dynamics of an embedded null horizon foliated by marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric background spacetime subjected to linear perturbations. We introduce a simple procedure which…

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature surfaces immersed into certain 3-dimensional Riemannian spaces, in particular into homogeneous 3-manifolds. As an application we…

We study the evolution of horizons of black holes in the $1+1+2$ covariant setting and investigate various properties intrinsic to the geometry of the foliation surfaces of these horizons. This is done by interpreting formulations of…

In this paper we generalize the main result of [13] in two different situations: in the first case for MOTSs of genus greater than one and, in the second case, for MOTSs of high dimension with negative $\sigma$-constant. In both cases we…

A popular approach in numerical simulations of black hole binaries is to model black holes as punctures in the fabric of spacetime. The location and the properties of the black hole punctures are tracked with apparent horizons, namely…

We present a rigorous proof of the Spacetime Penrose Inequality relating the ADM mass to the area of trapped surfaces in asymptotically flat initial data sets satisfying the dominant energy condition. The main theorem establishes that the…

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is…

We study the open and closed axisymmetric marginally outer trapped surfaces contained in leaves of constant Painlev\'e-Gullstrand time for Schwarzschild spacetimes. We identify a family of closed MOTS in the black hole interior…

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer…

The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…

In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…