We prove some related results concerning blow-up solutions for the Jang equation. First: it has been shown that, given an outermost marginally outer trapped surface (MOTS) Σ, there exists a solution to Jang's equation which blows up at Σ. Here we show that in addition, large classes of spherically symmetric initial dat…
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11 results for “MOTSs”
The paper proves the Null Penrose Inequality for Schwarzschild spacetimes.
problem Proving the Null Penrose Inequality for Schwarzschild spacetimes.
method Introducing quasi-round MOTSs and showing their stability and existence for specific horizons.
result Identifies sufficient conditions for the Null Penrose Inequality in Schwarzschild spacetimes.
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 -constant. In both cases we obtain a splitting result for the ambient manifold when it contains a stable closed MOT…
Study shows instability of certain MOTSs with continuous symmetry.
problem Stability of MOTSs with continuous symmetry.
method Analysis of initial data sets with continuous symmetry and non-preserved MOTSs.
result Exotic MOTSs are unstable except in exceptional cases.
Study proves existence of MOTTs in de Sitter spacetime.
problem Proving existence of marginally outer trapped tubes in de Sitter spacetime.
method Combining results from spacetimes satisfying null convergence condition and properties of CMC surfaces in S3.
result Existence of complete MOTTs with CMC sections in de Sitter spacetime.
We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data c…
We study the relationship between initial data sets with horizons and the existence of metrics of positive scalar curvature. We define a Cauchy Domain of Outer Communications (CDOC) to be an asymptotically flat initial set such that the boundary of is a collection of Marginally Outer (or In…
Let (M, g, k) be an initial data set for the Einstein equations of general relativity. We prove that there exist solutions of the Plateau problem for marginally outer trapped surfaces (MOTSs) that are stable in the sense of MOTSs. This answers a question of G. Galloway and N. O'Murchadha and is an ingredient in the pro…
New method proves rigidity of outermost black hole surfaces without bending.
problem Proving rigidity of outermost black hole surfaces without bending.
method Initial data approach to circumvent bending step.
result Obtained a pure initial data version of rigidity result.
In a recent work, Galloway [9] proved a local foliation theorem by MOTSs for a 3-dimensional initial data set with mean curvature in a 4-dimensional spacetime when (under suitable assumptions) has a stable spherical MOTS which achieves an upper bound for the area. H…
Paper proves existence of anisotropic dynamical horizons in gravitational collapse.
problem Existence of apparent horizons in gravitational collapse.
method Scale-critical hyperbolic method and non-perturbative elliptic techniques.
result Smooth and spacelike apparent horizons emerge from general initial data in gravitational collapse.