Quasi-Local Mass and the Existence of Horizons

Abstract

Abstract. In this paper, we obtain lower bounds for the BrownYork quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat complete manifolds. The method is based on analyzing Hawking mass and inverse mean curvature flow.

Capacity, quasi-local mass, and singular fill-ins

“…Given the afforementioned results, one wonders whether the capacity and the various notions of mass (ADM, Hawking, Brown-York) fit into one picture. We recall: An inequality between Brown-York mass and Hawking mass has been established by [33,26]. (See also [21]).…”

Positivity of Brown–York mass with quasi-positive boundary data

“…By the proof in [17,Theorem 2.5], we see that for t small enough, the slice N t = ∂{u < t} of the weak IMCF in Lemma 3.3 is the boundary of a minimizing hull in (Ω, g) with C 1,α smooth and Nt |A| 2 dσ < ∞, and m H (N t ) ≥ 0.…”

Black hole initial data with a horizon of prescribed geometry

“…For derivations of this equation see [2,16,14]. The equation has also been used successfully in [15,19]. For a discussion of the use of this equation to construct non-time-symmetric initial data see [3,4,13].…”