131 research outputs found
Existence of Black Holes Due to Concentration of Angular Momentum
We present a general sufficient condition for the formation of black holes
due to concentration of angular momentum. This is expressed in the form of a
universal inequality, relating the size and angular momentum of bodies, and is
proven in the context of axisymmetric initial data sets for the Einstein
equations which satisfy an appropriate energy condition. A brief comparison is
also made with more traditional black hole existence criteria based on
concentration of mass.Comment: 8 pages; final versio
Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation
The generalized Jang equation was introduced in an attempt to prove the
Penrose inequality in the setting of general initial data for the Einstein
equations. In this paper we give an extensive study of this equation, proving
existence, regularity, and blow-up results. In particular, precise asymptotics
for the blow-up behavior are given, and it is shown that blow-up solutions are
not unique.Comment: 33 pages; final versio
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