Existence of black holes due to concentration of angular momentum

Abstract

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.

Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces

“…They show a bound for the amount of angular momentum and charge that can be possessed by a body, in terms of its size. Alternatively, if quantum effects are taken into account, these inequalities reveal a minimum possible size for a spinning and/or charged particle [17,18] (see also [2]). Furthermore, a black hole existence criterion is given based on concentration of these two quantities.…”

“…Inequalities relating the size of black holes 1 to the angular momentum and charge that they contain have been studied extensively and optimal results have been obtained, see [9] and the references therein. More recently Dain [10,11] proposed extending these type of inequalities to arbitrary material bodies, and progress has been made in this direction [1,12,17,18,24]. There are, however, undesirable features associated with each of these works.…”

“…These problems are naturally related to the Trapped Surface and Hoop Conjectures [27,29], which seek a mathematical formulation of the folklore belief that if enough matter and/or gravitational energy are present in a sufficiently small region, then the system must collapse to a black hole. In [17,18] this paradigm has been generalized to show that black hole formation may arise from concentration of angular momentum or charge, although the measurement of size in these results relies on the Schoen/Yau radius. In this paper we will present new results concerning the existence of trapped surfaces due to concentration of matter, angular momentum, and charge which rely on elementary measurements of size.…”

Bekenstein bounds, Penrose inequalities, and black hole formation

“…This will be rigorously proven in spherical symmetry, and motivation will be given to indicate why the result should hold in generality. Related results concerning black hole existence due to concentration of angular momentum or charge have been given in [18,19,23], using different methods.…”

Mass, angular momentum, and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity

“…Another interesting aspects of the problem were studies of universal inequalities concerning size, angular momentum and charge of the body [21]- [25]. Among these problems a general and sufficient conditions for a formation of black holes due to the concentration of angular momentum and charge were presented [26,27].…”