Fragmentation of AdS$_5$-Kerr Black Holes, With Two Applications

Recent work has raised the exciting prospect that violations of the Kerr bound may be observable by the Event Horizon Telescope or the gravitational wave mission LISA. Furthermore, it has recently been suggested that some primordial black holes might have rapidly growing specific angular momenta. On the other hand, certain Quark-Gluon Plasmas, whose physics is often studied using techniques from black hole theory, have recently been observed to have very large vorticities. These observations prompt a question: is there a systematic way of understanding black holes with extremely high specific angular momenta? Holography suggests a way of attacking this problem. The basic idea is simple: whether or not Censorship is violated in physical spacetime, perhaps it is always respected in the dual bulk spacetime. When AdS5 Censorship holds, the specific angular momenta of the bulk black hole is strongly restricted, not by Censorship itself but by requiring stability against various effects such Emparan-Myers fragmentation. Consequently the specific angular momentum of the boundary system, which may be a field theory modelling the Quark-Gluon Plasma, or perhaps a primordial black hole, is constrained. We study such constraints and their implications in these two examples. 1. Using Holography to Bound Angular Momenta In our Universe, there is evidence [1] to suggest that there is an upper bound on the angular momentum of a black hole of given mass. Current observations are compatible with the following inequality: if A denotes the specific angular momentum (angular momentum per unit mass) of the black hole in four-dimensional spacetime, and M denotes its mass, then one has A ≤ GM, (1) where G is the gravitational constant in four spacetime dimensions. This is the “Kerr bound”. It is not immediately obvious that a black hole should be unable to contain an arbitrary quantity of angular momentum. Traditionally, of course, (1) is explained on the basis that, if it were violated, then, according to the Kerr model of a rotating black hole [2], the resulting object would cease to be a black hole, with all manner of allegedly unacceptable consequences. Recently, however, the validity of this Cosmic Censorship principle has been the subject of intense debate; see for example [3–9] for discussions of some of the subtleties involved. The question as to whether there are bounds on black hole specific angular momenta has become very topical, because it has been proposed that one might search for actual physical objects (“superspinars” [10]) violating the Kerr bound, using data from the Event Horizon Telescope [11, 12]. A potentially decisive test will be given by an analysis of gravitational waves, to be detected by the LISA experiment, from extreme mass ratio inspirals [13, 14]. The question then arises as to whether, if indeed the Kerr bound fails, there might be some other bound on the specific angular momenta of black holes. Furthermore, as part of the recent strong resurgence of interest in primordial black holes [15,16], it has been argued that some of these objects have specific angular momenta which grow [17–19], apparently to the point where they automatically test any bound on specific angular momentum. Finally, in (apparently) a completely different area, huge vorticities have recently been indirectly observed [20–23] in the Quark-Gluon Plasmas produced in heavy ion collisions. It is natural to ask whether there is any bound on these vorticities. This is relevant here, because these systems can be studied holographically by using a rotating black hole [24]: questions regarding the possible values of the vorticity can be transferred to questions about the possible specific angular momenta of the dual black hole. This last example suggests a strategy to answer these questions. If we can establish upper bounds on the specific angular momenta of five-dimensional asymptotically Anti-de Sitter-Kerr spacetimes, we may be able to use the AdS/CFT duality [25–27] to uncover similar bounds on four-dimensional systems. Our units are natural units such that A has units of length, the gravitational constant units of squared (respectively, cubed) length in four-dimensional (respectively, five-dimensional) spacetimes, and M has units length. We never use Planck units. Throughout this work, “Censorship” means the existence of an event horizon around all black holes; that is, we use only “weak” Censorship. For simplicity, and because the general case has no obvious dual interpretation, we focus here on five-dimensional black holes rotating about a single axis. Henceforth, we take “AdS5-Kerr” to mean this case.