Blackfolds, plane waves and minimal surfaces

Abstract

Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter spacetimes in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.

Forced fluid dynamics from blackfolds in general supergravity backgrounds

“…In the context of the blackfold formalism, most of the developments have focused so far on black hole solutions in flat spacetimes [16,26,27]. Preliminary aspects of black brane solutions in AdS spacetimes have been studied in [14,19,28,29] (see also [15]).…”

Black Holes in Higher Dimensions (Black Strings and Black Rings)

“…Subsequently, Jay Armas concentrated on the question of how to scan for horizons. Based on his results in 34 he provided evidence for the existence of rather involved horizon geometries and topologies, and he argued that also plane wave spacetimes allow for a very rich phase structure of higherdimensional black holes. As a key ingredient he employed results from classical minimal surface theory.…”

“…As a key ingredient he employed results from classical minimal surface theory. He then explicitly constructed blackfold solutions consisting of planes, helicoids, catenoids and Scherk surfaces 34 . Next Jay Armas considered the elastic expansion 35,36 .…”

“…The agreement remains excellent also in the presence of an electric charge, as shown for the case of black rings carrying Maxwell charge in Einstein-Maxwell-Dilaton theory with the Kaluza-Klein coupling constant 38 . In the last part of his talk Jay Armas considered worldvolume effective actions for black holes by integrating out further scales 39 . In particular, he presented novel geometries for black hole horizons in higherdimensional asymptotically flat spacetime, concentrating on helicoidal black rings in D > 5 and helicoidal black tori in D = 7.…”

Towards higher dimensional black rings

“…In the absence of methods for finding the exact solutions with non-spherical topology in higher dimensions several approximate techniques have been developed, for example, the matching asymptotic expansions [8] and the blackfold effective theory [9]. Along with numerical [10,11] and approximate [12] methods, the blackfolds have been used to shows existence of solutions with non-spherical topologies such as helical black strings/rings, non-uniform black cylinder and several other possibilities [13,14]. However, despite all recent results the exact solutions with non-spherical horizon topology are known only in D = 5.…”