Abstract
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 space-times 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.
Highlights
Black holes in higher-dimensions are hard to classify and to construct analytically, as Einstein equations become more intricate and complex as the number of space-time dimensions is increased
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
While the focus of this paper is on minimal surfaces and their relevance for black hole horizons, in appendix D we construct and study several classes of stationary geometries with non-zero constant mean extrinsic curvature that generalise (1.5) to plane wave space-times
Summary
Black holes in higher-dimensions are hard to classify and to construct analytically, as Einstein equations become more intricate and complex as the number of space-time dimensions is increased. Black branes share one common feature with soap films: they are characterised by a tension It was noted in [10] (and we will review this in section 2.5) that quite generally minimal surfaces in R3 may provide non-trivial geometries for static non-compact black brane horizons in asymptotically flat space-time.. Families of static black p-spheres with radius R in de Sitter space-time were constructed (for p odd) in [11] where the worldvolume geometry is described by4 The phenomenology of these geometries is slightly different from what we have encountered for minimal surfaces and can be thought of as being analogous to soap bubbles (rather than soap films) instead. While the focus of this paper is on minimal surfaces and their relevance for black hole horizons, in appendix D we construct and study several classes of stationary geometries with non-zero constant mean extrinsic curvature that generalise (1.5) to plane wave space-times
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