Prolate horizons and the Penrose inequality

Abstract

The Penrose inequality has so far been proven in cases of spherical symmetry and in cases of zero extrinsic curvature. The next simplest case worth exploring would be non-spherical, non-rotating black holes with non-zero extrinsic curvature. Following Karkowski et al.'s construction of prolate black holes, we define initial data on an asymptotically flat spacelike 3-surface with nonzero extrinsic curvature that may be chosen freely. This gives us the freedom to define the location of the apparent horizon such that the Penrose inequality is violated. We show that the dominant energy condition is violated at the poles for all cases considered.

6 pages, 5 figures

References in corpus (7)

• General Laws of Black-Hole Dynamics
• Gravitational Energy in Spherical Symmetry
• Collapsing Shells and the Isoperimetric Inequality for Black Holes
• The Penrose inequality and apparent horizons
• The constant mean curvature slices of asymptotically flat spherical spacetimes
• Trapped surfaces in prolate collapse in the Gibbons-Penrose construction
• Initial data for gravity coupled to scalar, electromagnetic and Yang-Mills fields