Trapped surfaces and the Penrose inequality in spherically symmetric geometries

Abstract

We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy condition outside the horizon. No restrictions are placed on the matter inside the horizon. The proof of the Penrose inequality gives a new necessary condition for the formation of trapped surfaces. This formulation can also be adapted to give a sufficient condition. We show that a modification of the Penrose inequality proposed by Gibbons for charged black holes can be broken in early stages of gravitational collapse. This investigation is based exclusively on the initial data formulation of General Relativity.

plain tex

References in corpus (1)

• Penrose Inequality for Gravitational Waves

Cited by in corpus (33)

• Gravitational Energy in Spherical Symmetry
• Spherically symmetric spacetimes with a trapped surface
• Present status of the Penrose inequality
• Trapped surfaces and symmetries
• Spherical steady accretion flows -- dependence on the cosmological constant, exact isothermal solutions and applications to cosmology
• The Penrose inequality and apparent horizons
• Mass and Angular Momentum in General Relativity
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Inequalities relating area, energy, surface gravity and charge of black holes
• Optical scalars in spherical spacetimes
• On the Penrose Inequality for general horizons
• Generalized inverse mean curvature flows in spacetime
• The Jang equation, apparent horizons, and the Penrose inequality
• Stability analysis on charged black hole with non-linear complex scalar
• Flat foliations of spherically symmetric geometries
• The constant mean curvature slices of asymptotically flat spherical spacetimes
• Absence of trapped surfaces and singularities in cylindrical collapse
• Extensions of the Charged Riemannian Penrose Inequality
• Selfgravitating nonlinear scalar fields
• Global solutions of a free boundary problem for selfgravitating scalar fields
• Comments on Penrose inequality with angular momentum for outermost apparent horizons
• On the Penrose inequality along null hypersurfaces
• The Penrose inequality for nonmaximal perturbations of the Schwarzschild initial data
• Initial data for gravity coupled to scalar, electromagnetic and Yang-Mills fields
• Black hole initial data in Gauss-Bonnet gravity: Momentarily static case
• On extensions of the Penrose inequality with angular momentum
• The Hawking energy on photon surfaces
• Spherically symmetric counter examples to the Penrose inequality and the positive mass theorem under the assumption of the weak energy condition
• Energy-minimizing two black holes initial data
• Uniformly Area Expanding Flows in Spacetimes
• Steady critical accretion onto black holes: selfgravity and sonic point characteristics
• Collapsing regions and black hole formation
• A lower bound of the Trautman-Bondi energy