A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Abstract

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.

arXiv commentContribution to the "Encuentros Relativistas Espanoles - Spanish Relativity Meeting ERE07" Proceedings, Tenerife, Spain (September 2007)

References in corpus (3)

• New conformally flat initial data for spinning black holes
• A double-domain spectral method for black hole excision data
• A new spectral apparent horizon finder for 3D numerical relativity

Cited by in corpus (6)

• Area - Angular momentum inequality for axisymmetric black holes
• Geometric inequalities for axially symmetric black holes
• Black-hole horizons as probes of black-hole dynamics II: geometrical insights
• An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
• Initial data for perturbed Kerr black holes on hyperboloidal slices
• Thermodynamic relations for entropy and temperature of multi-horizons black holes