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

¹ Instituto de Astrofísica de Andalucía, CSIC, Apartado Postal 3004, Granada 18080, Spain
² Laboratoire de l'Univers et de ses Théories, UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France
³ Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm, Germany

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.