Emergence of a thin shell structure during collapse in isotropic coordinates

Hugues Beauchesne, Ariel Edery

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Numerical studies of gravitational collapse in isotropic coordinates have recently shown an interesting connection between the gravitational Lagrangian and black hole thermodynamics. A study of the actual spacetime was not the main focus of this work and, in particular, the rich and interesting structure of the interior has not been investigated in much detail and remains largely unknown. We elucidate its features by performing a numerical study of the spacetime in isotropic coordinates during gravitational collapse of a massless scalar field. The most salient feature to emerge is the formation of a thin shell of matter just inside the apparent horizon. The energy density and Ricci scalar peak at the shell and there is a jump discontinuity in the extrinsic curvature across the apparent horizon, the hallmark that a thin shell is present in its vicinity. At late stages of the collapse, the spacetime consists of two vacuum regions separated by the thin shell. The interior is described by an interesting collapsing isotropic universe. It tends towards a vacuum (never reaches a perfect vacuum) and there is a slight inhomogeneity in the interior that plays a crucial role in the collapse process as the areal radius tends to zero. The spacetime evolves towards a curvature (physical) singularity in the interior, both a Weyl and Ricci singularity. In the exterior, our numerical results match closely the analytical form of the Schwarzschild metric in isotropic coordinates, providing a strong test of our numerical code.

Original languageEnglish
Article number044056
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - 23 Feb 2012
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Emergence of a thin shell structure during collapse in isotropic coordinates'. Together they form a unique fingerprint.

Cite this