Compact objects in general relativity: From Buchdahl stars to quasiblack holes

Abstract

A Buchdahl star is a highly compact star for which the boundary radius $R$ obeys $R=\frac{9}{8}{r}_{+}$, where $r_{+}$ is the gravitational radius of the star itself. A quasiblack hole is a maximum compact star, or more generically a maximum compact object, for which the boundary radius $R$ obeys $R=r_{+}$. Quasiblack holes are objects on the verge of becoming black holes. Continued gravitational collapse ends in black holes and has to be handled with the Oppenheimer-Snyder formalism. Quasistatic contraction ends in a quasiblack hole and should be treated with appropriate techniques. Quasiblack holes, not black holes, are the real descendants of Mitchell and Laplace dark stars. Quasiblack holes have many interesting properties. We develop the concept of a quasiblack hole, give several examples of such an object, define what it is, draw its Carter-Penrose diagram, study its pressure properties, obtain its mass formula, derive the entropy of a nonextremal quasiblack hole, and through an extremal quasiblack hole give a solution to the puzzling entropy of extremal black holes.

25 pages, 7 figures

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• All fundamental electrically charged thin shells in general relativity: From star shells to tension shell black holes and regular black holes and beyond
• Electrically charged spherical matter shells in higher dimensions: Entropy, thermodynamic stability, and the black hole limit
• Stability of regular black holes and other compact objects with a charged de Sitter core and a surface matter layer
• Stability of electrically charged stars, regular black holes, quasiblack holes, and quasinonblack holes
• Gibbons-Hawking action for electrically charged black holes in the canonical ensemble and Davies' thermodynamic theory of black holes
• The canonical ensemble of a self-gravitating matter thin shell in AdS