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

TL;DR

This paper explores highly compact stellar objects called Buchdahl stars and quasiblack holes, analyzing their properties, structures, and entropy, and clarifies their relation to black holes within general relativity.

Contribution

It introduces and develops the concept of quasiblack holes, providing examples, diagrams, and formulas, and offers insights into their entropy and relation to black holes.

Findings

Quasiblack holes are objects on the verge of becoming black holes.

Derived the mass formula and entropy for quasiblack holes.

Provided Carter-Penrose diagrams for quasiblack holes.

Abstract

A Buchdahl star is a highly compact star for which the boundary radius $R$ obeys $R=\frac98 r_+$, 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.