Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-12-07
Phys.Rev.D51:3992-3996,1995
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
two references and minor changes added
Scientific paper
10.1103/PhysRevD.51.3992
The collapse of thin dust shells in 2+1 dimensional gravity with and without a cosmological constant in analyzed. A critical value of the shell's mass as a function of its radius and position is derived. For $\Lambda < 0$, a naked singularity or black hole forms depending on whether the shell's mass is below or just above this value. The solution space is divided into four different regions by three critical surfaces. For $\Lambda < 0$, two surfaces separate regions of black hole solutions and solutions with naked singularities, while the other surface separates regions of open and closed spaces. Near the transition between black hole and naked singularity, we find ${\cal M} \sim c_{p}(p-p^*)^{\beta}$, where $\beta=1/2$ and ${\cal M}$ is a naturally defined order parameter. We find no phase transition in crossing from an open to closed space. The critical solutions are analogous to higher dimensional extremal black holes. All four phases coexist at one point in solution space correspondiong to the static extremal solution.
Peleg Yoav
Steif Alan
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