Quantum collapse of dust shells in 2 + 1 gravity

Abstract

This paper considers the quantum collapse of infinitesimally thin dust shells in 2 + 1 gravity. In 2 + 1 gravity a shell is no longer a sphere, but a ring of matter. The classical equation of motion of such shells in terms of variables defined on the shell has been considered by Peleg and Steif [1], using the 2 + 1 version of the original formulation of Israel [2], and Crisóstomo and Olea [3], using canonical methods. The minisuperspace quantum problem can be reduced to that of a harmonic oscillator in terms of the curvature radius of the shell, which allows us to use wellknown methods to find the motion of coherent wave packets that give the quantum collapse of the shell. Classically, as the radius of the shell falls below a certain point, a horizon forms. In the quantum problem one can define various quantities that give "indications" of horizon formation. Without a proper definition of a "horizon" in quantum gravity, these can be nothing but indications.It is a great pleasure to be able to contribute to this special volume in honor of Octavio Obregon. One of us [M.R.] has known Octavio for more than 30 years and has collaborated with him on many fruitful projects. We both want to wish him many more productive years and continued success.

Singularity free gravitational collapse in an effective dynamical quantum spacetime

“…Clearly it means that we would be able to probe gravitational collapse only whenever the approximation in which one can neglect the shell thickness remains valid. An investigation of the conditions under which this is possible was carried out in [1] (see also [2]). The authors considered a shell composed of a number N of (s-wave) scalar particles with mass m bound together by gravitational interaction.…”

Entropy of thin shells in a (2+1)-dimensional asymptotically AdS spacetime and the BTZ black hole limit

“…In 2+1 dimensions, as in the 3+1 case, it is also interesting to study the thermodynamics of self-gravitating thin shells, since the BTZ black hole can form from the gravitational collapse of such thin shells [17][18][19] which, when static, can be stable or unstable according to their intrinsic parameters [20]. In 2+1 dimensions, the thermodynamics of thin shells in spacetimes with zero cosmological constant has been studied [21].…”

Primordial black hole evaporation and spontaneous dimensional reduction

“…It has long been known theories of gravitation have a much simpler formulation in (2 + 1)-D [1,2,3,4,5,6,7,8,9,10] and (1 + 1)-D [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28], where associated quantum theories are exactly solvable [12]. A resurgence of interest in lower-dimensional physics has been spurred by a confluence of evidence that the effective dimensionality of spacetime may depend on the energy scale at which interactions take place [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44].…”