Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

Abstract

Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite non-trivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including non-spacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.

Radial asymptotics of Lemaître–Tolman–Bondi dust models

“…Since they allow us to examine non-linear effects analytically, or at least in a tractable way, there is an extensive literature (see [5,6] for comprehensive reviews) using them, mostly as models of cosmological inhomogeneities [7][8][9][10][11][12], but also in other theoretical contexts, such as gravitational collapse and censorship of singularities [14][15][16][17][18][19][20][21][22] or quantum gravity [23][24][25]. There is also a widespread literature considering LTB models as tools to probe how the cosmic acceleration associated to recent observations can be accounted for inhomogeneities, without introducing an exotic source like dark energy.…”

Semiclassical dynamics of horizons in spherically symmetric collapse

“…Techniques to handle inhomogeneous systems [17,18] are still under development [26][27][28] (see also Ref. [29]), but they do not easily reveal the physical picture.…”

“…Within the context of LQC, the status of the classical singularities that arise at the late time stages of the spherically symmetric gravitational collapse, has been studied in LQG [14][15][16][17][18][19][20]. Therein, different fields, such as the standard scalar [14,15,21] or the tachyon [16,22], have been considered to play the role of the collapsing matter source.…”

Inhomogeneous universe in f(T) theory

“…A particular case of these solutions is that of LT [8]. The models have been used in redshift drift [10], CMB [11], interpretation of supernova observations [12], averaging [13], formation of black holes [14], of galaxy clusters [15], superclusters [16], cosmic voids [18] and collapse from the perspective of loop quantum gravity [17].…”