Non-singular Brans-Dicke collapse in deformed phase space

TL;DR

This paper investigates how phase space deformation effects in Brans-Dicke theory can lead to non-singular gravitational collapse, resulting in bounces or oscillatory behaviors instead of singularities, contrasting with classical GR outcomes.

Contribution

It introduces non-commutative phase space effects into Brans-Dicke collapse models, revealing non-singular evolution and bounce phenomena absent in standard theories.

Findings

Non-commutative effects induce a bounce at minimum radius.

For large positive BD coupling, collapse dynamics differ from GR.

Negative BD coupling leads to damped oscillatory bounce.

Abstract

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature [1], that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.