Trapped surfaces and nature of singularities in Lyra's geometry

TL;DR

This paper investigates how spacetime torsion in Lyra's geometry influences gravitational collapse, showing that torsion parameters determine whether trapped surfaces form and affecting the nature of resulting singularities.

Contribution

It demonstrates the role of torsion in Lyra's geometry on collapse outcomes, linking torsion parameters to apparent horizon formation and singularity characteristics.

Findings

Collapse ends in a strong curvature singularity.

Torsion parameter influences trapped surface formation.

Exterior spacetime can become dynamic due to torsion effects.

Abstract

Motivated by the geometrical interpretation of Brans-Dicke (BD) scalar field which may also act as a torsion potential in Lyra geometry, we study the effects of spacetime torsion on the dynamics of a collapsing massive star. Taking the interior spacetime as the FLRW metric and the matter content as spherically symmetric, homogeneous perfect fluid with the equation of state (EoS) $p=w\rho$, we show that the collapse ends in a spacetime singularity which is of the strong curvature type in the sense of Tipler. Whether the trapped surfaces form during the dynamical evolution of the collapse depends on the torsion parameter, related to the BD coupling parameter, and the EoS subject to the conditions on physical reasonableness of the collapse configuration. Hence, the space of torsion and EoS parameters is divided into two portions, one for which the collapse process leads to the formation of apparent horizon and the other for which the apparent horizon is failed to form in the interior region. The nature of the singularity is examined from the exterior perspective, by searching for the existence of radial null geodesics reaching the faraway observers. Moreover, it is found that the effects of a dynamical torsion can be transferred to the outside region of the collapsing star, making the exterior region dynamic.