Trapped surfaces and the nature of singularity in Lyraʼs geometry

Abstract

Motivated by the geometrical interpretation of the 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) , we show that the collapse ends in a spacetime singularity which is of a 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 of the physical reasonableness of the collapse configuration. Hence, the space of the torsion and EoS parameters is divided into two portions, one for which the collapse process leads to the formation of the apparent horizon, and the other for which the apparent horizon fails 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.