Tidal forces in collapsing compact objects

TL;DR

This paper analyzes tidal forces in collapsing LTB spacetimes, revealing how inhomogeneities influence singularity strength and tidal deformation, with implications for observational signatures of gravitational collapse.

Contribution

It provides a detailed analysis of tidal forces in LTB models, highlighting the role of inhomogeneity and time-dependent effects near singularities, including the concept of a critical tidal boundary.

Findings

Tidal forces vary significantly near singularities in LTB spacetimes.

Inhomogeneities lead to diverse tidal deformation patterns.

Singularities exhibit infinite tidal deformation, indicating Ori-strong singularities.

Abstract

In this work, we investigate tidal forces in the Lemaitre-Tolman-Bondi (LTB) metric, focusing on both hidden and locally visible singularities. We discuss the strength of these singularities in terms of deformationally strong singularities. Specifically, we analyze tidal forces in LTB spacetime, calculating radial and angular tidal forces and Jacobi fields for the radially co-moving shell. To provide a comparative study, we consider both homogeneous and inhomogeneous cases. The matter field distribution at one-time slice can differ significantly from another, highlighting the potential for time-dependent tidal deformation as a distinct observational signature. We focus on a specific feature: the time-varying maximum of stretching in the radial tidal force, which we term the "critical tidal boundary." In the inhomogeneous case, close to singularity time ($t<t_{s}$), the magnitudes of tidal forces vary substantially, with significant differences in compressive and stretching forces within a small physical radius $R(t,r)$. The resulting singularity in the LTB metrics at the end state of gravitational collapse appears to be an Ori-strong singularity, characterized by infinite tidal deformation.