The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

TL;DR

This paper investigates the nature of singularities in generic gravitational collapse, demonstrating analytically and numerically that they are spacelike, local, and oscillatory, supporting the BKL conjecture.

Contribution

It provides analytical insights and numerical evidence confirming that singularities in inhomogeneous spacetimes are spacelike, local, and oscillatory, aligning with the BKL conjecture.

Findings

Singularities are spacelike, local, and oscillatory.

Nonlinear Einstein terms drive oscillatory approach to singularity.

Numerical simulations support the assumption of local homogeneous evolution.

Abstract

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.