Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3 \times R$

TL;DR

The paper provides numerical evidence supporting the conjecture that generic gravitational collapse exhibits locally oscillatory singularities, specifically in U(1) symmetric cosmologies on T^3 x R, aligning with the Belinskii, Lifshitz, and Khalatnikov conjecture.

Contribution

It demonstrates through numerical simulations that oscillatory behavior near singularities occurs in vacuum U(1) symmetric cosmological spacetimes, confirming a longstanding theoretical conjecture.

Findings

Exponential growth of a specific term in Einstein's equations near singularity.

Numerical simulations show oscillatory behavior consistent with predictions.

Supports the BKL conjecture on the nature of singularities in gravitational collapse.

Abstract

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.