Spike behavior in the approach to spacetime singularities

TL;DR

This paper presents high-resolution numerical simulations of spacetime singularities, revealing small-scale spike features and deriving an analytical formula that accurately describes their shape.

Contribution

The authors develop an analytical formula for spike shapes and demonstrate its accuracy in numerical simulations of spacetime singularities.

Findings

Spikes form during the approach to singularities.

The analytical formula matches simulation results.

Simulations resolve small-scale features effectively.

Abstract

We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale features (known as spikes) that form in this process. We find an analytical formula for the shape of the spikes and show that the spikes in the simulations are well described by this formula.