Spherical dust collapse in bimetric relativity: Bimetric polytropes

TL;DR

This paper develops a method to set initial conditions for spherically symmetric dust collapse in bimetric relativity, revealing early-stage similarities to general relativity and highlighting unique features like oscillating null cones.

Contribution

It introduces a numerical approach to solve initial data constraints in bimetric theory and simulates dust collapse, uncovering key dynamical features of the theory.

Findings

Collapse dynamics resemble general relativity in early stages

Null cones exhibit oscillations due to nonbidiagonality

No instabilities observed during initial evolution

Abstract

We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called a generalized Lane-Emden equation. Using a numerical code which solves the evolution equations in the standard 3+1 form, we also obtain a short term development of the initial data for these bimetric polytropes. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, the collapse of a dust cloud is similar to that in general relativity, and with no instabilities, albeit with small oscillations in the metric fields.