Spherical dust collapse in bimetric relativity: Bimetric polytropes

Understand

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.