Initial data and first evolutions of dust clouds in bimetric relativity

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 Lane–Emden-like equations. 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 spherical clouds. 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, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen–Birkhoff theorem in bimetric relativity.