Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity

Understand

We prove that Einstein's equations coupled to equations of Israel-Stewart-type, describing the dynamics of a relativistic fluid with bulk viscosity and nonzero baryon charge (without shear viscosity or baryon diffusion) dynamically coupled to gravity, are causal in the full nonlinear regime.

• We also show that these equations can be written as a first-order symmetric hyperbolic system, implying local existence and uniqueness of solutions to the equations of motion.
• We use an arbitrary equation of state and do not make any simplifying symmetry or near-equilibrium assumption, requiring only physically natural conditions on the fields.
• These results pave the way for the inclusion of bulk viscosity effects in simulations of gravitational-wave signals coming from neutron star mergers.