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

## TL;DR

This paper proves that Einstein's equations coupled with Israel-Stewart-type fluid dynamics with bulk viscosity are causal and well-posed in the full nonlinear regime, enabling more accurate neutron star merger simulations.

## Contribution

It demonstrates the causality and well-posedness of Einstein-Israel-Stewart equations with bulk viscosity without symmetry assumptions.

## Key findings

- Equations are causal in the full nonlinear regime.
- The system can be written as a symmetric hyperbolic first-order system.
- Results apply to arbitrary equations of state.

## Abstract

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.