Calculating the Vorticity of Spacetime in SpECTRE

Near the time of merger, numerical relativity is necessary to model gravitational waves from merging black holes and neutron stars, because near the time of merger all analytic approximations fail. SpECTRE is a next-generation numerical-relativity code being developed by the Simulating eXtreme Spacetimes (SXS) collaboration that will calculate these gravitational waves with high accuracy by scaling to large numbers of compute cores. Simulations of merging black holes yield not only the emitted gravitational waves but also the nonlinear dynamics of the strongly curved spacetime. Tendicity (a measure of how curvature stretches and squeezes an observer through tides) and vorticity (a measure of how curvature twists an observer through differential frame dragging) are useful tools for gaining physical insight into the behavior of curved spacetimes. Mathematically, tendicity and vorticity follow from the electric and magnetic parts of the Weyl curvature tensor, respectively. In this talk, I will discuss implementing and testing a calculation of the magnetic part of the Weyl tensor in SpECTRE, with the goal of using it to help explore the behavior of warped spacetime in SpECTRE’s high-accuracy simulations of binary black holes.