Magnetized binary black holes and neutron stars in equiliblium

For helically symmetric Einstein-Maxwell spacetimes with magnetized perfect fluids, generalized thermodynamic laws - The zeroth law, the constancy of surface gravity and electric potential, and the first law, a variation formula for the Noether charge Q associated with a helical Killing vector - Are derived. Applying Bekenstein and Oron's theory of ideal magnetohydrodynamics (MHD), the first law is written as δQ = 0 for a sequence of equilibrium solutions that models adiabatic binary inspiral due to gravitational wave emission. We introduce a possible formulation for computing such magnetized binary neutron stars and black holes in close circular orbits in quasi- equilibriums, and a project to develop computer code for such magnetized compact objects the Cocal code - Compact Object CALculator.