The 0th and 2nd Laws of Black Hole Mechanics in Einstein-Maxwell-Scalar Effective Field Theory

There has been recent progress in extending the 0th and 2nd laws of black hole mechanics to gravitational effective field theories (EFTs). We generalize these results to a much larger class of EFTs describing gravity coupled to electromagnetism and a real scalar field. We also show that the 0th law holds for the EFT of gravity coupled to electromagnetism and a charged scalar field.