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

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