# Maxwell equations in curved spacetime with cosmological constant

I am aware of Maxwell Equations in Curved Spacetime. But how do these equations change if the cosmological constant is not assumed to vanish?

Adding a cosmological constant $$\Lambda$$ won't change Maxwell's equations (which are obtained when you vary the action with respect to the field $$A_\mu$$), but it will change the equations of motion in the gravity sector. See Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, for instance.
• @G.Smith I believe Avantgarde means that, indeed, the solutions are different for different metrics; but the form of the equation itself (i.e., $dA=d^\dagger A=0$) is the same, whether you turn on $\Lambda$ or not. – AccidentalFourierTransform Jul 16 at 0:25