On the various aspects of electromagnetic potentials in spacetimes with symmetries

Abstract

We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields and the relation between the Bianchi identity and Maxwell's equations. In each of these examples, collinearity of currents with the Killing vector field is shown to be the crucial property.

20 pages; revised, published version

References in corpus (4)

• Stationary Black Holes as Holographs
• Thermodynamics of magnetized binary compact objects
• Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
• Is the Bianchi identity always hyperbolic?

Cited by in corpus (7)

• Black hole thermodynamics in the presence of nonlinear electromagnetic fields
• Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields
• Nonlinear electromagnetic fields and symmetries
• Constraints on the symmetry noninheriting scalar black hole hair
• Dynamical entropy of charged black objects
• Schwarzschild spacetime immersed in test nonlinear electromagnetic fields
• Symmetry Inheritance and Jebsen-Birkhoff Theorem