Speaker: Carlos Ramirez (KCL)
Title: Tomimatsu vs Smarr: A Tale of the Masses
Abstract: Recently, the validity Tomimatsu's mass formula has been put into doubt for dyonic black holes, as it supposedly does not reproduce the Smarr relation. In this talk, we clarify this issue by sligthly extending the classical Ernst formalism with the aid of the t- and ϕ-components of the dual electromagnetic potential Bµ, and the magnetic potential Φm. Similar to the known electric potential Φe , Φm also takes a constant value on the black hole horizon. Our analysis focuses on the dyonic Kerr-Newman black hole, examining the correct evaluation of the Komar mass within this stationary dyonic model.
Specifically, we rigorously establish the validity of the standard Tomimatsu mass formula and clarify that recent attempts to "improve" it can be attributed to a misunderstanding of the auxiliary role played by singular potentials in describing magnetic charges. Our approach ensures symmetry between electric and magnetic charges. Furthermore, our findings exclude the existence of Dirac strings of any kind within the physical framework of stationary black hole dyonic spacetimes.