Smarr formula for black holes endowed with both electric and magnetic charges

Abstract

The present paper clarifies how to consistently take into account the contribution of magnetic charges in the generalized Smarr mass formula by using properly the Tomimatsu's representation of Komar integrals. It is shown in particular that in all three examples of the dyonic solutions considered by us, the sum of the two electromagnetic terms in Smarr's formula can be cast into the form $\bar{\mathcal{Q}}{\Phi }_{ext}^H$, where $\mathcal{Q}$ is the complex charge and ${\Phi }_{ext}^H$ the complex extension of the electric potential.

11 pages, 3 figures; references added, title changed; published version

References in corpus (9)

• Equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes
• Stationary Dyonic Regular and Black Hole Solutions
• Stationary black diholes
• Equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes. II
• Singular sources in the Demianski-Newman spacetimes
• Generalized black diholes
• On the properties of the Ernst-Manko-Ruiz equatorially antisymmetric solutions
• On the Interaction of Electrons, Magnetic Monopoles, and Photons
• Comment on "Generalized black diholes"

Cited by in corpus (4)

• On the Smarr formulas for electrovac spacetimes with line singularities
• Corotating dyonic binary black holes
• Dyonic black holes: The theory of two electromagnetic potentials
• Dyonic black holes: The theory of two electromagnetic potentials. II