On the Smarr formulas for electrovac spacetimes with line singularities

Understand

Using the revised Komar-Tomimatsu approach, we derive Smarr mass formulas for stationary axisymmetric solutions of the Einstein-Maxwell equations containing line singularities (defects) on the polar axis.

• In terms of the rod structure associated with Weyl representation of the metric, the horizons and the defects are formally similar up to differences due to their timelike/spacelike character.
• We derive (previously unknown or incorrect) horizon and global Smarr formulas in presence of a Newman-Unti-Tamburino (NUT) parameter.
• To avoid the divergence of the Komar angular momentum of semi-infinite Dirac and Misner strings, it is necessary to use a symmetric tuning.