Smarr Mass formulas for BPS multicenter Black Holes

E. Torrente-Lujan

doi:10.1016/j.physletb.2019.135019

paper

Smarr Mass formulas for BPS multicenter Black Holes

arXiv:1908.11259 · doi:10.1016/j.physletb.2019.135019

Abstract

Mass formulas for multicenter BPS 4D black holes are presented. For example, ADM mass for a two center BPS solution can be related to the intercencenter distance $r$ , the angular momentum $J^{2}$ , the dyonic charge vectors $q_{i}$ and the value of the scalar moduli at infinity ( $z_{\infty}$ )by $M_{A D M}^{2} = A (1 + α J^{2} (1 + \frac{2 M _{A D M}}{r} + \frac{A}{r ^{2}}))$ where $A (Q), α (q_{i})$ are symplectic invariant quantities ( $Q$ , the total charge vector) depending on the special geometry prepotential defining the theory. The formula predicts the existence of a continuos class, for fixed value of the charges, of BH's with interdistances $r \in (0, \infty)$ and $M_{A D M} \in (\infty, M_{\infty})$ . Smarr-like expressions incorporating the intercenter distance are obtained from it: $d M \equiv Ω dJ + Φ_{i} d q_{i} + F d r,$ in addition to an effective angular velocity $Ω$ and electromagnetic potentials $Φ_{i}$ , the equation allows to define an effective "force", $F$ , acting between the centers. This effective force is always negative: at infinity we recover the familiar Newton law $F \sim 1/ r^{2}$ while at short distances $F \sim f_{0} + f_{1} / r^{2}$ . Similar results can be easily obtained for more general models and number of centers.

Smarr Mass formulas for BPS multicenter Black Holes

Abstract

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