Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes

TL;DR

This paper identifies specific 4-derivative extensions of Einstein-Maxwell theory that allow for multi-centered extremal black hole solutions with balanced forces, revealing constraints that preserve known solutions despite higher derivative corrections.

Contribution

It derives new, tighter constraints on 4-derivative couplings ensuring multi-black hole solutions remain force-free, including explicit examples in various dimensions.

Findings

Constraints are tighter than those protecting mass-charge ratios.

Majumdar-Papapetrou solutions are unmodified by certain 4-derivative terms.

Includes examples with curvature-squared supergravity and $F^4$ terms.

Abstract

We investigate which 4-derivative extensions of Einstein-Maxwell theory admit multi-extremal black hole solutions with gravitational force balanced by Coulomb force. We obtain a set of constraints on the 4-derivative couplings by exploring various probe limits in multi-black hole systems. It turns out that these constraints are tighter than those needed to protect the mass-charge ratio of extremal black holes from higher derivative corrections. In fact, they are so strong that the Majumdar-Papapetrou multi-black solutions are unmodified by the force-free combinations of the 4-derivative couplings. Explicit examples of such 4-derivative couplings are given in 4- and 5-spacetime dimensions. Interestingly these include curvature-squared supergravity actions and the quasi-topological $F^4$ term.