Duality covariant multi-centre black hole systems

TL;DR

This paper develops a duality covariant framework for multi-centre black hole solutions in four dimensions, using nilpotent orbits and linear Poisson equations to unify different systems.

Contribution

It introduces a unified, duality covariant formulation of non-BPS and almost-BPS multi-centre black hole systems using nilpotent orbits and linear equations.

Findings

Both systems are described by the same duality covariant equations.

The equations involve space-dependent abelian isometries conjugate to T-dualities.

The formulation simplifies the understanding of duality transformations in black hole solutions.

Abstract

We present a manifestly duality covariant formulation of the composite non-BPS and almost-BPS systems of multi-centre black hole solutions in four dimensions. The method of nilpotent orbits is used to define the two systems in terms of first order flow equations that transform covariantly under the duality group. Subsequently, we rewrite both systems of equations in terms of real, manifestly duality covariant, linear systems of Poisson equations. Somewhat unexpectedly, we find that the two systems are naturally described by the same equations involving space dependent abelian isometries that are conjugate to T-dualities by similarity transformations.