The Hesse potential, the c-map and black hole solutions

TL;DR

This paper introduces a new geometric formulation of the local c-map using the Hesse potential, enabling derivation of black hole attractor equations and construction of stationary solutions in four-dimensional vector multiplets.

Contribution

It presents a novel real formulation of the local c-map based on the Hesse potential, linking special Kahler geometry to black hole solutions.

Findings

Derived black hole attractor equations from geometric properties.

Constructed stationary solutions by lifting instanton solutions.

Provided a new geometric perspective on the c-map and black hole physics.

Abstract

We present a new formulation of the local c-map, which makes use of the real formulation of special Kahler geometry and the associated Hesse potential. As an application we use the temporal version of the c-map to derive the black hole attractor equations from geometric properties of the scalar manifold, and we construct various stationary solutions for four-dimensional vector multiplets by lifting instanton solutions of the time-reduced theory.