Generalized Attractor Points in Gauged Supergravity

TL;DR

This paper extends the attractor mechanism to general solutions in 4D N=2 gauged supergravity, providing algebraic conditions for various geometries including Lifshitz, Schrödinger, AdS, and dS vacua.

Contribution

It introduces a generalized attractor framework with an algebraic approach applicable to both supersymmetric and non-supersymmetric solutions in gauged supergravity.

Findings

Defined generalized attractor points via algebraic equations

Identified attractor geometries with constant anholonomy coefficients

Developed a potential whose critical points correspond to attractors

Abstract

The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schrodinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.