STU Black Holes as Four Qubit Systems

TL;DR

This paper models extremal stationary black hole solutions in the STU supergravity model as four-qubit entangled states, linking black hole classes to quantum entanglement properties and invariants.

Contribution

It extends previous three-qubit models to four qubits, incorporating the Ehlers SL(2,R) symmetry, and relates black hole solution classes to entanglement types and invariants.

Findings

Extremal black holes correspond to nilpotent four-qubit states.

Nonextremal black holes correspond to semisimple states.

Four algebraically independent invariants characterize entanglement classes.

Abstract

In this paper we describe the structure of extremal stationary spherically symmetric black hole solutions in the STU model of D=4, N=2 supergravity in terms of four-qubit systems. Our analysis extends the results of previous investigations based on three qubits. The basic idea facilitating this four-qubit interpretation is the fact that stationary solutions in D=4 supergravity can be described by dimensional reduction along the time direction. In this D=3 picture the global symmetry group $SL(2,R)^{\times 3}$ of the model is extended by the Ehlers SL(2,R) accounting for the fourth qubit. We introduce a four qubit state depending on the charges (electric, magnetic and NUT) the moduli and the warp factor. We relate the entanglement properties of this state to different classes of black hole solutions in the STU model. In the terminology of four qubit entanglement extremal black hole solutions correspond to nilpotent, and nonextremal ones to semisimple states. In arriving at this entanglement based scenario the role of the four algebraically independent four qubit SL(2,C) invariants is emphasized.