SLOCC and LU classification of black holes with eight electric and magnetic charges

TL;DR

This paper classifies black holes with eight electric and magnetic charges using SLOCC and LU entanglement classifications of three-qubit states, providing criteria and identifying specific entanglement classes relevant to black hole states.

Contribution

It introduces the first criteria for SLOCC and LU classification of eight-charge STU black holes based on three-qubit entanglement theory.

Findings

Criteria for SLOCC classification of black holes established.

Criteria for LU classification of black holes established.

Black hole states partitioned into five LU families based on entanglement entropy.

Abstract

In \cite{Linde}, Kallosh and Linde discussed the SLOCC classification of black holes. However, the criteria for the SLOCC classification of black holes have not been given. In addition, the LU classification of black holes has not been studied in the past. In this paper we will consider both SLOCC and LU classification of the STU black holes with four integer electric charges $q_{i} $ and four integer magnetic charges $p^{i}$, $i=0,1,2,3$. Two STU black holes with eight charges are considered SLOCC (LU) equivalent if and only if their corresponding states of three qubits are SLOCC (LU) equivalent. Under this definition, we give criteria for the classification of the eight-charge STU black holes under SLOCC and under LU, respectively. We will study the classification of the black holes via the classification of SLOCC and LU entanglement of three qubits. We then identify a set of black holes corresponding to the state W of three qubits, which is of interest since it has the maximal average von Neumann entropy of entanglement. Via von Neumann entanglement entropy, we partition the STU black holes corresponding to pure states of GHZ SLOCC class into five families under LU.