Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity

TL;DR

This paper investigates the conditions for marginal stability of two-center extremal black holes in N=8 supergravity, using matrix norms and triangle inequalities to analyze BPS and non-BPS solutions, confirming previous findings.

Contribution

It introduces a novel approach using matrix norms and triangle inequalities to determine marginal stability in supergravity black hole solutions.

Findings

Established existence of marginal stability for BPS and some non-BPS solutions.

Confirmed previous results through a new mathematical framework.

Analyzed split attractor flows in the context of supergravity.

Abstract

We study the conditions of marginal stability for two-center extremal black holes in N-extended supergravity in four dimensions, with particular emphasis on the N=8 case. This is achieved by exploiting triangle inequalities satisfied by matrix norms. Using different norms and relative bounds among them, we establish the existence of marginal stability and split attractor flows both for BPS and some non-BPS solutions. Our results are in agreement with previous analysis based on explicit construction of multi-center solutions.