The index of the cosmological horizon and the area-charge-inequality

TL;DR

This paper studies the index of marginally outer trapped surfaces (MOTS) on cosmological horizons in Kerr-Newman-de Sitter spacetime, linking geometric properties to physical parameters like mass, charge, and angular momentum.

Contribution

It provides new bounds on the index of MOTS based on mass and angular momentum assumptions, and relates the area-charge inequality to MOTS with index one in General Relativity.

Findings

Index of MOTS is at least one for small angular momentum.

Under a lower mass bound, the MOTS index is exactly one.

An area-charge inequality is established for MOTS with index one.

Abstract

In this article, we investigate the index of the MOTS given by a spatial cross section of the cosmological horizon in the Kerr-Newman-de Sitter spacetime. We show that its index is at least one in the symmetrized sense for a small positive parameter a, such parameter defines the angular momentum. Assuming a lower bound for the mass, we prove that this MOTS has index one. Also, considering an upper bound for the mass, we show that its index is at least two in the symmetrized sense. Moreover, we establish an estimate relating the area and the charge of a MOTS with index one in a Cauchy data satisfying the dominant energy condition, which give us a connection between MOTS with index one and General Relativity.