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

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.