Multiple Killing horizons: the initial value formulation for $\Lambda$-vacuum

In Mars et al (2018 Class. Quantum Grav. 35 155015) we have introduced the notion of 'multiple Killing horizon' and analyzed some of its general properties. Multiple Killing horizons are Killing horizons for two or more linearly independent Killing vectors simultaneously. In this paper we focus on the vacuum case, possibly with cosmological constant, and study the emergence of multiple Killing horizons in terms of characteristic initial value problems for two transversally intersecting null hypersurfaces. As a relevant outcome, a more general definition of near horizon geometry is put forward. This new definition avoids the use of Gaussian null coordinates associated to the corresponding degenerate Killing vector and thereby allows for inclusion of its fixed points. (paper)