arXiv subjects

Gustav H. Holzegel

Publications and source records attributed to Gustav H. Holzegel.

2 recordsLinked to original sources

arXiv2014

The Einstein-Klein-Gordon-AdS system for general boundary conditions

We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-AdS system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. The present paper furnishes a starting point for such global investigations.

gr-qc↗

arXiv2014

Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes

We study the global dynamics of free massive scalar fields on general, globally stationary, asymptotically AdS black hole backgrounds with Dirichlet-, Neumann- or Robin- boundary conditions imposed on $ψ$ at infinity. This class includes the regular Kerr-AdS black holes satisfying the Hawking Reall bound $r_+^2 > |a|l$. We establish a suitable criterion for linear stability (in the sense of uniform boundedness) of $ψ$ and demonstrate how the issue of stability can depend on the boundary condition prescribed. In particular, in the slowly rotating Kerr-AdS case, we obtain the existence of linear scalar hair (i.e. non-trivial stationary solutions) for suitably chosen Robin boundary conditions.

gr-qc↗