Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 005, 15 pages      arXiv:2207.14563      https://doi.org/10.3842/SIGMA.2023.005
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

On Asymptotically Locally Hyperbolic Metrics with Negative Mass

Piotr T. Chruściel a and Erwann Delay b
a)  Faculty of Physics, University of Vienna, Boltzmanngasse 5, A 1090 Vienna, Austria
b)  Laboratoire de Mathématiques d'Avignon, Avignon Université, F-84916 Avignon and F.R.U.M.A.M., CNRS, F-13331 Marseille, France

Received August 01, 2022, in final form January 17, 2023; Published online January 23, 2023

Abstract
We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology of apparent horizons and of the conformal boundary at infinity, and with controlled mass. In particular we obtain new classes of solutions with negative mass.

Key words: scalar curvature; asymptotically hyperbolic manifolds; negative mass.

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