Advances in Theoretical and Mathematical Physics

Volume 27 (2023)

Number 5

Hyperbolic energy and Maskit gluings

Pages: 1333 – 1403

DOI: https://dx.doi.org/10.4310/ATMP.2023.v27.n5.a2

Authors

Piotr T. Chruściel (Gravitational Physics, University of Vienna, Austria)

Erwann Delay (Laboratoire de Mathématiques, Avignon Université, Avignon, France)

Raphaela Wutte (Institute of Theoretical Physics, TU Wien, Austria)

Abstract

We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.

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P.T.C. was supported in part by the Austrian Science Fund (FWF) under project P29517-N27 and by the Polish National Center of Science (NCN) 2016/21/B/ST1/00940.Part of this research was performed while PTC was visiting the Institute for Pure and Applied Mathematics (IPAM) at UCLA, which is supported by the National Science Foundation (Grant No. DMS- DMS-1925919).

E.D. was supported by the grant ANR-17-CE40-0034 (project CCEM) and by the grant ANR-23-CE40-0010-02 (project EINSTEIN-PPF) of the French National Research Agency.

R.W. was supported by the Austrian Science Fund FWF under the Doctoral Program W1252-N27 Particles and Interactions.

Published 15 July 2024