Hyperbolic energy and Maskit gluings

2021/11/30 by Chruściel, Piotr T., Delay, Erwann, Wutte, Raphaela
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2112.00095

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.

Related

• Gluing-at-infinity of two-dimensional asymptotically locally hyperbolic manifolds
• Scalar curvature deformation and mass rigidity for ALH manifolds with boundary
• Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature
• Asymptotically hyperbolic metrics on the unit ball with horizons
• Hyperbolic positive energy theorems