Hyperbolic energy and Maskit gluings

TL;DR

This paper derives a formula for the energy of ALH manifolds formed by gluing at infinity and demonstrates the existence of complex ALH manifolds with specific geometric properties and negative mass.

Contribution

It introduces a new energy formula for ALH manifolds obtained via gluing and constructs examples with higher genus infinity and negative mass.

Findings

Derived a formula for the energy of glued ALH manifolds.

Proved existence of ALH manifolds with higher genus infinity and negative mass.

Showed manifolds can have toroidal black hole boundaries.

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.