Is nonrelativistic gravity possible?

TL;DR

This paper demonstrates that nonrelativistic gravity can be formulated as a consistent Hamiltonian system and can produce solutions identical to those of relativistic gravity, including certain black holes.

Contribution

It introduces a Hamiltonian formalism for nonrelativistic gravity, showing its consistency and equivalence to relativistic solutions under specific conditions.

Findings

Nonrelativistic gravity can be described by a consistent Hamiltonian formalism.

Solutions of nonrelativistic gravity can match those of relativistic gravity, including black holes.

Nonrelativistic gravity can reproduce (anti-)de Sitter black holes and IR limits of Horava gravity.

Abstract

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.