Direct correspondence between Newtonian gravitation and general relativity
- Resource Type
- Working Paper
- Authors
- Buchert, Thomas
- Source
- Phys. Rev. D 108, L101502 (2023)
- Subject
- General Relativity and Quantum Cosmology
Astrophysics - Cosmology and Nongalactic Astrophysics
- Language
We present a strategy to obtain equations of general relativity for an irrotational dust continuum within a flow-orthogonal foliation of spacetime from the equations of Newtonian gravitation, and vice versa, without employing a weak field expansion or a limiting process on the speed of light. We argue that writing Newton's equations in a Lagrangian frame and relaxing integrability of vector gradients is sufficient to obtain equations that are identical to Einstein's equations in (3+1)-form when respecting the Lorentzian signature of the time parametrization. We discuss implications and provide an outlook on how to extend the obtained correspondence to more general spacetimes.
Comment: 6 pages; matches published version in PRD Letters