Direct correspondence between Newtonian gravitation and general relativity
arXiv:2306.12253 · doi:10.1103/PhysRevD.108.L101502
Abstract
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.
arXiv comment6 pages; matches published version in PRD Letters
References in corpus (15)
- On average properties of inhomogeneous fluids in general relativity I: dust cosmologies
- Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
- Connection between Newtonian simulations and general relativity
- Newtonian and Relativistic Cosmologies
- Lagrangian theory of structure formation in relativistic cosmology I: Lagrangian framework and definition of a nonperturbative approximation
- On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies
- Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
- Methods for studying the accuracy of light propagation in N-body simulations
- On the Newtonian Limit of the Weyl Tensor
- Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves
- Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
- Gauss-Bonnet-Chern approach to the averaged Universe
- Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)
- On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
- Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation