Gravity between Newton and Einstein

Abstract

Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein's theory of gravity that does not assume weak fields and which admits an action principle.

arXiv commentEssay written for the Gravity Research Foundation 2019 Awards for Essays on Gravitation; Honorable Mention

References in corpus (5)

• Newtonian Gravity and the Bargmann Algebra
• Action Principle for Newtonian Gravity
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• (In)finite extensions of algebras from their Inonu-Wigner contractions

Cited by in corpus (36)

• Non-Relativistic Gravity and its Coupling to Matter
• Review on Non-Relativistic Gravity
• A Non-Relativistic Limit of NS-NS Gravity
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Oddity in nonrelativistic, strong gravity
• Non-Lorentzian theories with and without constraints
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Non-Riemannian gravity actions from double field theory
• Aspects of Non-Relativistic Quantum Field Theories
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Geometrizing non-relativistic bilinear deformations
• Symmetries of post-Galilean expansions
• The Non-Relativistic Geometric Trinity of Gravity
• Conformal Invariance of the Newtonian Weyl Tensor
• Underdetermination in Classic and Modern Tests of General Relativity
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Coset space actions for nonrelativistic strings
• A coupling prescription for post-Newtonian corrections in Quantum Mechanics
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Non-relativistic gravity theories in four spacetime dimensions
• Stringy Newton Gravity with $H$-flux
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• A free Lie algebra approach to curvature corrections to flat space-time
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Hydrodynamics in the Carrollian regime
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Gravitational redshift revisited: inertia, geometry, and charge
• Deriving Schwarzschild and Kerr from the Einstein Equivalence Principle
• Space-time Schrödinger symmetries of a post-Galilean particle
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory