Rastall gravity is equivalent to Einstein gravity

Abstract

Rastall gravity, originally developed in 1972, is currently undergoing a significant surge in popularity. Rastall gravity purports to be a modified theory of gravity, with a non-conserved stress-energy tensor, and an unusual non-minimal coupling between matter and geometry, the Rastall stress-energy satisfying nabla_b [T_R]^{ab} = {λ/4} g^{ab} nabla_b R. Unfortunately, a deeper look shows that Rastall gravity is completely equivalent to Einstein gravity --- usual general relativity. The gravity sector is completely standard, based as usual on the Einstein tensor, while in the matter sector Rastall's stress-energy tensor corresponds to an artificially isolated part of the physical conserved stress-energy.

V1: 5 pages. V2: 6 pages; 5 added references, some added discussion, no changes in physics conclusions. V3: 7 pages, 2 added references, some added discussion, no changes in physics conclusions

References in corpus (12)

• Einstein and Rastall Theories of Gravitation in Comparison
• Rotating black hole in Rastall theory
• Thermodynamics of Black Holes in Rastall Gravity
• Noncommutative geometry inspired black holes in Rastall gravity
• Einstein Static Universe in Rastall Theory of Gravity
• The path integral of unimodular gravity
• Gaussian black holes in Rastall Gravity
• The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion
• Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields
• Cosmology from a Lagrangian formulation for Rastall's theory
• Third gravitational wave polarization mode in Rastall theory and analogy with f(R) theories
• The topological terms of interacting harmonic gravitational connections within the Maxwell-like gauge approach of gravity

Cited by in corpus (75)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Rotating black hole in Rastall theory
• The Kiselev black hole is neither perfect fluid, nor is it quintessence
• Gravitationally decoupled strange star model beyond standard maximum mass limit in Einstein-Gauss-Bonnet gravity
• Impact of the Rastall parameter on perfect fluid spheres
• A New Model of Quintessence Compact Stars in Rastall Theory of Gravity
• Non-trivial class of anisotropic compact stellar model in Rastall gravity
• Complexity and Isotropization based Extended Models in the context of Electromagnetic Field: An Implication of Minimal Gravitational Decoupling
• Decoupling gravitational sources by MGD approach in Rastall gravity
• Thermodynamics in Rastall Gravity with Entropy Corrections
• Kerr-Newman-NUT-Kiselev black holes in Rastall theory of gravity and Kerr/CFT Correspondence
• The shadow and photon sphere of the charged black hole in Rastall gravity
• Cosmological consequences in the framework of generalized Rastall theory of gravity
• Rastall gravity extension of the standard $\Lambda$CDM model: theoretical features and observational constraints
• Shadows of black hole surrounded by anisotropic fluid in Rastall theory
• To conserve, or not to conserve: A review of nonconservative theories of gravity
• A connection between Rastall-type and f(R, T) gravities
• Thin-shell wormholes in Rastall gravity
• Cosmic dynamics and qualitative study of Rastall model with spatial curvature
• Impact of Rastall gravity on mass, radius and sound speed of the pulsar PSR J0740+6620
• Quasinormal Modes of Non-Linearly Charged Black Holes surrounded by a Cloud of Strings in Rastall Gravity
• Gravity Effects on Hawking Radiation from Charged Black Strings in Rastall Theory
• Palatini $f(R)$ gravity in the solar system: post-Newtonian equations of motion and complete PPN parameters
• Linear growth index of matter perturbations in Rastall gravity
• Qualitative study of anisotropic Rastall cosmologies
• The criteria of the anisotropic quark star models in Rastall gravity
• Kerr black hole surrounded by a cloud of strings and its weak gravitational lensing in Rastall gravity
• Generalized Rastall's gravity and its effects on compact objects
• Decomposition of total stress-energy for the generalised Kiselev black hole
• Quasinormal mode and spectroscopy of a Schwarzschild black hole surrounded by a cloud of strings in Rastall gravity
• Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling
• Tunneling Analysis of Kerr-Newman Black Hole-Like Solution in Rastall Theory
• A thermodynamics revision of Rastall gravity
• Implications of the Conformal Constraint on Sound Speed on the Radius of PSR J0952-0607 within Rastall Gravity
• Quasinormal Modes and Greybody factors of de Sitter Black holes surrounded by Quintessence in Rastall gravity
• Compact stars in Rastall gravity: hydrostatic equilibrium and radial pulsations
• Hawking-Ellis classification of stress-energy: test-fields versus back-reaction
• Rapidly rotating compact stars in Rastall's gravity
• More on the fact that Rastall = GR
• Geometry and covariance of symmetric teleparallel theories of gravity
• Shadow, absorption and Hawking radiation of a Schwarzschild black hole surrounded by a cloud of strings in Rastall gravity
• Generalized Oppenheimer-Snyder Gravitational Collapse into Regular Black holes
• General Effective Field Theory of Teleparallel Gravity
• Peculiar thermal states in the first-order thermodynamics of gravity
• Cosmological implications of Rastall-$f(R)$ theory
• Quasinormal modes, temperatures and greybody factors of black holes in a generalized Rastall gravity theory
• Nonminimally coupled Weyl gravity
• Observational Constraints on the Rastall gravity from Rotation Curves of Low Surface Brightness Galaxies
• Rotating black holes and exotic compact objects in the Kerr/CFT correspondence within Rastall gravity
• Quadratic Rastall Gravity: from low-mass HESS J1731-347 to high-mass PSR J0952-0607 pulsars
• Tidal Love numbers of neutron stars in Rastall gravity
• Nonconservative traceless type gravity
• Cosmological fluids in the equivalence between Rastall and Einstein gravity
• Implications of Rastall Theory on Stellar Solutions admitting Vanishing Complexity: A New Perspective
• Null Fluid collapse in Rastall theory of gravity
• Generalized nonconservative gravitational field equations from Herglotz action principle
• Effects of Rastall parameter on perturbation of dark sectors of the Universe
• Analytical solutions of the geodesic equation in the space-time of a black hole surrounded by perfect fluid in Rastall theory
• Lemaitre-Tolman-Bondi Static Universe in Rastall-like Gravity
• Can electromagnetic charge inhabit in Rastall gravity?
• Generating exact polytropes in non-conservative unimodular geometries
• Conservative wormholes in generalized $\kappa (\mathcal{R},\mathcal{T})$-function
• Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*
• Rotational mass of anisotropic neutron stars within Rastall gravity
• Gravitational radiation from binary systems in Unimodular gravity
• Primordial Black Hole Formation in Rastall Gravity: Shifted Collapse Threshold and Exponential Abundance Sensitivity
• Gravity theories with local energy-momentum exchange: a closer look at Rastall-like gravity
• Modeling Gravastar Structure admitting Kuchowicz Spacetime in Rastall Gravity Theory
• Rotating neutron stars with chaotic magnetic fields in general relativity and Rastall gravity
• Impact of Rastall gravity on hydrostatic mass of galaxy clusters
• A Modified Gravitational Theory of the Matter Sector of the Type $\varphi (R,T){\mathcal{L}}_m$
• Accelerated expansion as manifestation of gravity: when Dark Energy belongs to the left
• Singularity Avoidance in Gravitational Collapse of an Inhomogeneous Fluid in Rastall Gravity
• A note on the comments of arXiv:2003.10154 [gr-qc] to our paper Nonminimally Coupled Boltzmann Equation I: Foundations (arXiv:2002.08184 [gr-qc])
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory