Non-Riemannian Gravity and the Einstein-Proca System

Abstract

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.

9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravity

References in corpus (5)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Black Holes with Weyl Charge and Non-Riemannian Waves
• An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
• An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions
• Solutions for Neutral for Axi-Dilaton Gravity in 4-Dimensions

Cited by in corpus (37)

• Lagrange formulation of the symmetric teleparallel gravity
• Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings
• Searches for the role of spin and polarization in gravity
• Metric-affine gauge theory of gravity II. Exact solutions
• Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity
• An axially symmetric solution of metric-affine gravity
• Dark Matter Gravitational Interactions
• Rotating Black Holes in Metric-Affine Gravity
• Cosmology of Quadratic Metric-Affine Gravity
• Computer algebra in gravity: Programs for (non-)Riemannian spacetimes. I
• Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries
• Plebański-Demiański-like solutions in metric-affine gravity
• Colliding waves in metric-affine gravity
• Geometric Proca with Matter in Metric-Palatini Gravity
• Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism
• Possible effects of spacetime non-metricity on neutrino oscillations
• The Maxwell-Chern-Simons gravity and its cosmological implications
• Dirac equation in spacetimes with torsion and non-metricity
• General teleparallel metrical geometries
• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity
• Multipole solutions in metric--affine gravity
• Uniqueness theorems for static black holes in metric-affine gravity
• A nonminimally coupled Einstein-Maxwell model in a non-Riemann space-time with torsion
• Isomorphism between Non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories
• Generalized Reissner-Nordström solution in Metric-Affine Gravity
• A class of colliding waves in metric-affine gravity, nonmetricity and torsion shock waves
• Nonmetricity and torsion induced by dilaton gravity in two dimension
• On the geometric foundation of classical gauge gravitation theory
• The Distributional Stress-Energy Quadrupole
• Effective Levi-Civita Dilaton theory from Metric Affine Dilaton Gravity
• Gauge theory of gravity: Electrically charged solutions within the metric--affine framework
• Non-minimally coupled Dirac equation with torsion: Poincaré gauge theory of gravity with even and odd parity terms
• Alexandru Proca (1897--1955) the Great Physicist
• On the solutions of the Cartan equation in Metric Affine Gravity
• Self-gravitating line sources of weak hypercharge
• On the triviality of certain non-Riemannian models of gravitation