Schouten-Codazzi Gravity
arXiv:2411.06257 · doi:10.1088/1361-6382/ad922e
Abstract
We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By assuming as source the energy momentum of General Relativity, we form a second order system with its geometric sector given by the sum of the Schouten tensor and a generic second order symmetric tensor complying with the following properties: (i) it must satisfy the Codazzi differential condition and (ii) it must be concomitant with the invariant characterization based on the algebraic structure of curvature tensors for specific spacetimes or classes of spacetimes. We derive and briefly discuss the properties of SCG solutions for static spherical symmetry (vacuum and perfect fluid), FLRW models and spherical dust fluids. While we do recognize that SCG is ``work in progress'' in an incipient stage that still requires significant theoretical development, we believe that the theory provides valuable guidelines in the search for alternatives to General Relativity
To appear in Classical and Quantum Gravity. 22 pages, 2 appendices
References in corpus (18)
- 3+1 Formalism and Bases of Numerical Relativity
- The Cotton tensor in Riemannian spacetimes
- On limits of spacetimes -- a coordinate-free approach
- Emergence of the Cotton tensor for describing gravity
- Gravity at cosmological distances: Explaining the accelerating expansion without dark energy
- A note on Harada's Conformal Killing gravity
- Dark energy in conformal Killing gravity
- Cotton gravity and 84 galaxy rotation curves
- Killing tensors and canonical geometry
- Codazzi tensors and their space-times, and Cotton gravity
- The Wagner Curvature Tensor in Nonholonomic Mechanics
- Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes
- General spherically symmetric solution of Cotton gravity
- Friedmann equations in the Codazzi parametrization of Cotton and extended theories of gravity and the Dark Sector
- Limits of the energy-momentum tensor in general relativity
- Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
- Response to a critique of "Cotton Gravity"
- Spacetime with prescribed hidden symmetry