arXiv subjects

Sebastian Najera

Publications and source records attributed to Sebastian Najera.

3 recordsLinked to original sources

arXiv2024

Schouten-Codazzi Gravity

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

gr-qc↗

arXiv2024

Exact solutions of Cotton Gravity in its Codazzi formulation

The "Codazzi formulation", based on a Codazzi tensor, provides a more robust and straightforward theoretical framework for "Cotton Gravity" (CG) than its original formulation in terms of the Cotton tensor. Using this formulation we provide a self-consistent procedure to generate non-trivial exact solutions in CG that generalize well known General Relativity (GR) solutions. We re-derive a known CG solution that generalizes the Schwarzschild solution of GR, showing that it is the unique vacuum solution of static spherical symmetry in CG, extending this result to a CG generalization of the Reissner-Nordstrom solution of GR, all of which places a strong case supporting the fulfillment of Birkhoff's theorem. When applied to Friedman-Lema\^ıtre-Robertson-Walker (FLRW) models CG naturally identifies the $Λ$CDM model as the unique FLRW dust model with constant negative spatial curvature. We also obtain CG generalizations of the Lema\^ıtre-Tolman-Bondi (LTB) and Szekeres dust solutions of GR, allowing for time and space dependent changes from decelerated to accelerated evolution, without necessarily assuming a dark energy source. The CG generalization of static perfect fluid spheres allows in the weak field regime to model the flattening of rotation velocities in spherical galactic systems without assuming dark matter. We also generalize non-static spherically symmetric perfect fluid solutions with a shear-free 4 velocity. Our results suggest the need for further research using the Codazzi formulation to explore the potential for applications of CG to current open problems in gravitational systems.

gr-qc↗

arXiv2023

Cotton Gravity: the cosmological constant as spatial curvature

We derive Friedman-Lemaitre-Robertson-Walker (FLRW) models as non-trivial solutions of "Cotton Gravity" (CG), a recently proposed gravity theory alternative to General Relativity (GR) based on the Cotton tensor. Using an equivalent formulation, we show that CG leads to FLRW models with a modified expression for spatial curvature in terms of the Ricci scalar of hypersurfaces orthonormal to the 4-velocity. Considering models compatible with a well posed initial value formulation leads to operationally the same FLRW models in GR, but endowed with a precise covariant characterization of the positive/negative cosmological constant as the case with constant negative/positive spatial curvature. Under CG, the $Λ$CDM model becomes the unique FLRW dust model with constant negative spatial curvature.

gr-qc↗