Spherically symmetric solutions with dust and radiation sources in Schouten-Codazzi Gravity
Abstract
We examine in this paper exact solutions of Schouten-Codazzi gravity (SCG), a second order metric theory in which a Codazzi tensor is added to the Einstein field equations. We consider two spherically symmetric geometries that describe null radiation and inhomogeneous dust, corresponding to generalized Vaidya and Lemaître-Tolman-Bondi (LTB) spacetimes. The Codazzi tensor has to comply the Codazzi equations, this imposes restrictions on the geometry of spacetime that are determined up to two integration functions that naturally generate an effective ``cosmological constant'' and an additional degree of freedom. We show that for the Vaidya geometry, these Codazzi contributions modify the Misner-Sharp mass, while the LTB models have as an evolution equation a cubic polynomial whose coefficients depend on the Codazzi integration functions. This leads to a broader class of dynamics than those of General Relativity, and allows for an accelerated expansion and ever-expanding models without the introduction of ``dark energy''. Overall, our analysis suggests that Schouten-Codazzi gravity provides an appealing framework for applications in cosmology.
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BibTeX
@misc{najera2026spherically,
title = {{Spherically symmetric solutions with dust and radiation sources in Schouten-Codazzi Gravity}},
author = {Sebastián Nájera and Roberto A. Sussman and Juan Carlos Hidalgo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26775},
eprint = {2610.26775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spherically symmetric solutions with dust and radiation sources in Schouten-Codazzi Gravity
AU - Sebastián Nájera
AU - Roberto A. Sussman
AU - Juan Carlos Hidalgo
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26775
UR - https://arxiv.org/abs/2610.26775
AB - We examine in this paper exact solutions of Schouten-Codazzi gravity (SCG), a second order metric theory in which a Codazzi tensor is added to the Einstein field equations. We consider two spherically symmetric geometries that describe null radiation and inhomogeneous dust, corresponding to generalized Vaidya and Lemaître-Tolman-Bondi (LTB) spacetimes. The Codazzi tensor has to comply the Codazzi equations, this imposes restrictions on the geometry of spacetime that are determined up to two integration functions that naturally generate an effective ``cosmological constant'' and an additional degree of freedom. We show that for the Vaidya geometry, these Codazzi contributions modify the Misner-Sharp mass, while the LTB models have as an evolution equation a cubic polynomial whose coefficients depend on the Codazzi integration functions. This leads to a broader class of dynamics than those of General Relativity, and allows for an accelerated expansion and ever-expanding models without the introduction of ``dark energy''. Overall, our analysis suggests that Schouten-Codazzi gravity provides an appealing framework for applications in cosmology.
ER -