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Schouten-Codazzi gravity
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DOI：10.1088/1361-6382/ad922e.png)
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Abstract
En 中文
We propose a new phenomenological second order gravity theory to be denotedas 'Schouten-Codazzi' Gravity' (SCG), as it is based on Schouten and Codazzitensors. The theory is related, but is clearly distinct from Cotton gravity. Byassuming as source the energy momentum of General Relativity, we form asecond order system with its geometric sector given by the sum of the Schoutentensor and a generic second order symmetric tensor complying with the follow-ing properties: (i) it must satisfy the Codazzi differential condition and (ii) itmust be concomitant with the invariant characterization based on the algebraicstructure of curvature tensors for specific spacetimes or classes of spacetimes.We derive and briefly discuss the properties of SCG solutions for static spher-ical symmetry (vacuum and perfect fluid), FLRW models and spherical dustfluids. While we do recognize that SCG is 'work in progress' in an incipientstage that still requires significant theoretical development, we believe that thetheory provides valuable guidelines in the search for alternatives to General Relativity.
Keywords:
alternative gravity theories
exact solutions
Cotton gravity
dark sector
Schouten and Codazzi tensors
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3.7
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1.3W
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3.0W
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