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On the viability of $f(Q)$ gravity models
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abstract
In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in $f(R)$ theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally $f(Q)$ model specific. We further prove that the energy conservation criterion is equivalent to the affine connection's field equation of $f(Q)$ theory, and except the $f(Q)=\alpha Q+\beta$ model, the non-linear $f(Q)$ models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless $Q$ itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support.
Forward citations
Cited by 3 Pith papers
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Neutron stars in $f(Q) = Q +\xi Q^2$ gravity
In f(Q)=Q+ξQ² gravity with realistic EOSs, negative ξ increases neutron-star maximum masses while positive ξ decreases them, with exterior spacetime remaining Schwarzschild.
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Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the impact on the $\sigma_8$ tension
A sqrt(Q) correction in f(Q) gravity suppresses structure growth without altering the expansion history; fitted to RSD/DESI data it can bring sigma8 into agreement with Planck, at the cost of a sigma8-M degeneracy.
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Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
The paper formulates nonmetric Einstein-Dirac-Maxwell equations in f(Q) gravity and presents parametric off-diagonal black hole, wormhole, and toroid solutions generated by arbitrary functions, without explicit soluti...
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