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We numerically test quasi-periodic oscillations using threetheoretically-motivated models of spacetime adopting neutron star sources.Then, we compare our findings with a spherically-symmetric spacetime inferredfrom $F(R)$ gravity, with constant curvature, showing that it fully-degenerateswith our previous metrics, that have been adopted in the context of generalrelativity. To do so, we work out eight neutron stars in low mass X-ray binarysystems and consider a Reisser-Nordstr\"{o}m solution plus a de Sitter phasewith unspecified sign for the cosmological constant term. In particular, weinvestigate three hierarchies, \textit{i.e.}, the first dealing with a genuineSchwarzschild spacetime, the second with de Sitter phase whose sign is notfixed \emph{a priori} and, finally, a Reisser-Nordstr\"{o}m spacetime with anadditional cosmological constant contribution. We perform Markov chain MonteCarlo analyses, based on the Metropolis-Hastings algorithm, and infer1--$\sigma$ and 2--$\sigma$ error bars. For all the sources, we find suitableagreement with spherical solutions with non-zero cosmological constant terms,\textit{i.e.}, with either de Sitter or anti-de Sitter solutions. From ourfindings, we notice that the existence of topological contribution to the netcharge, suggested from $F(R)$ extensions of gravity, seems to be disfavored.Finally, we focus on the physics of the cosmological constant term hereinvolved, investigating physical consequences and proposing possible extensionsto improve our overall treatments.

Numerical analysis of quasi-periodic oscillations with spherical spacetimes