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arXiv · 2406.04417

Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity

Federico Scali·Oliver Fabio Piattella
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Abstract

We address the question of how to build a class of $f(R)$ extensions of General Relativity which are compatible with solar system experiments, without making any preliminary assumption on the properties of $f$. The aim is reached by perturbatively solving the modified Einstein equations around a Schwarzschild background and retrieving a posteriori the corresponding $f(R)$. This turns out to be non analytical in $R=0$ and should be intended as the leading correction to the Einstein-Hilbert action in the low curvature limit. The parameters characterizing the $f(R)$ class are then set by constraining the corrections to four different local tests with the observations. The result is a class of $f(R)$ theories built up from a purely bottom-up approach and compatible with the local tests. At a more general level, this result can help constraining exact $f(R)$ models working in Cosmology, since it provides the correct local limit. Further developments and possible extensions of the approach to Cosmology are also discussed.

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Federico Scali, Oliver Fabio Piattella. 2024-06-06. Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity. https://doi.org/10.1103/physrevd.110.064042

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