In static f(R) gravity, the sign of an effective matter-plus-scalaron convergence term determines whether the radial metric ratio B/A increases or decreases, and equal endpoint values force the term to vanish.
Consistency Condition of Spherically Symmetric Solutions in $f(R)$ Gravity
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In this work we study the spherical symmetric solutions of $f(R)$ gravity in the metric formalism. We show that for a generic $f(R)$ gravity, the spherical symmetric solution is consistent with the modified gravity equations except in the case of imposing an extra condition for the metric.
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Scalaron-modified null focusing and radial monotonicity in static f(R) gravity
In static f(R) gravity, the sign of an effective matter-plus-scalaron convergence term determines whether the radial metric ratio B/A increases or decreases, and equal endpoint values force the term to vanish.