  The static, spherical solutions that exhibit an antisymmetry between the
temporal and radial coordinates in $f(R)$ gravity theories are presented. I
present the constraint for this antisymmetry and show that pure $R^2$ models
produce these solutions. An asymptotic expansion approach is taken to find the
solutions, presenting first and second order corrections to the Schwarzschild
metric. The null geodesics and photon sphere are determined for these
corrections. Furthermore, I show that electromagnetic fields produce this
antisymmetry as well. The metric solutions are analyzed in the context of black
holes, bringing forward potentially a new class of black holes in modified
gravity theories.
