Black Hole Solutions with Scalar Fields and Anisotropic Matter in Non-Minimal $Y(R)F^2$ Gravity

Özcan Sert

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arXiv · 2609.14120

Black Hole Solutions with Scalar Fields and Anisotropic Matter in Non-Minimal $Y(R)F^2$ Gravity

Özcan Sert

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Abstract

We investigate exact spherically symmetric and static black hole solutions in a non-minimally coupled Einstein--Maxwell theory of the $Y(R)F^2$ type, extended by a minimally coupled real scalar field and an anisotropic matter distribution. The Maxwell field is coupled to the spacetime curvature through an arbitrary function of the Ricci scalar, while the scalar field is described by a kinetic term and a scalar potential. We obtain exact solutions for power-law and logarithmic forms of the non-minimal coupling function and analyze the corresponding spacetime geometries. In particular, we identify a special $β=-1/3$ case for which the general power-law solution becomes singular and derive a new logarithmic metric by solving the field equations independently. The resulting configurations are asymptotically flat and exhibit modified gravitational properties associated with the interplay between the scalar field, anisotropic matter, and non-minimal electromagnetic coupling. We further show that the magnetic solutions admit electrically charged counterparts through an electromagnetic duality transformation, under which the metric and scalar sector remain invariant while the non-minimal coupling function is inverted. The obtained solutions provide a useful framework for investigating black hole horizons, thermodynamic properties, geodesic motion, and astrophysical phenomena such as galactic rotation curves in curvature-dependent electromagnetic theories.

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Özcan Sert. 2026-09-12. Black Hole Solutions with Scalar Fields and Anisotropic Matter in Non-Minimal $Y(R)F^2$ Gravity. https://arxiv.org/abs/2609.14120

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