Noether Symmetry Approach to the Non-Minimally Coupled $Y(R)F^2$ Gravity

Abstract

We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic properties of these black holes.

arXiv comment14 pages, 2 figures

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• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Exact Analytical Taub-NUT like Solution in f(T) Gravity
• New Rotating Black Hole Solutions With Imperfect Fluid Energy-Momentum Tensor In $f(R)$ Gravity
• Holographic Aspects of Non-minimal $R^3{F}^2$ Black Brane in an EFT Framework
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field