Studying the Scalar-Hair black hole in the context of Thermo-Optical and tidal force properties

This study is devoted to testing the primary scalar hair black hole for various black hole properties, including thermal analysis, optical properties, weak gravitational lensing and tidal force effects. In studying thermodynamics, we probe geometric mass, thermal temperature, specific heat capacity, and Gibbs free energy. For optical features, we study weak gravitational lensing in the uniform and non-uniform plasma field, black hole shadows, red-blue shift, and the horizon structure. We explore the thermodynamical and observational features of a spherically symmetric static scalar hair black hole under a generalized Renyi entropy scheme. The thermodynamical features of temperature, heat capacity and Gibbs free energy under the influence of scalar hair parameters q, λ and η are examined and it is found that they exhibit rich phase structures and stability conditions. The black hole shadow, red/blue shifts and gravitational lensing effects under a uniform plasma and SIS plasma environment are also examined and it is found that scalar hair effects and non-extensive entropy have significant implications on black hole strong-field features, which may be used as a potential test of scalar-tensor gravity through observational evidence. In the end, we study the tidal force effects of the primary scalar hair black hole. We found that our black hole solution produced the admissible effects while probing all these features.

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