Constraining LQG graph with light surfaces: Properties of BH thermodynamics for mini-super-space, semi-classical polymeric BH

This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on the geometry symmetries. We study here a recently developed model, where the geometry is determined by a metric quantum modification outside the horizon. This is a regular static spherical solution of mini-super-space BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized delineating certain polymeric functions on the basis of the properties of the horizons and the emergence of a singularity in the limiting case of the Schwarzschild geometry. We discuss particular metric solutions on the base of the parameters of the polymeric model related to similar properties of structures, the metric Killing bundles (or metric bundles MBs), related to the BH horizons' properties. A comparison with the Reissner-Norstrom geometry and the Kerr geometry with which analogies exist from the point of their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect their main distinctive phenomenological evidence of LQG origin on the basis of the detection of stationary/static observers and the properties of light-like orbits within the analysis of the (conformal invariant) MBs related to the (local) causal structure. This approach could be applied in other quantum corrected BH solutions, constraining the characteristics of the underlining LQG-graph, as the minimal loop area, through the analysis of the null-like orbits and photons detection. The study of light surfaces associated with a diversified and wide range of BH phenomenology and grounding MBs definition provides a channel to search for possible astrophysical evidence. The main BHs thermodynamic characteristics are studied as luminosity, surface gravity, and temperature. Ultimately, the application of this method to this spherically symmetric approximate solution provides us with a way to clarify some formal aspects of MBs, in the presence of static, spherical symmetric spacetimes.