Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH (2004.14988v1)

Abstract: This work discusses observational evidences of quantum effects on geometry in a black hole (BH) astrophysical context. We study properties of a family of loop quantum corrected regular BH solutions and their horizons, focusing on the geometry symmetries. We explore a recent model where the geometry is determined by a metric quantum modification outside the horizon: a regular static spherical solution of minisuperspace BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized by some polymeric functions and the emergence of a singularity in the limiting Schwarzschild geometry. We discuss particular metric solutions for similar properties of structures, the metric Killing bundles (metric bundles MBs), related to the BH horizons properties. A comparison with the Reissner-Nordstrom geometry and the Kerr geometry, similar for their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect phenomenological evidence of LQG origin by the detection of stationary/static observers and the properties of lightlike orbits with 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 photons detection. Light surfaces associated with a diversified range of BH phenomenology and grounding MB definition provide a research channel of possible astrophysical evidence. The BHs thermodynamic characteristics are studied, luminosity, surface gravity, and temperature. Ultimately the application of this method to this spherically symmetric approximate solution provides a way to clarify some formal aspects of MBs in the presence of static spherical symmetric spacetimes.