This paper explores the computation of Hawking temperatures for black holes within various f( Q) gravity models using the RVB (Robson–Villari–Biancalana) method. This topological approach reveals an additional term in the temperature calculation, which we propose is a residue arising from the contour integral [ ], where f( z) represents a function related to the black hole’s metric or curvature. By analyzing several specific f( Q) models including f( Q) = Q + α Q², f( Q) = Q + βln ( Q), [ ], f( Q) = Q ⁿ as well as the Reissner–Nordstrm, Kerr, and Kerr–Newman black holes, we demonstrate that the correction term C can be consistently interpreted as this residue, providing new insights into black hole thermodynamics in modified gravity frameworks. We also expand on important physical aspects such as black hole stability, late-stage evaporation, extremality bounds in charged and rotating spacetimes, and potential novel phases emerging from different forms of f( Q).

Recently, one of my articles got some interesting results about Kerr black hole superradiant stability. That result contained some conclusions that violated the "No Hair Theorem". We know that the "No Hair Theorem" is the inference product of general relativity. I boldly believe that it may lead to a little progress in cosmological research.

This paper investigates the thermodynamic phase structure and microscopic interactions of Reissner–Nordström (RN) black holes within the framework of f( R) gravity. The academic rationale is to explore how modifications to Einstein’s gravity influence the critical behavior of charged black holes. We employ the tools of thermodynamic geometry, specifically the Ruppeiner curvature, to probe the nature of interactions among the black hole’s microscopic constituents. Our analysis reveals that the thermodynamic behavior is highly sensitive to the functional form of f( R) and the background space–time geometry. For models with a constant initial curvature scalar, RN black holes exhibit thermodynamic properties analogous to an ideal gas. However, for models where the initial curvature scalar is non-constant, corresponding to a cosmological constant with negative power terms, we uncover a first-order phase transition analogous to that of a Van der Waals fluid. This transition is characterized by the canonical “swallowtail” catastrophe in the Gibbs free energy landscape. The divergence of the Ruppeiner curvature scalar is shown to precisely coincide with the critical points of this phase transition, providing a geometric signature of the underlying change in the black hole’s microstructure. Our results demonstrate that f( R) gravity parameters and background topology are critical determinants of black hole stability, offering a new window into the phenomenological consequences of modified gravity theories.

According to traditional theory, the Schwarzschild black hole does not produce super radiation. If the boundary conditions are set in advance, the possibility is combined with the wave function of the coupling of the boson in the Schwarzschild black hole, and the mass of the incident boson acts as a mirror, so even if the Schwarzschild black hole can also produce super-radiation phenomena.