Mannheim–Kazanas Black Holes: Horizons, Temperatures and Thermodynamics

Static black holes in conformal Weyl gravity differ from their Einstein counterparts in a simple but important way: the Mannheim–Kazanas geometry is encoded in a Bach-flat lapse function whose radial dependence is richer than that of Schwarzschild–de Sitter. We study the de Sitter branch of this solution in the Schwarzschild gauge, keeping the characteristic linear term together with the quadratic de Sitter term. In the branch continuously connected to the positive-mass Schwarzschild–de Sitter spacetime, a regular static region between a black-hole horizon and a cosmological horizon exists precisely when \(-\frac{1}{3}<\beta\gamma<\frac{2}{3}\), and \(0<\kappa<\frac{1+3\beta\gamma}{27\beta^2}\). In this window, the singularity at the origin is hidden, the two positive horizons obey \(0