Heuristic Derivation of Black Hole Properties Using Dimensional Analysis

Black holes have many interesting and non-obvious properties. The precise details of the features of standard black holes (i.e., those without charge or spin) generally requires calculational techniques involving general relativity, quantum mechanics, thermodynamics, etc. [1]. We demonstrate that many, if not all, of the important aspects of black holes may be estimated, up to a pure number proportionality constant, by the appropriate application of the method of dimensional analysis [2]. In particular, for a black hole having mass M, we ``calculate'' its radius, surface area, density, temperature, and life-time.\\ \\$[1]$ M. Blecher, General Relativity (World Scientific, Singapore, 2016) [2] H.E. Huntley, Dimensional Analysis (Dover, New York, 1967).