Standard model of black holes evaporation - Application to the Bekenstein-Hawking radiation for Scharzschild black holes

Objective; This report presents a formal standard model to describe the evaporation of Schwarzschild black holes (without rotation or charge) from a reference case. The objective is to determine a universal relationship between the mass of a black hole and its evaporation time, normalized with respect to a cosmologically relevant example type. Methodology; The construction of the model is based on four sequential steps. First, we establish the fundamental equations of Hawking radiation resulting in the relation tevap = χM³ relating the evaporation time to the cube of mass, with calculation of the universal constant χ as a function of the physical constants G, ℏ , c and π. Secondly, we choose a reference case by selecting a black hole whose evaporation time equals the current age of the universe, which is 13.8 billion years, giving a reference mass Mref ≈ 1,73.1011 kg. Thirdly, we introduce the dimensionless parameter; μ = log₁₀ , which transforms physical relations into simple power laws of the form 10nμ. Fourthly, we derive the mean evaporation rate and establish its normalized form R(μ) = 10-2μ, distinguishing this mean rate from the divergent instantaneous rate in the final phase.