Mass Evolution of Schwarzschild Black Holes

In the classical theory of general relativity, black holes can only absorb and not emit particles. When quantum mechanical effects are taken into account, then the black holes emit particles as hot bodies with temperature proportional to κ, its surface gravity. This thermal emission can lead to a slow decrease in the mass of the black hole, and eventually to its disappearance, also called black hole evaporation. This characteristic allows us to analyze what happens with the mass of the black hole when its temperature is increased or decreased and how the energy is exchanged with the external environment. This paper has the aim to make a discussion about the mass evolution, due to Hawking radiation emission, of Schwarzschild black holes with different initial masses and external conditions as the empty space, the cosmic microwave background with constant temperature, and with temperature varying in accordance with the eras of the universe. Our main contributions are to take into account these variations in the temperature of the cosmic background radiation and use them into the black holes dynamics and also to analyze the asymptotic behavior of the solutions. As a result, we have the complete evaporation of the black holes in most cases, although their masses can increase in some cases, and even diverge for specific conditions.