Some Studies on the Validation of the Revised Second Law of Black Hole Thermodynamics

Four different laws of black hole thermodynamics are named Zeroth Law, First Law, Second Law and Third Lawl. As quantum effect violates Hawking’s Area Theorem and thereby the Second Law, we needed to revise the second law, which emerged as the Revised Second Law of Black Hole Thermodynamics. This includes into consideration the entropy due to thermal radiation or quantum radiation, usually called Hawking Radiation surrounding the black Hole. Including this component of entropy, it is possible to validate the non-decreasing entropy stated by the Second Law. Here we are establishing that even the unrevised or original version of the Second Law of Black Hole Thermodynamics can be validated for some giant or supergiant black holes. For an abnormally massive black hole, when its huge gravity performs a huge amount of surrounding matter accretion, the rate of matter accretion exceeds a certain critical value. For those black holes, the loss of Mass due to Hawking Radiation cannot balance the increase of Mass due to matter accretion. This results in a continuous gain of Mass by the deposit of accreted Mass in the black holes, resulting in an increase of the Mass and thereby the area of the Black Hole. As the area is directly proportional to entropy, the entropy of the black Hole continuously increases. This is only the entropy due to the geometric structure of the Black Hole. Thus for some giant or supergiant black holes where the rate of surrounding matter accretion dominates over quantum effect thermal evaporation, the original or unrevised Second Law also gets validated – without adding the entropy due to thermal radiation. So from small black holes up to some medium-sized ones, where the rate of matter accretion is below a critical value, we only need to revise the Second Law by adding the entropy due to quantum effect. On the contrary, if the size of the black Hole is huge enough such that the rate of matter accretion is beyond a certain critical value, even the original, unrevised Second Law of non-decreasing entropy due to the geometric structure of the black Hole is validated.