would a black hole that formed just after the big bang with mass of 10^6 be the same size today?
No, the black holes formed after the big bang will not be of the same size today. The black holes formed just after the big bang are known as Primordial Black holes and these black holes lose mass and energy over time due to the emission of Hawking Radiation. The emission is inversely proportional to the size of Black holes. Therefore after a long time, it is also known that the Black Holes will evaporate. Hence the Black Holes formed just after big bang will not be of the same size today.
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