Document Abstract
In this research paper, we investigate the formation of black holes in the early universe and their
fundamental role in galaxy formation and cosmic evolution. By examining key theoretical frameworks
such as the Friedmann equations, Jeans instability, the Chandrasekhar limit, Bekenstein-Hawking
entropy, and Hawking radiation, we aim to understand how black holes emerged from primordial
conditions. These mathematical tools allow us to describe the universe's expansion, the collapse of gas
clouds into dense objects, and the critical mass at which objects become black holes. Our study of
Hawking radiation reveals that a black hole's lifetime increases with its mass, suggesting that super
massive black holes live longer than their smaller counterparts. This research enhances our
understanding of the early universe and provides insights into galaxy formation and black hole evolution
over time. It is found that as πΊπ¬ increases, the expansion of the universe at late times becomes more
pronounced. The universe with a high πΊπ¬ = 0.9 expands exponentially, showing the dominance of dark
energy over gravitational forces from matter. For smaller values of πΊπ¬, such as 0.2 or 0.5, the universe
expands more slowly in the past and continues to grow steadily but not as rapidly. It also observed that
for black holes with smaller masses (e.g., stellar-mass black holes), the rate of mass loss is relatively
high. The graph sharply declines as mass decreases, indicating that small black holes (e.g., those with
less than a few solar masses) would evaporate quickly compared to their more massive counterparts.