“Solar Mass & Dark Energy Dependence Characteristics Study of Black Holes and their role in Galaxy formation and Cosmic Evolution”

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 Ω_Λ increases, the expansion of the universe at late times becomes more pronounced. The universe with a high Ω_Λ = 0.9 expands exponentially, showing the dominance of dark energy over gravitational forces from matter. For smaller values of Ω_Λ, 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.