4D black holes and their parameters

Abstract

General relativity (GR) is the generalization of Special Relativity and Newtonian gravity that provides a description of gravity in spacetime curvature. According to Einstein, the curvature in spacetime creates gravity, and the curvature created due to the mass. Heavy objects deform the spacetime fabric more. That’s why all the planets revolve around the sun due to its mass. The black hole (BH) is a consequence of Einstein Field Equations (EFE). When the giant stars collapse due to the disappearance of the energy that holds them, then a BH forms. A BH is a region in space where the gravity is so strong that not even light can escape. Where all laws of physics are violated. There are various types of astrophysical BHs, where M87* and Sgr A* are captured by the Event Horizon Telescope [1]. Both lie in their respective galaxies. Every BH is defined by some parametric constraints, such as the Schwarzschild BH defined by its parameters, which is mass denoted by M. The Schwarzschild metric is given by: 𝑑𝑠2 = −𝑓(𝑟)𝑑𝑡2 +𝑓(𝑟)−1𝑑𝑟2 + 𝑟2(𝑑𝜃2+𝑠𝑖𝑛2𝜃𝑑φ2) , (1) where, 𝑓(𝑟) = 1 − 2𝑀 𝑟 , In this thesis, we will find these constraints by using Quasi-Periodic Oscillations (QPOs). 1