A Study of Black Holes and Beyond: Shadows and Relativistic Orbits

TL;DR

This thesis explores the shadows and relativistic orbits of black holes and naked singularities, deriving new models and analyzing observational data to distinguish between different compact objects.

Contribution

It introduces novel models of rotating naked singularities, derives shadow shapes for various spacetimes, and analyzes relativistic orbits of stars near black holes.

Findings

Shadow shapes for rotating JNW and Kerr spacetimes derived.

Relativistic orbit equations for different spacetimes formulated.

Astrometric analysis of S2 star's orbit in the presence of scalar fields.

Abstract

This doctoral thesis is organized into seven chapters. The first chapter introduces readers to the formation of black holes and naked singularities as an end state of continuous gravitational collapse. The physical and geometrical properties of the Schwarzschild black hole, JMN-1 naked singularity, and JNW naked singularity are summarised. The motivation and objectives to be derived are based on the literature reviews. The second chapter deals with the shadows of the mentioned compact objects. The equations of motion are explicitly calculated for general spherically symmetric and static spacetimes using the ray-tracing formalism and the null geodesics. The third chapter focuses on the construction of rotating naked singularity using the NJA. The NJA is used without complexification method and obtain rotating JNW naked singularity spacetime. The general formalism of the shadow shape is derived for rotating spacetime and obtain the shadow shapes for the rotating JNW, Kerr and deformed Kerr spacetimes. In the fourth chapter, the precession of timelike-bound orbits is investigated in the Schwarzschild, JMN-1, and JNW spacetimes. The fully relativistic orbit equations are derived for the provided models. The approximate solutions of the orbit equations are used to characterize the nature of orbital precession. The next chapter is on the precession of timelike bound orbits in the rotating Kerr and JNW spacetimes. The sixth chapter deals with the relativistic orbits of S-stars and discusses the orbital parameters of the real and apparent orbits. Astrometric data of the S2 star has been adopted from the available literature and use numerical techniques to study the relativistic orbits of the S2 star in the presence of a scalar field. The final chapter aims at summarising the results followed by some futuristic scopes that probe the nature of Sgr A* with a possible black hole mimicker.