Titlebook: General Relativity and Gravitational Waves; Essentials of Theory Sanjeev Dhurandhar,Sanjit Mitra Textbook 2022 The Editor(s) (if applicable

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The Geometry of Curved Spaces and Tensor Calculus,e laws of special relativity are valid. We further describe geodesics as special curves in a curved spacetime. We show how the deviation of neighbouring geodesics can be used to measure the curvature of a spacetime. Further, the Ricci tensor and scalar curvature are defined from which the Einstein tensor is built.

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2198-7882 s for researchers entering the field.Is the first introducto.This book serves as a textbook for senior undergraduate students who are learning the subject of general relativity and gravitational waves for the first time. Both authors have been teaching the course in various forms for a few decades a

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Introduction

The Geometry of Curved Spaces and Tensor Calculus,n a tensor—because tensors are coordinate independent quantities. For this purpose, we need to define parallel transport of vectors or in general of tensors. We limit ourselves to Riemannian parallel transport which is relevant to general relativity. It is defined here in a natural way using Cartesi

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Schwarzschild Solution and Black Holes,tion. Historically it was the first solution obtained to Einstein’s equations by Karl Schwarzschild in 1916. In full vacuum, this is a black hole solution with an event horizon at .. Since the primary property of the event horizon is its one way character, we discuss the concept of a one-way membran