Tensor Calculus in General Relativity: A Bridge Between Mathematics and Theoretical Physics

Abstract

Tensor calculus serves as the mathematical framework underpinning the theory of General Relativity, bridging the gap between abstract mathematical concepts and their physical applications. This paper explores the fundamental principles of tensor calculus, its critical role in formulating Einstein's field equations, and its impact on our understanding of spacetime and gravity. We delve into key tensor operations, including differentiation and contraction, and examine their applications in solving problems in general relativity. By highlighting both historical developments and modern advancements, this study underscores the profound connection between tensor calculus and theoretical physics, demonstrating its significance in describing the universe's structure and dynamics.