Posts in category: ADV-MATHEMATICS

The concept of curved spacetime, introduced by Albert Einstein in his General Theory of Relativity (GR), revolutionized our understanding of gravity. One of the most important solutions to Einstein’s field equations is the Schwarzschild solution, wh ...

Einstein’s field equation is the foundation of General Relativity—a theory that describes how gravity works. The equation: R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu} may look complicated, but let’s break it down step by ste ...

The energy-momentum tensor, also known as the stress-energy tensor, is a fundamental concept in the General Theory of Relativity (GTR). It describes the distribution and flow of energy and momentum in spacetime, acting as the source of the gravitati ...

Poisson’s equation is a fundamental equation in mathematical physics, appearing in electrostatics, gravitation, and fluid dynamics. In the context of General Relativity, it serves as an approximation of Einstein’s Field Equations under certain condi ...

Albert Einstein’s theory of relativity revolutionized our understanding of space, time, and gravity. Two fundamental principles at the heart of this theory are the Principle of Equivalence and the Principle of Covariance. These principles provide th ...

Albert Einstein's Special Theory of Relativity revolutionized our understanding of physics by introducing the transformation equation of momentum and energy. The theory redefined how we perceive time, space, and energy in high-speed contexts, partic ...

1. Introduction to Tensors 1.1 What Is a Tensor? So, what is a tensor? At its core, a tensor is a mathematical object that generalizes scalars, vectors, and matrices to higher dimensions. If you've ever dealt with vectors or matrices, you're a ...