Introduction Wormholes, often romanticized in science fiction, are solutions to the Einstein field equations that act as bridges between two separate points in spacetime. In theoretical cosmology, wormholes represent not only potential shortcuts ...
Euler’s Equation of Motion in Fluid Dynamics
Fluid dynamics, a branch of fluid mechanics, deals with the motion of fluids and their interactions with solid boundaries. One of the fundamental equations governing fluid flow is Euler's equation of motion. Named after the Swiss mathematician and p ...
Schwarzschild’s Exterior Solution for the Gravitational Field of an Isolated Particle
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 in General Relativity for Beginners
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 ...
Energy Momentum Tensor in the General Theory of Relativity
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 as an Approximation of Field Equations
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 ...
Principle of Equivalence and Principle of Covariance
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 ...
Transformation Equation of Momentum and Energy: Special Theory of Relativity
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 ...
Understanding Mathematical Modelling: Definition, Importance, Classification, and Process
Introduction to Mathematical Modelling Definition of Mathematical Modelling Mathematical modelling is the process of using mathematical structures and concepts to represent real-world systems. This involves translating a problem into mathemati ...
What is a Tensor?: A Comprehensive Guide to the Building Blocks of Modern Science
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 ...