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general relativity

Basic understanding of a metric tensor: Disassemble the concept of a distance over Riemannian Manifolds

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Preamble Gaussian Curvature (Wikipedia)One of the core concepts in Physics is so called metric tensor. This object encodes any kind of geometry. Combined genius of Gauß,  Riemann and their contemporaries lead to such a great idea, probably one of the achievements of human quantitative...

Insights into Bekenstein entropy with an intuitive mathematical definitions: A look into Thermodynamics of Black-holes

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Jacob Bekenstein (Wikipedia) Preamble Thermodynamics of black holes has appeared as one of the most interesting areas of research in theoretical physics [Wald1994], specially after LIGO's massive success. The striking results of Jacob Bekenstein  [Bekenstein1973] in proposing a formulation of...

In Einstein’s General Theory of Relativity, space and time...

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In Einstein’s General Theory of Relativity, space and time are unified in a single entity called spacetime. This is the “stage” in which the laws of physics operate. In Einstein’s theory, the presence of mass and energy warps spacetime, and it is this curvature that affects objects in the way we...