Archives for Cosmology
Hawking Radiation, How black holes evaporate
Stephen Hawking's seminal paper on black hole radiation, often referred to as **Hawking Radiation**, explains how black holes, previously thought to only absorb matter and energy, can actually emit radiation…
Schwarzschild Solution for a Black Hole
Schwarzschild Solution for a Black Hole 1. Schwarzschild Metric: The Schwarzschild solution is the simplest solution to Einstein's field equations in general relativity. It describes the spacetime geometry surrounding a…
Scalar Wave Equation in a Schwarzschild Background
Scalar Wave Equation in Schwarzschild Background: For the Schwarzschild metric, the scalar wave equation becomes: (1−2GMc2r)−1∂2Φ∂t2−1r2∂∂r(r2(1−2GMc2r)∂Φ∂r)−1r2sinθ∂∂θ(sinθ∂Φ∂θ)−1r2sin2θ∂2Φ∂ϕ2=0.\left(1 - \frac{2GM}{c^2r}\right)^{-1} \frac{\partial^2 \Phi}{\partial t^2} - \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \left(1 - \frac{2GM}{c^2r}\right)…
Kaluza-Klein theory and general relativity
The relationship between Kaluza-Klein theory and general relativity is a foundational aspect of the former. Kaluza-Klein theory extends general relativity by incorporating additional dimensions beyond the familiar four-dimensional spacetime. Here…
Gravitational Redshift, Inertia, and the Role of Charge
The document titled "Gravitational Redshift, Inertia, and the Role of Charge" by Johannes Fankhauser and James Read explores several nuanced aspects of gravitational redshift and related phenomena. Here is…
Colliding Neutron Stars and Baryonic Pollution
Colliding neutron stars - Gravitational waves, neutrino emission, and gamma-ray bursts - by M. Ruffert1 and Janka2 This document discusses the collision of neutron stars in the context of their…
Hawking Radiation and Black Hole Thermodynamics
The document titled "Hawking Radiation and Black Hole Thermodynamics" by Don N. Page provides a comprehensive review of the theoretical developments in the understanding of black holes, focusing on their…
Brownian Motion and Stellar Dynamics – Chandrasekhar Paper
Stellar Encounters as an Example of Brownian Motion Stellar encounters as an example of Brownian motion, outlines the similarities between stellar dynamics and the classical theory of Brownian motion. It…
Roger Penrose and the Big Bang Theory
The big bang would have required a very low entropy state. While most physicists just take such an initial state for granted, Penrose argues that such 'improbable' states don't just…
An earth like Planet needs more than just water
The presence of water is a pre-requisite. However, it is also crucial to be able to a) Keep (retain) that water. This isn't as easy as it sounds - both…