Tag Archive for: black holes

Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details
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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsIn a previous article, I described in general terms the model of gravitational…

The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview
Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsMost people who have spent any time at all studying GR are familiar with the…

Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes
Introduction
The theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief…

I Know the Math Says so, but Is It Really True?
I'm sure anyone who has hung out long enough here on Physics Forums has encountered threads that go something like this (I'll use an example based on threads…

Gaia Astrometry: Detecting Gravitational Waves Guide
Overview
Gravitational waves (GWs) are disturbances in spacetime produced by massive objects moving asymmetrically. Only the most massive and most relativistic…

VHE Gamma Rays from Sgr A*: Black Holes and CTA Observations
Researchers simulating the accretion flow around Sagittarius A*, the supermassive black hole at the Milky Way's center, have found that magnetic reconnection…

The Four Laws of Black Hole Thermodynamics Explained
Black hole thermodynamics consists of four laws that mirror the ordinary laws of thermodynamics: a zeroth law of uniform surface gravity, a first law relating…

Mass Inflation in Black Holes: Poisson-Israel Theory Explained
Mass inflation is the phenomenon in which the internal mass parameter of a rotating or charged black hole grows without bound near the Cauchy horizon,…

Killing Vector Field & Surface Gravity in Kerr BH Explained
Killing Vector Field
The Killing vector field is a vector field on a differentiable manifold that preserves the spacetime metric. In other words, it generates…

Radial Infall into a Static Mass: Equations & Guide
From Exploring Black Holes by John Wheeler and Edwin Taylor. The relations below apply to any object falling radially toward a static, spherically symmetric…

The Schwarzschild Metric: The Photon Sphere
A Short Proof of Birkoff's Theorem derived the Schwarzschild metric in units of ##G = c = 1##:\begin{equation} ds^2 = -\left(1 - \frac{2M}{r}\right)dt^2…

The Schwarzschild Geometry: Physically Reasonable?
In the last article, we looked at various counterintuitive features of the Schwarzschild spacetime geometry, as illustrated in the Kruskal-Szekeres…

The Schwarzschild Geometry: Spacetime Diagrams
When we left off in part 2, we were looking at the metric for the Schwarzschild geometry in Kruskal-Szekeres coordinates:$$
ds^2 = \frac{32…

The Schwarzschild Geometry: Coordinates
At the end of part 1, we looked at the form the metric of the Schwarzschild geometry takes in Gullstrand-Painleve coordinates:$$
ds^2…

The Schwarzschild Geometry: Key Properties
Not long after Einstein published his Field Equation, the first exact solution was found by Karl Schwarzschild. This solution is one of the…

Struggles with the Continuum: General Relativity
Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this…

A Black Hole Problem From Greg Egan’s “Incandescence”
The following problem was inspired by reading Greg Egan's "Incadescence". Consider a body, orbiting a Schwarzschild black hole and tide locked to it,…

Do Black Holes Really Exist?
Introduction
The purpose of this article is to discuss the title question from several different viewpoints, to show that it isn't as simple as it looks.…

Why the Big Bang Wasn’t a Black Hole: Cosmology Explained
The Big Bang was not a black hole because it happened everywhere in space at once rather than at a single point, and because the near-perfect homogeneity…

Time Dilation & Redshift of Schwarzschild Black Holes
Time dilation near a Schwarzschild black hole
The following is an overview of the time-dilation and gravitational-redshift effects of a static (Schwarzschild)…

Will All Matter Be Converted to Photons?
Will all matter be converted into black holes and then photons?
No. There is a misconception that a lot of laypeople seem to be picking up recently from…

An Equation for the Centrifugal Force Reversal Near A Black Hole
My goal in this article is to derive a simple equation for the proper acceleration of an observer traveling on a circular path around a Schwarzschild black…

Star Death Explained: White Dwarfs to Black Holes
Stellar death outcomes depend on the star's initial mass: stars below roughly 8 solar masses end as white dwarfs, while more massive stars undergo core…
