Schwarzschild Metric Articles

Tag Archive for: Schwarzschild metric

Kerr Spacetime

Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes

/
5 Comments
Introduction The theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief…
gps3

The Schwarzschild Metric: A Newtonian Comparison

/
2 Comments
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…
gps2

The Schwarzschild Metric: The Photon Sphere

/
2 Comments
 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…
gps1

The Schwarzschild Metric: GPS Satellites

/
4 Comments
 A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then…
SchwarzschildGeometry2

The Schwarzschild Geometry: Coordinates

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

Learn Orbital Precession in the Schwarzschild and Kerr Metrics

/
7 Comments
The Schwarzschild Metric A Lagrangian that can be used to describe geodesics is [itex]F = g_{\mu\nu}v^\mu v^\mu[/itex], where [itex]v^\mu = dx^\mu/ds[/itex]…

A Black Hole Problem From Greg Egan’s “Incandescence”

/
8 Comments
The following problem was inspired by reading Greg Egan's "Incadescence".  Consider a body, orbiting a Schwarzschild black hole and tide locked to it,…
redshiftblackholes

Time Dilation & Redshift of Schwarzschild Black Holes

/
76 Comments
Time dilation near a Schwarzschild black hole The following is an overview of the time-dilation and gravitational-redshift effects of a static (Schwarzschild)…