General Relativity Articles

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Learn the Math

I Know the Math Says so, but Is It Really True?

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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…
Minkowski Spacetime

Understanding Precession in Special and General Relativity

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The Absolute Derivative In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…
Kerr Spacetime

Exploring Fermi-Walker Transport in Kerr Spacetime

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In the last two posts in this series, we developed some tools for looking at Fermi-Walker transport in Minkowski spacetime and then applied them in Schwarzschild…
Minkowski_Spacetime_2

Learning Fermi-Walker Transport in Schwarzschild Spacetime

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In the first post in this series, we introduced the concepts of frame field, Fermi-Walker transport, and the "Fermi derivative" of a frame field, and developed…
Minkowski Spacetime

Fermi-Walker Transport in Minkowski Spacetime

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This is the first of several posts that will develop some mathematical machinery for studying Fermi-Walker transport. In this first post, we focus on Minkowski…
information definition

How to Better Define Information in Physics

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When I ask questions about the conservation of information I frequently get the reply, “It depends on what you mean by information.”   So, I researched…
maxima

How to Solve Einstein’s Field Equations in Maxima

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A few months ago, pervect pointed me to a post by Chris Hillman which is an introduction to the usage of Maxima for General Relativity. Maxima is a free…
SchwarzschildGeometry4

The Schwarzschild Geometry: Physically Reasonable?

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 In the last article, we looked at various counterintuitive features of the Schwarzschild spacetime geometry, as illustrated in the Kruskal-Szekeres…
SchwarzschildGeometry3

The Schwarzschild Geometry: Spacetime Diagrams

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 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…
SchwarzschildGeometry2

The Schwarzschild Geometry: Coordinates

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 At the end of part 1, we looked at the form the metric of the Schwarzschild geometry takes in Gullstrand-Painleve coordinates:$$ ds^2…
SchwarzschildGeometry1

The Schwarzschild Geometry: Key Properties

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

Exploring General Relativity as a Gauge Theory

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The fundamental interactions of the Standard Model are described by Yang-Mills theory. This is a gauge theory, which means the following: (1) Choose a…
Newton-Cartan-Theory

The Revival of Newton-Cartan Theory in General Relativity

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It's a calculation which you can find in any textbook on General Relativity (GR): when gravity is weak and does not vary with time, and when particles…
universeexpand

Learn about the Big Bang and the Expansion of the Universe

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The "ordinary Big Bang and expansion" (no inflation, no dark energy) Einstein's General Relativity allows a solution (FLRW metric) where an empty Universe…
observableuniverse

Radius of the Observable Universe in Light-years Is Greater than Its Age

The radius of the observable universe is about 46 billion light-years, which is considerably greater than its age of about 14 billion years. The radius…
universespinning

Can We Tell Whether the Universe Is Rotating?

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If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing…