# Relativity Articles

In plain English, Special Relativity says:

1. The laws of the universe in a non-accelerating reference frame are the same everywhere.
2. The speed of light is constant.

### Why There Are Maximum Mass Limits for Compact Objects

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In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic…

### Oppenheimer-Snyder Model of Gravitational Collapse: Implications

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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsIn the last article in this series, we finished up with a metric for the Oppenheimer-Snyder…

### What Are Tensors and Why Are They Used in Relativity?

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If you try learning general relativity, and sometimes special relativity, on your own, you will undoubtedly run into tensors. This article will outline…

### 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

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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsMost people who have spent any time at all studying GR are familiar with the…

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### Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes

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

### Tolman Law in a Nutshell

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The Tolman law describes how the temperature in a fixed gravitational field depends on the position (see https://arxiv.org/abs/1803.04106 for a pedagogic…

### The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors

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This Insight was inspired by the discussion in "electric field seen by an observer in motion", which tries to understand the relation between two expressions:…

### Is Pressure A Source Of Gravity?

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In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…

### Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

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In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…

### Maxwell’s Equations in a Static, Spherically Symmetric Spacetime

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In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going…

### The Einstein Field Equation in a Static, Spherically Symmetric Spacetime

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This will be the first of several articles which will provide, for reference, useful equations for static, spherically symmetric spacetimes. This is a…

### Learn Relativity Using the Bondi K-calculus

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Although Special Relativity was formulated by Einstein (1905), and given a spacetime interpretation by Minkowski (1908) [which helped make special relativity…

### Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity

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Traditional presentations of special relativity place emphasis on "velocity", which of course has an important physical interpretation... carried over…

### Struggles with the Continuum: Spacetime Conclusion

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We've been looking at how the continuum nature of spacetime poses problems for our favorite theories of physics --- problems with infinities.…

### Struggles with the Continuum: General Relativity

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

### Learn Orbital Precession in the Schwarzschild and Kerr Metrics

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

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A spacetime is often described in terms of a tetrad field, that is, by giving a set of basis vectors at each point. Let the vectors of the tetrad be denoted…

### Learn About Relativity on Rotated Graph Paper

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This Insight is a follow-up to my earlier tutorial Insight (Spacetime Diagrams of Light Clocks). I gave it a different name because I am placing more…

### Learn About Spacetime Diagrams of Light Clocks

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We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45 degrees. Many quantitative…

### Struggles with the Continuum – Relativity and Quantum

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In this series, we're looking at mathematical problems that arise in physics due to treating spacetime as a continuum---basically, problems…

### Why Is the Speed of Light the Same in All Frames of Reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be…

### A Geometrical View of Time Dilation and the Twin Paradox

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Based on the number of questions we receive on the topic at Physics Forums, there is a lot of confusion in the general public about how time dilation works…

### Does Gravity Gravitate: The Wave

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In the first two posts in this series, we looked at different ways of interpreting the question "does gravity gravitate?" We left off at…

### Can I Send a Signal Faster than Light by Pushing a Rigid Rod?

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One common proposal for achieving faster than light communication is to use a long perfectly rigid object and mechanically send signals to the other end…

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### PF’s policy on Lorentz Ether Theory and Block Universe

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What is the PF's policy on Lorentz Ether Theory and Block Universe?Debates about the superiority or "truth" of modern Lorentz Ether Theory (LET) and…

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### Struggles With the Continuum: Point Particles and the Electromagnetic Field

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In these posts, we're seeing how our favorite theories of physics deal with the idea that space and time are a continuum, with points described…

### Why Does C Have a Particular Value, and Can It Change?

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Short answer: Because c (speed of light) has units, its value is what it is only because of our choice of units, and there is no meaningful way to test…

### How Fast Do Changes in the Gravitational Field Propagate?

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General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel…

### Do Photons have Mass?

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Do photons have mass? The quick answer: NO.However, this is where it gets a bit confusing for most people. This is because in physics, there are several…

### Learn the Relativistic Work-Kinetic Energy Theorem

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I was bothered for a long time by the reasons for the relativistic validity of the work-kinetic energy relation ##\Delta E=Fd##, which holds without any…

### Learn A Short Proof of Birkhoff’s Theorem

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Birkhoff's theorem is a very useful result in General Relativity, and pretty much any textbook has a proof of it. The one I first read was in Misner, Thorne,…

### What Is the Bell Spaceship Paradox, and How Is It Resolved?

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Bell describes two spaceships that start out at rest relative to each other, with an elastic string between them, one end attached to each ship, which…

### What is relativistic mass and why it is not used much?

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It happens that the term relativistic mass is used, in particular in the introductory text on special relativity. It should be noted that whether or not…