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The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity) — Joh. Ambr. Barth, 1916; this book assumes some familiarity with the special theory of relativity. v
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The theory is based on two fundamental principles: Relativity: The laws of physics do not change.Even for objects moving at inertial, constant speed frames of reference. Speed of light: It is the ...
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- Why Is General Relativity Important?
- General Relativity in A Nutshell: A Quick Overview
- The Underlying Postulates of General Relativity
- The Mathematics of General Relativity Explained Intuitively
- Metric Tensor: The “Fundamental tensor” of General Relativity
- Christoffel Symbols & Their Geometric Meaning
- Curvature Tensors & How They Relate to Gravity in General Relativity
- The Energy-Momentum Tensor
- Geodesics & How Objects Move in Curved Spacetime
- Tidal Forces in General Relativity
Before we get started on what general relativity actually is, there is an important aspect to be discussed: why should you even care about this topic? Sure, you’ve clicked on this article, so you’re probably interested to learn more, but still; what makes general relativity an important theory? Here is a list of a few of the most important applicat...
Here, I will present a quick overview of the whole theory of general relativity, which will lay down the most important ideas and help you see the big picture. After that, we will look into each of these things in much more detail. Now, you may have heard the phrase “gravity is the curvature of spacetime” at some point. This phrasing can, however, ...
Every theory is always based on a few underlying principles or postulates, which pretty much lead to the specifics and the results of the theory. General relativity is no different. Really there are two main postulates that general relativity is based on, which are the following: 1. The principle of general covariance: this is mainly a mathematical...
In this section, we’ll go over the important mathematical tools used in general relativity, such as themetric tensor and the Christoffel symbols. We’ll also explore the physical and geometric interpretationsof these. It’s important, however, to realize that the focus of this article is not necessarily in the math, but rather what the math actually ...
Arguably the most important tensor in general relativity is the metric tensor, which I did mention earlier already. But what is the metric tensor actually and what is it used for? In short, the metric tensor is used to define lengths and other geometric properties of spacetime in general relativity. The metric generalizes these properties to any cu...
The next important concept we’ll look at are the Christoffel symbols, which come up in the geodesic equation and in describing spacetime curvature (both which we will talk about in more detail later). Christoffel symbols are mathematical objects that describe how basis vectors change in a coordinate system. In general relativity, Christoffel symbol...
By now, it should be clear that gravity is described by spacetime curvature in general relativity. The point of this section is to explain how spacetime curvature is actually described mathematically, which is by using different curvature tensors. To give some insight into why the different curvature tensors have the form they have, it is important...
As you may know by now, gravity is described by spacetime curvature. But according to Newtonian physics, gravity is caused by mass, such as the mass of a planet. So far, we have not talked about what actually causes gravity or the curvature of spacetime in general relativity. The answer is a bit more complicated in general relativity than just mass...
We are now ready to actually get to the interesting physics concepts of general relativity. The key idea is the notion of geodesics, which are in their most simple sense, just trajectories through spacetime. Fundamentally, a geodesic is just a straight line. If you happen to be in a curved spacetime, however, straight lines will naturally follow th...
The effects of tidal forces can be seen as the rise of sea levels caused by the Moon’s gravity. However, tidal forces are always present when an object is in a gravitational field and these may cause the object to get deformed. Newtonian gravity explains this by the fact that different parts of an object experience a different gravitational force a...
As an introduction, special relativity is the study of high velocities, those close to the speed of light. Special relativity is based on two fundamental principles; the constancy of the speed of light and the universality of the laws of physics, which lead to the ideas of spacetime and 4-vectors.
A No-Nonsense Introduction to General Relativity. Sean M. Carroll Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL, 60637. carroll@theory.uchicago.edu. c 2001. 1 Introduction. General relativity (GR) is the most beautiful physical theory ever invented.
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theory of relativity was because the mathematics involved produced some difficulties to iron out. There are two different theories of relativity: general and special. For simplicity’s sake hereinafter in this book, we will call Einstein’s special theory of relativity: Theory S. And we will call Einstein’s general theory of relativity ...
The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity)—Joh. Ambr. Barth, 1916; this book assumes some familiarity with the special theory of relativity. T
