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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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- 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...
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Course Description. The theory of special relativity, originally proposed by Albert Einstein in his famous 1905 paper, has had profound consequences on our view of physics, space, and time. This course will introduce you to the concepts behind special relativity including, but not limited to, length contraction, time dilation, the Lorentz ….
General relativity is the theory of space and time and gravity. The essence of the theory is simple: gravity is geometry. The effects that we attribute to the force of gravity are due to the bending and warping of spacetime, from falling cats, to orbiting spinning planets, to the motion of the cosmos on the grandest scale. The purpose of
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we discuss the historical motivations that led Einstein to his theory of special relativity. Section 1.2 covers the two postulates of relativity, from which everything in the theory can be obtained. Section 1.3 is the heart of the chapter, where we derive the three main consequences of the postulates (loss of simultaneity, time dilation, and length
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General relativity is a beautiful scheme for describing the gravitational ̄eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible ...
In comparison with the special theory of relativity, which applies in flat spacetime, the general theory is quite complicated. Whereas the essential building block of the special theory, namely the Lorentz transformation, can be quickly derived from simple physical principles, the general theory requires the introduction of curved spacetime
