Physical theories modified by general relativity

The theory of general relativity changed how scientists understand space, time, and gravity. Before general relativity, many physical theories were based on ideas from Euclidean geometry, where space is flat and straight lines never meet. However, general relativity showed that space and time can curve and bend, especially near very massive objects like stars or black holes.

Because of this, scientists needed to adjust existing theories about physical, electromagnetic, and quantum effects to work in these curved spaces. These adjusted theories are known as physical theories modified by general relativity. They help explain how light bends around massive objects, how the orbits of planets behave, and even how the universe itself expands.

Understanding these modified theories is important for modern physics. They connect general relativity with other areas of science, helping researchers solve problems that were impossible to answer with older theories. This work continues to influence space exploration, astronomy, and our overall picture of the cosmos.

This article will use the Einstein summation convention.

Classical mechanics and special relativity

Classical mechanics and special relativity are grouped together because special relativity acts as a bridge between general relativity and classical mechanics, sharing many of its features.

In both classical mechanics and special relativity, space or spacetime is seen as flat, allowing the use of simple coordinate systems. However, general relativity changes this by allowing spacetime to curve. This means we need new ways to describe motion and gravity. In general relativity, objects move along paths called geodesics, which are influenced by the curvature of spacetime. This approach replaces the older idea that forces cause acceleration, instead showing that mass and energy shape the very fabric of space and time, affecting how objects move.

Main article: Newtonian foundation of general relativity Main article: Theoretical motivation for general relativity

Electromagnetism

Main article: Maxwell's equations in curved spacetime

General relativity changes how we describe electromagnetic phenomena. It uses a new version of Maxwell's equations, which are different from those used in special relativity. These new equations include extra terms called Christoffel symbols.

These changes affect how electromagnetic fields interact with charged objects. The equations show how the electromagnetic field, represented by F^ab, and the sources of the field, represented by J^a, behave in space that is not flat. Even without sources, the basic equations stay the same as in special relativity.