Lecture

General Relativity: Einstein Equations

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In course

PHYS-427: Relativity and cosmology I

Introduce the students to general relativity and its classical tests. ...

Description

This lecture covers the Lagrangian formulation of General Relativity, introducing the Einstein-Hilbert action and deriving the Einstein equations in vacuum. It discusses the Newtonian limit, scalar gravity, and the minimal-coupling principle, leading to the generalization of the gravitational field equations. The instructor explains the concepts of geodesic equations and the independence of photon trajectories from the mass density. The lecture concludes with a detailed analysis of the Einstein equations and their implications in the context of General Relativity.

Official source

Ontological neighbourhood

Physics

Relativity: General relativity

Related concepts (32)

Gravitational field

In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). Equivalently, it is measured in meters per second squared (m/s2). In its original concept, gravity was a force between point masses.

General relativity

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime.

Alternatives to general relativity

Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity. There have been many different attempts at constructing an ideal theory of gravity. These attempts can be split into four broad categories based on their scope. In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification.

Vacuum solution (general relativity)

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field.

Tests of general relativity

Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954.

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