What geometry does general relativity use?

A version of non-Euclidean geometry, called Riemannian Geometry, enabled Einstein to develop general relativity by providing the key mathematical framework on which he fit his physical ideas of gravity.

Is general relativity non-Euclidean?

A non-Euclidean universe was too strange for many to accept at first. Yet it was non-Euclidean geometry that paved the way for Albert Einstein’s theory of general relativity in the early 1900s and the modern understanding of space-time.

What is the main idea of the general theory of relativity?

What is general relativity? Essentially, it’s a theory of gravity. The basic idea is that instead of being an invisible force that attracts objects to one another, gravity is a curving or warping of space. The more massive an object, the more it warps the space around it.

What is intrinsic and extrinsic curvature?

Intrinsic curvature comes from the parallel translation of a vector tangent to the path of translation. If a vector is translated around a loop and it fails to come back onto itself that is intrinsic curvature. Extrinsic curvature is computed by the parallel translation of a vector normal to a surface or space.

Does general relativity use differential geometry?

General relativity then makes the force of gravity a mere mater of the curvature of spacetime. Underlying all of this is the mathematics of differential geometry. The effects of relativity will at first distort the orbits from their classical closed ellipses, and then make them only calculable numerically.

What is general relativity and special relativity?

Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.

What is extrinsic geometry?

Properties of a curve or surface which depend on the coordinate space that curve or surface is embedded in are called extrinsic properties of the curve. For example, the slope of a tangent line is an extrinsic property since it depends on the coordinate system in which rises and runs are measured.