# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Richard777 on 08/12/2016 19:44:19

Title: Can vector, co-vector pairs simply lead to the Schwarzschild metric?
Post by: Richard777 on 08/12/2016 19:44:19
Each point in the continuum may be associated with a vector and a co-vector (vector pair).

Both represent deformation of the continuum. One is a displacement vector, representing the displacement of a point in the continuum due to stress. The co-vector (incremental vector) represents a gradient of displacement.

Two frames of reference are required. The origin of each frame is a point in the continuum. This gives four field vectors (a vector pair at each origin).

A field is defined if the components of the vector pairs are related in some manner. The vector components (and geometries) are related by field rules.

If the vector types and the field rules are suitably defined, then the Schwarzschild metric may be simply obtained.

Can the Schwarzschild metric be simply derived in this manner?
Title: Re: Can vector, co-vector pairs simply lead to the Schwarzschild metric?
Post by: jeffreyH on 08/12/2016 20:34:03
The following wikipedia article may be useful.

https://en.m.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution (https://en.m.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution)

The metric has an inbuilt symmetry due to its nature. I haven't examined your pdf yet so cannot comment further.