cross-posted from: https://slrpnk.net/post/5710029

Institution: Wikiversity
Lecturer: Boud Roukema
Subject: #physics #specialrelativity #generalrelativity
Description: Special relativity and steps towards general relativity is a one-semester Wikiversity course that uses the geometrical approach to understanding special relativity and presents a few elements towards general relativity. The course may be used in a traditional university, within the conditions of the free licensing terms indicated at the bottom of this Wikiversity web page. It may be modified and redistributed according to the same conditions, for example, via the Wikiversity and Wikimedia Commons web sites.

I was reading some works – true pearls! – by Synge: his conference contribution Tensorial integral conservation laws in general relativity (1959/1962) and his book Relativity: The General Theory (1960). In these works Synge introduces an extremely interesting definition of four-momentum and of rotational momentum, based on two-point tensors. The definition is interesting because (1) it involves the full Riemann tensor, not just the Einstein tensor, (2) it includes the (or rather, defines a) four-momentum and rotational momentum of the gravitational field, (3) it obeys a conservation law as opposed to a balance law (the equation ∇⋅T=0 expresses in general just balance, not conservation).

The definition for rotational momentum is also interesting because it appears as the natural generalization of the one in Newtonian mechanics, which is based on the affine structure of its 3D space. Roughly speaking, in Newtonian mechanics we have (r-a)∧p, where a is a fixed point, r the point of i