Analysing the elasticity difference tensor of general relativity
E.G.L.R. Vaz, Irene Brito
TL;DR
This paper investigates the elasticity difference tensor in general relativity, analyzing its properties through the space-time connection and comparing principal directions with eigendirections of the material metric, with examples in symmetric space-times.
Contribution
It provides a new analysis of the elasticity difference tensor using space-time connection and compares principal directions with eigendirections in symmetric space-times.
Findings
Principal directions are compared with eigendirections of the material metric.
Examples include spherically symmetric and axially symmetric space-times.
The analysis offers insights into the tensor's behavior in different geometries.
Abstract
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and axially symmetric space-times are then presented.
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