kurious
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What is a time-like killing vector?
The discussion centers around the concept of a time-like Killing vector, exploring its definition, properties, and implications in the context of isometries and the metric tensor in general relativity. Participants delve into mathematical formulations and examples, particularly in relation to stationary black holes.
Participants generally agree on the definitions and mathematical formulations related to Killing vectors and their properties. However, there are nuances in the interpretations and implications of these concepts, indicating that multiple views remain on the broader implications of time-like Killing vectors.
Some discussions involve assumptions about the signature of the metric tensor, which may affect the interpretation of time-like vectors. The discussion also touches on the mathematical rigor required in defining isometries and Killing vectors, which may not be fully resolved.
A few preliminaries - A coordinate transformation which leaves the components of the metric tensor invariant is called an isometry. This means that when the coordinates are change from the primed coordinates, x', to the unprimed coordinates x, the metric tensor remains unchanged, i.e. is the same function of the coordinates. This meanskurious said:What is a time-like killing vector?
That depends on the signature of the metric tensor.Atheist said:time-like: A vector v is timelike if [tex]g_{ij} v^{i} v^{j} >0[/tex].
kurious said:What is a time-like killing vector?