- #1
Prez Cannady
- 21
- 2
Depending on the source, I'll often see EFE written as either covariantly:
$$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = 8 \pi GT_{\mu\nu}$$
or contravariantly
$$R^{\alpha\beta} - \frac{1}{2}Rg^{\alpha\beta} = 8 \pi GT^{\alpha\beta}$$
Physically, historically, and/or pragmatically, is there a reason for this? Or is it just the result of habit and preference with the understanding that you can raise and lower indices as required once you've solved for mass-energy or curvature?
I mean, mathematically I might use the bottom formulation when playing with covectors, but when would a relativist do that in practice in his every day work? Or do physicists not really concern themselves about the convention just so long as the indices line up at the end of the day?
$$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = 8 \pi GT_{\mu\nu}$$
or contravariantly
$$R^{\alpha\beta} - \frac{1}{2}Rg^{\alpha\beta} = 8 \pi GT^{\alpha\beta}$$
Physically, historically, and/or pragmatically, is there a reason for this? Or is it just the result of habit and preference with the understanding that you can raise and lower indices as required once you've solved for mass-energy or curvature?
I mean, mathematically I might use the bottom formulation when playing with covectors, but when would a relativist do that in practice in his every day work? Or do physicists not really concern themselves about the convention just so long as the indices line up at the end of the day?