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location United Kingdom
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visits member for 3 years, 2 months
seen 46 mins ago

Manual worker. Live in England. Formal scientific education "peaked" many years ago when I failed maths and chemistry A-level and scraped a bare pass in physics. Still enjoy pottering about in maths and physics.


Jun
5
accepted Minkowski metric and definition of coordinate differentials?
Jun
5
asked Minkowski metric and definition of coordinate differentials?
Mar
27
awarded  Popular Question
Mar
12
awarded  Popular Question
Mar
10
awarded  Notable Question
Jan
28
awarded  Popular Question
Jan
8
awarded  Nice Question
Dec
19
accepted Riemann curvature tensor symmetries confusion
Dec
19
comment Riemann curvature tensor symmetries confusion
@StanLiou: Thanks. Final question. Can the Ricci tensor therefore be defined using other index permutations that don't involve the Riemann tensor having the same 1 and 2 or 3 and 4 indices as the metric, ie $R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\nu\rho}$ , $R_{\mu\nu}=g^{\sigma\rho}R_{\mu\sigma\rho\nu}$ , $R_{\mu\nu}=g^{\sigma\rho}R_{\mu\sigma\nu\rho}$ ?
Dec
18
comment Riemann curvature tensor symmetries confusion
Oh, showing my huge ignorance, I thought you could just sort of “cancel” any upper and lower index. I didn't know about symmetric/anti-symmetric. Does that mean that $g^{\alpha\beta}R_{\alpha\beta\gamma\mu}=g^{\alpha\beta}R_{\gamma\mu\alpha\beta}‌​=0$ ? Would that also mean (swapping the metric tensor indices) that $g^{\beta\alpha}R_{\alpha\beta\gamma\mu}=g^{\beta\alpha}R_{\gamma\mu\alpha\beta}‌​=0$ ? So, if I avoid the Riemann tensor having the same 1 and 2 or 3 and 4 indices as the metric, can I state the Ricci tensor as (for example) $R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$ ?
Dec
18
asked Riemann curvature tensor symmetries confusion
Nov
7
awarded  Popular Question
Sep
18
revised Getting started general relativity
additional information
Sep
10
awarded  Informed
Sep
9
comment Index raising and lowering - how does it work?
I've no idea what this means.
Sep
9
accepted Index raising and lowering - how does it work?
Sep
9
comment Index raising and lowering - how does it work?
I'm afraid I don't understand where the “integrability condition” comes from. However, I can live with that as (I think) I get the gist that all gradients are covectors but not all covectors are gradients, and therefore $g_{\mu\nu}V^{\nu}=\partial_{\mu}\phi$ is only sometimes true. How about going the other way? Does $g_{\mu\nu}V^{\nu}$ always give a tangent vector to a parametrised curve, and how would you show that? Apologies if you've already shown this and I've just got lost in the maths.
Sep
9
asked Index raising and lowering - how does it work?
Aug
28
awarded  Popular Question
Aug
5
answered Understanding Tensors