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Results tagged with metric-tensor
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user 310843
The variables used in general relativity to describe the shape of spacetime. If your question is about metric units, use the tag "units", and/or "si-units" if it is about the SI system specifically.
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Connection between the metric tensor and mass
The general expression of a line element in a space with metric tensor $g_{\mu \nu}$ is $$ds = \sqrt{ g_{\mu \nu} dX^{\mu} dX^{\nu} }$$
If we consider a curve $X^{\mu}(\tau)$ parametrised by $\tau$, t …
- 347
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Why does the line element expression contain only second order differential terms? [duplicate]
The general expression of the line element $ds^2$ is $$ds^2 = g_{ij}dX^{i}dX^{j},$$ where $g_{ij}$ is an element of the metric tensor.
Is there a rigorous proof of why there are no terms in the expres …
- 347
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Difference between upper and lower indices in Einstein notation
Consider a $(2,0)$ tensor $X^{\mu \nu}$ that can be represented in matrix form by:
$$X^{\mu \nu} =
\pmatrix{
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
m & n & o & p}\tag{1}$$
Here $a, b, c, …
- 347