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Results tagged with general-relativity
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user 272562
A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
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Volume element of manifolds via wedge products
I'm following Carroll's book on General Relativity and in chapter 2, section 2.10, he claims that the volume element can be identified with
$$d^nx=dx^0\wedge\ldots \wedge dx^{n-1}.$$
I understand why …
- 186
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Variation of the metric determinant
I know this question has been answered here for example but I want to make emphasis in a new aspect. Consider the variation of the metric determinant $\delta g$ with respects to variations of the metr …
- 186
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Noether/Hilbert energy-momentum tensor
In chapter 4 of Carroll's book Spacetime and geometry he finds using the Hilbert action that the energy-momentum tensor for a scalar field is (see eq. (4.79))
$$T_{\mu\nu}^{\phi}=\nabla_\mu\phi\nabla_ …
- 186