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Results tagged with differential-geometry
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user 45318
Mathematical discipline which studies some properties of smooth manifolds, which allow to generalize calculus to beyond $\mathbb{R}^n$. General relativity is written in this language.
11
votes
1
answer
971
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Evaluating the Einstein-Hilbert action
The Einstein-Hilbert action is given by,
$$I = \frac{1}{16\pi G} \int_{M} \mathrm{d}^d x \, \sqrt{-g} \, R \, \, + \, \, \frac{1}{8\pi G}\int_{\partial M} \mathrm{d}^{d-1}x \, \sqrt{-h} \, K$$
inclu …
- 739
4
votes
0
answers
195
views
$M^{+}_4$ Randall-Sundrum Brane Calculation
The basic Randall-Sundrum model is given by the metric,
$$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$
where $\sigma$ …
- 739
1
vote
0
answers
54
views
Fields transforming under an exceptional Lie group
We may think of tensors as sections of an associated vector bundle to a principal $\mathrm{GL}(n,\mathbb R)$ bundle, with a fibre chosen to be $\mathbb R^m \times (\mathbb R^*)^n$ - these play a role …
- 739