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Results tagged with differential-geometry
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user 311860
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.
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Tetrad formalism for a metric with signature $(+,-,-,-)$
I have studied tetrad formalism.
For example, consider the Minkowski metric in 4D
$$\text{d}s^2 = -\text{d}t^2 + \text{d}r^2 + r^2 \text{d}\theta^2 + r^2 \sin^2θ \text{d}\phi^2$$
For this, we construc …
- 313
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Normal to the hypersurface
I have a given metric and I want to choose a spacelike hypersurface and find the normal to that hypersurface. I know that if the hypersurface is spacelike, then the normal is timelike.
The given metri …
- 313
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Understanding the derivation of Killing horizon surface gravity
In the book "A Relativist's Toolkit" by Eric Poisson, he explains surface gravity in section 5.2.4
The equation 5.40 says
$$ (-t^\mu t_\mu)_{;\alpha} = 2 \kappa t_\alpha \tag{5.40}$$
where $t^\alpha$ …
- 313