29 lines
930 B
Markdown
29 lines
930 B
Markdown
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# Math
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Inline radiation: $E = h\nu$ redshifted by $\sqrt{g_{tt}}$.
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$$E = h\nu\,\sqrt{g_{tt}(r)} = \text{konst.} \quad (1)$$
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The metric reads $ds^2 = -g_{tt}(r)c^2dt^2 + dr^2 + r^2d\Omega^2$, and a
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photon loses energy as $\frac{E(t)}{E_0} = e^{-Ht}$.
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$$1+z = \frac{\nu(r_1)}{\nu(r_2)} = \sqrt{\frac{g_{tt}(r_1)}{g_{tt}(r_2)}}. \quad (2)$$
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Prices are not math: the ticket costs $5 and the guide $10 per group.
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The metric in prose right above its display form
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$$g_{tt}(r) = 1 - \frac{r_s}{r}$$
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continues in a sentence after it.
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$$r_h = \frac{\sigma}{\sqrt{2\pi G \rho_{\text{amb}}}},
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\qquad M_h = \frac{2\sigma^2 r_h}{G}. \quad (7)$$
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An equation broken across lines keeps its prose out of mathematics
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$\nabla^2 h =
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(8\pi/\kappa a)u$: the binding is the force of a cell $\kappa a = c^4/G$,
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and the source is the energy.
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$$\raisebox{1em}{E} = h\nu$$
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Inline degradation too: $\raisebox{1em}{E}$ stays visible where it stands.
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