# Math

Inline radiation: $E = h\nu$ redshifted by $\sqrt{g_{tt}}$.

$$E = h\nu\,\sqrt{g_{tt}(r)} = \text{konst.} \quad (1)$$

The metric reads $ds^2 = -g_{tt}(r)c^2dt^2 + dr^2 + r^2d\Omega^2$, and a
photon loses energy as $\frac{E(t)}{E_0} = e^{-Ht}$.

$$1+z = \frac{\nu(r_1)}{\nu(r_2)} = \sqrt{\frac{g_{tt}(r_1)}{g_{tt}(r_2)}}. \quad (2)$$

Prices are not math: the ticket costs $5 and the guide $10 per group.

The metric in prose right above its display form
$$g_{tt}(r) = 1 - \frac{r_s}{r}$$
continues in a sentence after it.

$$r_h = \frac{\sigma}{\sqrt{2\pi G \rho_{\text{amb}}}},
\qquad M_h = \frac{2\sigma^2 r_h}{G}. \quad (7)$$

An equation broken across lines keeps its prose out of mathematics
$\nabla^2 h =
(8\pi/\kappa a)u$: the binding is the force of a cell $\kappa a = c^4/G$,
and the source is the energy.

$$\raisebox{1em}{E} = h\nu$$

Inline degradation too: $\raisebox{1em}{E}$ stays visible where it stands.