Effective acoustic geometry for relativistic viscous fluids

We employ the Hadamard-Papapetrou method of field discontinuities to determine the effective metric that describes the propagation of acoustic perturbations in isentropic fluids. It is shown that, when dissipative effects are present, small perturbations in fast-moving fluids have a natural description in terms of an effective acoustic geometry. As an application of our results, a model for an acoustic black hole in viscous fluid is investigated.

Figure 1

Plot of $h(\overline{r})$. Singularities occur at $\overline{r}=0$, $\overline{r}=1/2$, and $\overline{r}={\overline{r}}_3$.

Figure 2

The ratio $p_{\mathrm{ext}}/\rho (1)$ as a function of the maximum radius.

Figure 3

Energy density as a function of $\overline{r}$.

Figure 4

Pressure as a function of $\overline{r}$.

Figure 5

Profile of the equation of state $p=p(\rho )$.

Figure 6

Exponent $\gamma$ as a function of $\overline{r}$.