[Users] typo in GRHydro thorn guide?

[Bruno Giacomazzo]

The GRHydro thorn guide (
https://einsteintoolkit.org/thornguide/EinsteinEvolve/GRHydro/documentation.html)
contains the following sentence: "However, in the vacuum limit the
continuity equations describing the fluid break down. *The speed of sound
tends to the speed of light* and everything fails (especially the
conversion from conserved to primitive variables)."

   A student of mine wrote that the sound speed tends to the speed of light
if rho tends to zero citing this, but is this correct?

For example, taking a polytropic EOS P=k*rho^\gamma, the sound speed
squared is (assuming c=1)

cs^2= \gamma * k * rho^\gamma / (rho*h)

with

rho*h=rho+rho*eps+P=rho+\gamma*P/(\gamma-1)

So cs^2 goes like rho^\gamma/(rho+\rho^gamma) and if \gamma>1 then cs^2->0
for rho->0 (while it goes to 1 if rho-> infinity).

Am I missing something?

Cheers,
Bruno

-- 

Prof. Bruno Giacomazzo
Department of Physics
University of Milano-Bicocca
Piazza della Scienza 3
20126 Milano
Italy

email: bruno.giacomazzo at unimib.it
phone: (+39) 02 6448 2321
web: http://www.brunogiacomazzo.org

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