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The idea here is that the speed of sound in more dense object is more. for $e.g.$ $v_{Aluminium} = 6420 m/s$, $v_{water} = 1498 m/s$ and $v_{air}= 346 m/s$

As the density of medium goes on increasing the speed of sound in that medium increases. Black holes are very dense objects, then what can we say about the speed of sound in black hole

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  • $\begingroup$ Neutron stars are very dense objects with a well defined surface defining where the star's matter starts. A black hole forms when the matter cannot resist gravitational collapse to a singularity surrounded by an event horizon. But the singularity is not in spacetime so you can't think of a black hole as a 'more dense' version of a neutron star. See this question and answers $\endgroup$
    – Alfred Centauri
    Commented May 25, 2017 at 2:21

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In cosmology, the speed of sound is given by $c_s^2=dp/d\rho$ where $p$ is the pressure of the fluid and $\rho$ is the energy density of the fluid.

For a schwartzchild black hole, this suggests that the speed of sound everywhere except at the singularity would be zero (since a Schwartzchild black hole is nothing but a singularity and event horizon).

For a more exotic model of a black hole, or a black hole that does not contain a singularity inside it you would need to know the equation of state for the fluid (or whatever stuff there is) inside the event horizon.

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  • $\begingroup$ Does this answer make sense at all? In what direction would sound travel inside a black hole? $\endgroup$
    – user126422
    Commented May 25, 2017 at 3:10
  • $\begingroup$ Inward. Inside an event horizon future timelike directions point towards the singularity, such that all trajectories will (eventually) hit the singularity. Now as to the form of the actual equation of state of fluid inside a black hole (either made of normal matter or more exotic hypothetical stuff), the speed of sound might take on more interesting forms. $\endgroup$
    – Bob
    Commented May 25, 2017 at 3:23
  • $\begingroup$ Ok, got it, I thought you meant that a signal could travel across the black hole! (well, in a rotating black hole it actually can, I believe) $\endgroup$
    – user126422
    Commented May 25, 2017 at 3:34

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