It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$, where $c$ is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent overview of several models that were shown to behave this way. There is no proof for this conjecture, but if it holds true, then then answer to your question is that the speed of sound does not approach the speed of light, even at high densities.

Regarding black holes: the fact that in a classical description all mass is concentrated at a singularity is a sign that the theory breaks down at that point. In the context of quantum gravity, this problem should no longer arise.

It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$, where $c$ is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent overview of several models that were shown to behave this way. There is no proof for this conjecture, but if it holds true, then the answer to your question is that the speed of sound does not approach the speed of light, even at high densities.

Regarding black holes: the fact that in a classical description all mass is concentrated at a singularity is a sign that the theory breaks down at that point. In the context of quantum gravity, this problem should no longer arise.

It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent overview of several models that were shown to behave this way. There is no proof for this conjecture, but if it holds true, then then answer to your question is that the speed of sound does not approach the speed of light, even at high densities.

Regarding black holes: the fact that in a classical description all mass is concentrated at a singularity is a sign that the theory breaks down at that point. In the context of quantum gravity, this problem should no longer arise.

It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$, where $c$ is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent overview of several models that were shown to behave this way. There is no proof for this conjecture, but if it holds true, then then answer to your question is that the speed of sound does not approach the speed of light, even at high densities.

Regarding black holes: the fact that in a classical description all mass is concentrated at a singularity is a sign that the theory breaks down at that point. In the context of quantum gravity, this problem should no longer arise.