Why we assume that there is a singularity at the centre of Black hole? Isn't it possible that there is a different state of matter exist at such a high pressure which we haven't able to explain using quantum mechanics yet. The idea of infinite density at the centre seems weird. For example according to Netownian gravity which is inverse square law of distance from centre we divide the region of space for the planet or star in two different region and then we are able to get linear gravitational field inside the body and inverse square law outside it. This way we remove the singularity at the centre of the equation.
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1The equations tell us that there is a singularity at the center of the black hole. We do not assume anything. – Prahar Jul 11 '21 at 07:25
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Possible duplicates: https://physics.stackexchange.com/q/24934/2451 , https://physics.stackexchange.com/q/18981/2451 and links therein. – Qmechanic Jul 11 '21 at 07:28
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@Prahar The equations produce the metric. It is your interpretation of the metric that may or may not produce a singularity. Karl Schwarzschild interpreted the $r$ coordinate as spacelike distance from the origin. In this interpretation the “inner” spacetime does not exist, so there is no curvature singularity. – safesphere Jul 11 '21 at 16:24
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@Deep Your question is based on a false premise of “The idea of infinite density at the centre”. - A Schwarzschild singularity is not a point, but an infinitely long line. As the collapsing matter approaches the singularity, the diverging tidal forces rip all point-like elementary particles apart lining them up in a row. At that point the density is finite. After that nothing changes other than the empty space shrinking around. So the “infinite density” near a singularity is no more “weird” than an “infinite density” of any point-like particle far away from a black hole. – safesphere Jul 13 '21 at 05:15