A black hole is a core of infinite density

The argument

At the centre of every black hole, on this account, lies a singularity: a point containing the entire mass of a collapsed star in a single, indefinitely small volume. Because density is mass divided by volume, compressing a stellar mass toward zero extent drives the density toward infinity, and the gravitational force associated with it does the same. The singularity is therefore not a very small object inside the black hole but the limiting case of compression, where the quantities used to describe matter no longer take finite values. This point of infinite density and gravity is presented as the source of everything else about the object. The surrounding black hole, including the region from which nothing escapes, exists because of the gravitational force concentrated at the centre; the structure is generated by the singularity rather than containing it incidentally. The consequence proponents emphasise is that the known laws of physics break down there and become unpredictable. Those laws are formulated in terms of finite densities, finite curvatures and finite forces, so a location where all three are unbounded is one where the equations return no meaningful answer rather than a surprising one. The singularity marks the boundary of what current physical theory can describe. The account also explains what the extreme gravity does to the geometry of the surrounding region. The immense gravity warps four-dimensional spacetime so severely that the paths available to anything inside collapse onto a single dimension, directed inward. This has a consequence for motion and for time alike: objects falling into the black hole can only move toward the singularity, with no trajectory that leads back out, and time does not exist for them in a recognisable form, because the distinction between moving through space and moving through time that holds elsewhere no longer applies.

Premises

Counter-arguments

A singularity has never been observed, so while it could be mathematically or theoretically true, it can't be confirmed. The event horizon of a black hole, the boundary that light cannot pass out of, surrounds the singularity, so no information can escape from the singularity. Therefore we will never be able to see a singularity or observe it, and cannot know that it exists.

Rejecting the premises

[Rejecting P1] The premise states a prediction of general relativity as though it were an observation, and then reports the reason to doubt it. Where the known laws break down, the quantity they predict — infinite density — is usually read as the theory failing rather than as a fact about nature; singularities are what a classical theory produces in a regime where a quantum account of gravity is expected to be required. [Rejecting P2] The description of infall is better established than the description of the centre, and it does not support it. That trajectories inside the horizon lead inward, and that an outside observer's notion of time no longer applies, are consequences of the geometry near the horizon, none of which requires a point of infinite density at the middle. [Rejecting C] The conclusion also makes the least observable feature definitive. What is actually established about black holes concerns the horizon — its size, its relation to mass and spin, and in the imaged cases the shadow it casts — while the counter's point stands that no information from inside can reach us, so the core cannot be the defining feature of a structure described entirely from outside.