If the laws of physics break in a singularity...?
As far as we know, if you entered an extremely massive (say trillion solar mass) black hole, you'd have many hours of life left before you were crushed in the center. During that time you could do experiments to measure the "laws of physics", and you would find they are no different from the laws of physics outside the black hole. Then you'd die. The trouble with this idea (and this is the subject of current research) is that the time you spent inside the black hole would be AFTER an infinite time had passed on the outside. Surely this is impossible, and wouldn't the Black Hole evaporate by the Hawking process before you could really get inside? So something else must be going on, something relating to quantum gravity that we don't (yet?) understand.
I think of black holes as garbage disposals. what goes in doesn't come out in THIS Universe. If it DOES come out, the laws of physics may be totally different in that universe. Density implies volume. A mathematical singularity has NO volume. It is a point. BTW, the laws of physics and quantum mechanics break down at the event horizons, NOT IN the singularity.
‘If’ is a rather large assumption.
General Relativity allows a static unchanging gravitational field to exist outside the event horizon due to mass inside it. But nothing that happens inside the horizon can cause any change on the outside. As others said, it would take an infinite amount of time for you or any matter to fall across the event horizon, relative to far away observers. Hawking radiation will evaporate away the black hole before a singularity forms. Even if general relativity predicts a singularity, quantum gravity effects might stop a point of infinite density and infinite gravity from forming. We don't know for sure. Quantum gravity theory has not been discovered yet.
Q How far is infinity ? Twice the length of half of it
Singularities may not exist, they are thought of as a mathematical abstraction. The existence black holes does not require them.
they break down cos maths cant cope with a zero (or its inverse- infinity) when t= 0 and d = 0 (at the singularity ) then time ceases to exist and gravity becomes infinite (BTW "caroloklanola" - they dont)
It’s actually worse than you think. A black hole can also have angular momentum (Kerr metric) and charge (Reissner–Nordström metric) or both (Kerr–Newman metric). So, mass, charge, and angular momentum can all have external manifestations even though they are presumed sourced at the singularity. There are two main ways of dealing with this. The first is that it highly unlike singularities actually physically exist. The singularity theorem by Roger Penrose proved that a singularity - under general relativity - had to exist under certain ASSUMPTIONS about the energy contained within the black hole. Many think those assumptions can be violated. There is also a modification to general relativity called the Einstein-Cartan theory that introduces a torsion (a twisting) of spacetime. General relativity itself is a torsion free theory. The ramifications of this is that the spin energy of densely packed quantum spins will introduce a torsion in the spacetime metric that generates a kind of repulsive gravity that prevents the singularity from forming. The second way of looking at isn’t nearly as neat. Think about what happens to something approaching the event horizon from the perspective of an outside observer. It might have mass, be rotating rapidly, and have charge. From the external perspective, it never makes it across the event horizon. Therefore all of its properties - mass, angular momentum, and charge never reach the singularity - if it exists- or cross the event horizon from the outside perspective so those properties still exist to the external universe.