Curved space-time can have discontinuities {singularity, relativity}|, when geodesics are not continuous and/or points do not have neighborhoods. Those space-time events have no past or no future points, and so start or stop world-lines.
gravity
If gravity is high enough to prevent light from exiting a space region, space-time curvature becomes so great, with curvature radius equal Planck distance, that space closes on itself. The space region has a surface from which nothing can escape. As orthogonal light rays converge, spatial surface {trapped surface} has decreasing area. Space-time geodesics do not continue infinitely in space-time but stop at space boundary.
causes
Stellar and galactic-center collapse can make singularities, such as black holes.
Perhaps, Big Bang, white holes, Big Crunch, and/or black hole are space-like or light-like singularities. Perhaps, universe beginning was a singularity and began time. For black holes and Big Crunch, tidal distortions can be large. For Big Bang, at low entropy, tidal distortions (described by Weyl curvature tensor) are small. Perhaps, white holes violate the second thermodynamics law.
physical law
At space-time singularities, all physical laws break down, so field equations do not hold. Because space-time has high curvature, singularities violate CPT symmetry. Space-time-curvature radius is approximately Planck length, so space-time separations are approximately zero.
physical law: quantum mechanics
Quantum-mechanical-system states develop in unitary, deterministic, local, linear, and time-symmetric evolution in Hilbert configuration space. By Liouville's theorem, phase-space volumes are constant. However, "reduction of state vector" is asymmetric in time, and "collapse of wave function" adds phases and information, so phase-space volumes are not constant, and past and future have different boundary conditions, just as singularities have discontinuities between space-time pasts and futures. Quantum-mechanics measurements cause wave-function collapse.
Perhaps, quantum-mechanics measurements and wave-function collapse relate to general-relativity singularity space-time points and their formation. Perhaps, general relativity disrupts, or makes unstable superpositions of, quantum states and breaks equilibrium at measured states (objective reduction). General relativity has non-local negative-gravity potential energy and has positive-energy gravity waves, while state-vector-reduction time depends on inverse diameter and energy.
Physical Sciences>Physics>Relativity>General Relativity>Curvature>Singularity
5-Physics-Relativity-General Relativity-Curvature-Singularity
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Date Modified: 2022.0224