Hawking's Singularity Theorem

A Hawking's Singularity Theorem is a singularity theorem that proves the existence of singularities in cosmological spacetimes under expansion conditions and energy constraints.

• AKA: Hawking Singularity Theorem, Cosmological Singularity Theorem, Big Bang Singularity Theorem.
• Context:
  • It can typically prove Big Bang Singularities in expanding universes.
  • It can typically apply Time-Reverse Arguments to cosmological evolution.
  • It can typically require Energy Conditions for matter content.
  • It can typically assume Cosmological Homogeneity at large scales.
  • It can often complement Penrose's Singularity Theorem for black holes.
  • It can often utilize Raychaudhuri Equation in geometric analysis.
  • It can often inspire Quantum Cosmology through initial singularity problems.
  • It can range from being a Classical Hawking's Singularity Theorem to being a Quantum-Modified Hawking's Singularity Theorem, depending on its theoretical framework.
  • It can range from being a Strong Hawking's Singularity Theorem to being a Weak Hawking's Singularity Theorem, depending on its assumption strength.
  • It can range from being a Past Hawking's Singularity Theorem to being a Future Hawking's Singularity Theorem, depending on its temporal direction.
  • It can range from being a Isotropic Hawking's Singularity Theorem to being an Anisotropic Hawking's Singularity Theorem, depending on its symmetry assumptions.
  • ...
• Example:
  • Related Cosmological Theorems, such as:
    • Hawking-Penrose Theorem combining both approaches.
    • Borde-Guth-Vilenkin Theorem for inflationary cosmology.
  • Applications, such as:
    • Big Bang Singularity Analysis for universe origin.
    • Cyclic Universe Constraint for cosmological models.
  • ...
• Counter-Example:
  • Penrose's Singularity Theorem, which focuses on gravitational collapse rather than cosmological expansion.
  • No-Boundary Proposal, which avoids initial singularity through quantum effects.
• See: Singularity Theorem, Penrose's Singularity Theorem, General Relativity Theory, Cosmology, Big Bang Theory, Einstein's Field Equations, Energy Condition.

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