The Singularity Theorems of General Relativity and Their Low Regularity Extensions

Area of Science:

• Physics
• Mathematics
• General Relativity

Background:

• Review of classical singularity theorems in General Relativity.
• Recent extensions to Lorentzian metrics of low regularity are explored.
• Motivation stems from understanding the nature of predicted singularities.

Purpose of the Study:

• Provide a pedagogical introduction to classical singularity theorems.
• Focus on the analytical aspects of the arguments.
• Highlight recent advances in low regularity cases.

Main Methods:

• Emphasis on focusing results for causal geodesics.
• Analysis in both smooth and low regularity metric cases.
• Utilizing a regularization approach for distributional curvature.

Main Results:

• Detailed pedagogical review of singularity theorems.
• Extension of theorems to low regularity Lorentzian metrics.
• Demonstration of proofs for singularity theorems using regularization.

Conclusions:

• The study provides a comprehensive overview of singularity theorems.
• Highlights the significance of low regularity extensions.
• Offers insights into related research and future directions.