2015/04/27 by Ovidiu Cristinel Stoica, Stoica, Ovidiu Cristinel
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Causal sets #Causal structure #Computer science #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General relativity #Gravitational singularity #Manifold (fluid mechanics) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Measure (data warehouse) #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Theoretical physics #gr-qc #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1504.07110
arxiv created 2015/04/27 · openalex publication_date 2015/04/27 · arxiv updated 2015/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is more fundamental. But there are cases when seemingly healthy causal structure and measure determine a singular metric. Here it is shown that this is not a bug, but a feature, because big-bang and black hole singularities are instances of this situation. But while the metric is special at singularities, being singular, the causal structure and the measure are not special in an explicit way at singularities. Therefore, considering the causal structure more fundamental than the metric provides a more natural framework to deal with spacetime singularities.