Conformal transformations of spacetimes without observer horizons

2025/05/16 by García-Heveling, Leonardo, Zeghib, Abdelghani
#53C50 (primary) 58D19 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2505.11148

Abstract

We prove that for a certain class of Lorentzian manifolds, namely causal spacetimes without observer horizons, conformal transformations can be classified into two types: escaping and non-escaping. This means that successive powers of a given conformal transformation will either send all points to infinity, or none. As an application, we classify the conformal transformations of Einstein's static universe. We also study the question of essentiality in this context, i.e. which conformal transformations are isometric for some metric in the conformal class.

Citations

• Isometries of spacetimes without observer horizons
• The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds
• The conformal group of a compact simply connected Lorentzian manifold
• Maximal extension of conformally flat globally hyperbolic space-times
• About pseudo-Riemannian Lichnerowicz conjecture
• Domain of Dependence

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