Geometry of Spacetime Asymptotics in General Relativity
About the project
General relativity describes gravity as a manifestation of spacetime curvature. Its fundamental mathematical language is Lorentzian geometry, which has proved remarkably successful in describing a broad range of physical phenomena, from black holes to the evolution of the universe. Despite these successes, standard metric methods are not always sufficient for studying asymptotic regions of spacetimes or their behaviour near initial singularities. In such regimes, conformal and projective structures can provide insights that are not readily accessible within a purely Lorentzian metric framework. The aim of the project is to adapt the mathematical formalism natural to conformal and projective geometries to investigate fundamental problems in general relativity whose complete resolution lies beyond the reach of methods based solely on metric structure.
Team
PhD Student
TBA
Results
Previous results related to the project
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arXiv
Asymptotia of Kerr–de Sitter Black Holes
Class. Quantum Grav. 42, 20LT02
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arXiv
Boundary Curvature Scalars on Conformally Compact Manifolds
J. Phys. A: Math. Theor. 58, 315402
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arXiv
Stress and Geometry for Isotropic Singularities
Phys. Rev. Lett. 133, 011401
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arXiv
Higher fundamental forms of the conformal boundary of asymptotically de Sitter spacetimes
Class. Quantum Grav. 40, 015001