Project description
Laying the foundations of sub-Lorentzian geometry
Sub-Lorentzian geometry is the non-holonomic analogue of Lorentzian geometry and the Lorentzian counterpart of sub-Riemannian geometry. Despite progress in non-smooth Lorentzian geometry and the maturity of sub-Riemannian geometry, it remains underexplored, although relevant to higher-dimensional theories, quantum gravity and analogue gravity. Supported by the Marie Skłodowska-Curie Actions programme, the SUBLOR project will integrate sub-Lorentzian structures into Lorentzian length spaces and metric spacetimes, analyse causal properties and study geodesics via Pontryagin’s maximum principle. It will characterise infinitesimal geometry through timelike metric tangents and a Lorentzian ball-box theorem, and develop curvature theory using optimal transport and Hamiltonian curvature. SUBLOR will systematise the field and clarify its role in constrained spacetimes and fundamental physics.
Objective
"The project SUBLOR aims to establish the foundations of sub-Lorentzian geometry, the non-holonomic analogue of Lorentzian geometry, within the new synthetic theory of Lorentzian length spaces and metric spacetimes. While recent developments have extended Lorentzian geometry to the non-smooth setting, spacetimes with non-holonomic constraints have been overlooked, despite their central role in modern geometry. Sub-Riemannian geometry has flourished into a thriving field of geometric analysis, whereas its Lorentzian counterpart has seen little development. SUBLOR will address this gap by:
(1) Integrating sub-Lorentzian structures into the framework of Lorentzian length spaces and metric spacetimes. Sub-Lorentzian geometry will be defined in the general control-theoretic setting, its causal structure and topologies analysed, and Pontryagin's maximum principle applied to the study of geodesics, showing that sub-Lorentzian manifolds are Lorentzian length spaces.
(2) Characterising the infinitesimal geometry of sub-Lorentzian manifolds. The timelike metric tangents will be shown to be quotients of sub-Lorentzian Carnot groups, and a Lorentzian version of the Ball-Box theorem (a ""Diamond-Box"" theorem) will be established.
(3) Developing a theory of curvature for sub-Lorentzian geometry. The optimal-transport-based timelike curvature-dimension conditions and their variants will be investigated, and the more intrinsic Hamiltonian curvature will be introduced through Jacobian fields and expansions of the time-separation function.
By building these three foundational layers, which also underpin the success of sub-Riemannian geometry, SUBLOR will systematise sub-Lorentzian geometry, highlight a novel class of spacetimes, and open the way for future applications in higher-dimensional models, quantum gravity, and analogue gravity."
Fields of science (EuroSciVoc)
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CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics geometry
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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(opens in new window) HORIZON-MSCA-2025-PF
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1010 Wien
Austria
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