Project description
Tackling fundamental questions in general relativity with advanced mathematical tools
Einstein equations, a system of non-linear partial differential equations, are central to understanding gravitational dynamics in general relativity. Recent advances in partial differential equations, differential geometry and microlocal analysis have deepened understanding of gravitational dynamics. The ERC-funded ExBHGravRad project focuses on two key mathematical problems. First, it will examine the stability and instability of extremal Kerr black holes, which are rapidly rotating objects at the boundary between black holes and naked singularities. Resolving this could reveal how these extreme black holes behave when perturbed. Second, it will investigate late-time tails in gravitational radiation by analysing the dynamics of perturbations in both flat space-time and black hole space-times. The proposed research could advance the understanding of the strong cosmic censorship conjecture.
Objective
"The Einstein equations constitute a system of geometric, nonlinear partial differential equations that describe gravitational dynamics in the framework of Einstein's theory of general relativity. The last decade has seen tremendous progress towards understanding dynamical aspects of the Einstein equations. At the mathematical level, great insight has been gained due to recent advances in the study of partial differential equations, differential geometry and microlocal analysis. The present proposal builds upon these advances in the context of the following two mathematical problems.
Stability and instability of extremal black holes: Extremal Kerr black holes describe rapidly rotating solutions to the Einstein equations. They sit at the transition between black holes and ""naked singularities"" and exhibit critical geometric features.
This proposal addresses the stability and instability properties of extremal Kerr black holes and is motivated by recent advances by the PI, which cover linear and nonlinear aspects. A successful resolution would give fundamental, new insights into the fate of perturbed extremal black holes and the transition between black holes and naked singularities.
The late-time analysis of gravitational radiation: Gravitational radiation provides an observational window into deep mathematical aspects of general relativity. In this proposal, we investigate a key feature that is amenable to mathematical analysis: the existence of late-time tails in gravitational radiation.
Recent work by the PI and collaborators has lead to the first proof of the existence of late-time tails in a toy model setting, also known as Price's Law. This proposal considers the full setting of the nonlinear Einstein equations via the analysis of late-time tails in the dynamics of perturbations of both flat spacetime and black hole spacetimes. A successful resolution would have important implications for the Strong Cosmic Censorship conjecture."
Fields of science (EuroSciVoc)
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.
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 mathematical analysis
- natural sciences mathematics pure mathematics geometry
- social sciences law
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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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-ERC - HORIZON ERC Grants
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-STG
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04109 Leipzig
Germany
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