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Non-linear perturbations of cosmological models and black hole spacetimes

School of Mathematical Sciences

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2020 for self-funded students.

This project will be supervised by Dr Juan Valiente-Kroon.

One of the outstanding challenges in General Relativity —the relativistic theory of gravity—is to gain analytic control of the solutions to the Einstein field equations in the large: physical questions in General Relativity require knowledge of the non-linear behaviour and properties of solutions to non-linear partial differential equations. Such undertaking is, very often, only feasible in the case where the solutions under consideration are suitably close —that is, a perturbation— to an (usually) explicitly known background solution. The standard approach to this problem has been the study the evolution and properties of linearised perturbations. This approach, however, offers a limited understanding of non-linear mechanisms. The objective of the present project is to analyse fully non-linear evolution problems in a range of settings in General Relativity ranging from Cosmology to the theory of black holes. The insights gained from the study of non-linear perturbations is key to understand the physical content of General Relativity as the background solution are often attractors of the theory.

The approach to these problems will be based on a number of techniques of conformal geometry and the theory of partial differential equations recently developed by the supervisor —see the bibliography enclosed—. The project will be mainly analytical, but it will involve certain amount of computer algebra and some numerical simulations.

The application procedure is described on the School website. For further inquiries please contact Dr Juan Valiente-Kroon at .

Funding Notes

This project can be undertaken as a self-funded project. Self-funded applications are accepted year-round for a January, April or September start.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.


JA Valiente Kroon. Conformal methods in General Relativity. Cambridge Monographs in Mathematical Physics. Cabridge University Press (2016).

C Lübbe & JA Valiente Kroon. On de Sitter-like and Minkowski-like spacetimes. Class. Quantum Grav. 26, 145012 1 to 26 (2009). Named research highlight by the editorial board of the journal.

C Lübbe & JA Valiente Kroon. A stability result for purely radiative spacetimes. J. Hyp. Diff. Eqns. 7, 545-579 (2010)

T Bäckdahl & JA Valiente Kroon. A geometric invariant measuring the deviation from Kerr data. Phys. Rev. Lett. 104, 231102 (2010). Available at arXiv:1001.4492[gr-qc]

C Lübbe & JA Valiente Kroon. The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field. J. Geom. Phys. 62, 1548-1570 (2012)

C Lübbe & JA Valiente Kroon. A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies. Ann. Phys. 328, 1-25 (2013). Available at arXiv:1111.4691[gr-qc]

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