Numerical simulations of instabilities in general relativity
University of Cambridge
Applied Mathematics and Theoretical Physics
Doctor of Philosophy (PhD)
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Kunesch, M. (2018). Numerical simulations of instabilities in general relativity (Doctoral thesis). https://doi.org/10.17863/CAM.30498
General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein’s equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.
general relativity, black holes, cosmic censorship, numerical relativity, higher dimensions, AdS, adaptive mesh refinement
My PhD was funded by an STFC studentship initially and by the European Research Council Grant No. ERC-2014-StG 639022-NewNGR in my final year. Furthermore, I received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant agreement No. 690904. The simulations presented in this thesis were carried out on the following supercomputers: *) The COSMOS Shared Memory system at DAMTP, University of Cambridge, operated on behalf of the STFC DiRAC HPC Facility. This sytem is funded by BIS National E-infrastructure capital Grant No.~ST/ J005673/1 and STFC Grants No.~ST/H008586/1, No.~ST/K00333X/1. *) MareNostrum III and MareNostrum IV at the Barcelona Supercomputing Centre through the grants FI-2016-3-0006 and PRACE Tier-0 PPFPWG respectively. *) Stampede and Stampede2 at the Texas Advanced Computing Center, University of Texas at Austin, through the NSF-XSEDE grant No.~PHY-090003 and an allocation provided by Intel for their Parallel Computing Centres. *) SuperMike-II at Louisiana State University under allocation NUMREL06. *) Cartesius, SURFsara, in the Netherlands through the PRACE DECI grant NRBA.
This record's DOI: https://doi.org/10.17863/CAM.30498
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