Eric Furugori: Proposed project -- Numerical study of the stability of AdS using spectral methods
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Motivation
- Critical gravitational collapse: interesting link between black hole formation and familiar phase transitions (water -> vapor, ferromagnetic
transition in spin systems)
- AdS (Anti-de Sitter spacetime, negative cosmological constant): very active research field in string theory and related due to AdS-CFT
correspondence (Maldacena The Large N Limit of Superconformal Field Theories and Supergravity, most highly cited
paper in INSPIRES by a large margin, > 9300)
- Recent numerical studies (Bizon & Rostworowski [BP], 2011) have revealed instability of AdS which is related to critical collapse: used
- Massless scalar field
- Spherical symmetry
- Extent of instability of great interest. Does it persist when
- Fields with self-interactions (e.g. mass, nonlinear terms, ...) are used
- Different types of fields are used (vector, tensor)
- Symmetries are relaxed (not spherical)
- ...
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Project Aim
- Repeat BP calculation using spectral methods (BP used finite difference techniques)
- Possibly extend calculation to look at one or more outstanding issues concerning long-term stability for
fields with interactions
- Become familiar with relativity, numerical relativity, accurate computational solution of time dependent PDEs
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Novelty
- No computations of critical collapse using spectral methods (SM)
- SM have been very successful in other areas of numerical relativity, most notably for high
accuracy calculations of black hole collisions
- Accurate treatment of critical collapse may benefit from SM
- Completion of basic project will be publishable
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Background
- Bizon & Rostworowski On weakly turbulent instability of anti-de Sitter space
- Balasubramanian et al Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
- Buchel et al Scalar Collapse in AdS
- Buchel et al Boson stars in AdS spacetime
- Nick Trefethen
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Project Proposal
- Solve wave equation in (t,r) coordinates -> t(t,s), s compactified using spectral techniques
- Learn a bit of General Relativity
- Solve wave equation on Schwarzchild background using spectral techniques
- Rework of GR Hydro Summer School problem
- Study Bizon & Rostworowski problem using spectral techniques
- If time - extend to massive scalar field, look at long term stability of boson stars in AdS