Eric Furugori: Proposed project -- Numerical study of the stability of AdS using spectral methods

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1 Motivation

  1. Critical gravitational collapse: interesting link between black hole formation and familiar phase transitions (water -> vapor, ferromagnetic transition in spin systems)
  2. 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)

2 Project Aim

  1. Repeat BP calculation using spectral methods (BP used finite difference techniques)
  2. Possibly extend calculation to look at one or more outstanding issues concerning long-term stability for fields with interactions
  3. Become familiar with relativity, numerical relativity, accurate computational solution of time dependent PDEs

3 Novelty

  1. No computations of critical collapse using spectral methods (SM)
  2. Accurate treatment of critical collapse may benefit from SM
  3. Completion of basic project will be publishable

4 Background

  1. Bizon & Rostworowski On weakly turbulent instability of anti-de Sitter space
  2. Balasubramanian et al Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
  3. Buchel et al Scalar Collapse in AdS
  4. Buchel et al Boson stars in AdS spacetime
  5. Nick Trefethen

5 Project Proposal

  1. Solve wave equation in (t,r) coordinates -> t(t,s), s compactified using spectral techniques
  2. Learn a bit of General Relativity
  3. Solve wave equation on Schwarzchild background using spectral techniques
  4. Study Bizon & Rostworowski problem using spectral techniques
  5. If time - extend to massive scalar field, look at long term stability of boson stars in AdS