Piotr Bizoń

Piotr Bizoń

Asymptotically anti-de Sitter spacetimes

Over the past two decades asymptotically anti-de Sitter (AdS) spacetimes have come to play a central role in theoretical physics, primarily due to the AdS/CFT correspondence which is the conjectured equivalence between string theory on an asymptotically AdS spacetime and a conformally invariant quantum field theory (CFT) living on the boundary of this spacetime. One of the main open mathematical issues in this context is the problem of nonlinear stability of the exact AdS spacetime (the ground state of Einstein's gravity with a negative cosmological constant). The distinctive feature of asymptotically AdS spacetimes is the presence of the timelike boundary at spatial and null infinity which acts as a mirror at which the waves propagating outwards bounce off and return to the bulk. This leads to complex nonlinear wave interactions in the bulk, understanding of which is the key to the problem of stability of the AdS spacetime. After studying this problem for several years together with Andrzej Rostworowski, in 2011 we published numerical evidence for the instability of AdS space against black hole formation under generic arbitrarily small perturbations [1] . On the basis of nonlinear perturbation analysis, we conjectured that the instability is due to the resonant mode mixing that transfers energy from low to high frequencies, or equivalently from coarse to fine spatial scales, until eventually an apparent horizon forms. This work has opened up new research directions which we have been explored since then by many groups. One of the most important follow-up results was the derivation of the explicit resonant approximation for the Einstein-scalar-AdS system in spherical symmetry [2] . Using this approximation we supported our AdS instability conjecture via the analyticity strip method [3] .

  1. P. Bizoń, A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107, 031102 (2011) ↩
  2. B. Craps, O. Evnin, J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 1501, 108 (2015) ↩
  3. P. Bizoń, M. Maliborski, A. Rostworowski, Resonant dynamics and the instability of anti-de Sitter spacetime, Phys. Rev. Lett. 115, 081103 (2015) ↩