A proof of the instability of AdS for the Einstein--null dust system with an inner mirror

Apr 27, 2017
84 pages
Published in:
  • Anal.Part.Diff.Eq. 13 (2020) 6, 1671-1754
  • Published: Sep 12, 2020
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Abstract: (MSP)
The statement of the main theorem is as follows: We construct a family of mirror radiir0𝜀> 0 and initialdata 𝒮𝜀,𝜀∈ (0,1], converging, as𝜀→ 0, to the AdS initial data𝒮0 in a suitable norm,such that, for any 𝜀∈ (0,1], themaximal development (ℳ𝜀,g𝜀)of 𝒮𝜀 containsa black hole region. Our proof is based on purely physical space arguments and involvesthe arrangement of the null dust into a large number of beams which are successivelyreflected off {r= r0𝜀}and ℐ, in aconfiguration that forces the energy of a certain beam to increase after each successive pair ofreflections. As 𝜀→ 0,the number of reflections before a black hole is formed necessarily goes to+∞. Weexpect that this instability mechanism can be applied to the case of more generalmatter fields.
Note:
  • 78 pages
  • AdS instability
  • black hole
  • null dust