Abstract
We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity. Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators from the asymptotic boundary (a ‘black tsunami’); a pinch-off of the horizon that likely reveals a naked singularity; and competition between these two behaviours, such as a nakedly singular pinch-off that subsequently gets covered by a black tsunami. The holographic dual describes different patterns of heat flow due to the Hawking radiation of two black holes placed at the antipodes of a spherical universe. We also present a model that describes, in any D, the burst in the holographic stress-energy tensor when the signal from a bulk self-similar naked singularity reaches the boundary. The model shows that the shear components of the boundary stress diverge in finite time, while the energy density and pressures from the burst vanish.
Highlights
We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity
Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators from the asymptotic boundary (a ‘black tsunami’); a pinch-off of the horizon that likely reveals a naked singularity; and competition between these two behaviours, such as a nakedly singular pinch-off that subsequently gets covered by a black tsunami
A naked singularity should correspond to some pathology of the CFT in the infinite N limit that would be absent at finite N
Summary
We have fol√lowed the dynamical evolution of unstable black strings with different values of r0 < 1/ 2, numerically solving (2.9) and (2.10) with initial data corresponding to perturbations that excite different modes of the uniform solution. Contrary to what happens in the tsunami, this requires a flow towards x → ±∞ and the absorption of horizon generators at the boundary These final ditch configurations are well approximated by static solutions of the effective theory that are stable to small perturbations. In the large D effective theory, the central black hole is slowly leaking its energy to the outer two droplets through a very small, string-like horizon. For r0 < 1/2, there are multiple competing unstable modes, and the dynamics becomes complicated
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
