Interior structure and complexity growth rate of holographic superconductor from M-theory

Abstract

We study the interior dynamics of a top-down holographic superconductor from M-theory. The condense of the charged scalar hair necessarily removes the inner Cauchy horizon and the spacetime ends at a spacelike singularity. Although there is a smooth superconducting phase transition at the critical temperature, the onset of superconductivity is accompanied by intricate interior dynamics, including the collapse of the Einstein-Rosen bridge, the Josephson oscillations of the condensate, and the final Kasner singularity. We obtain analytically the transformation rule for the alternation of different Kasner epochs. Thanks to the nonlinear couplings of the top-down theory, there is generically a never-ending chaotic alternation of Kasner epochs towards the singularity. We compute the holographic complexity using both the complexity-action and the complexity-volume dualities. In contrast to the latter, the complexity growth rate from the complexity-action duality has a discontinuity at the critical temperature, characterizing the sudden change of the internal structure before and after the superconducting phase transition.

Anisotropic Flows into Black Holes

“…Indeed, we see fluctuations in the a-function which leave an imprint on the derivative. This and the other fluctuations in the interior functions (Appendix B.2) are reminiscent of the Josephson oscillations in the holographic superconductor [30,31]. Furthermore, such oscillations in the derivative allow it to reach 0 (numerically).…”

“…Phase transitions It would be interesting to conduct a more thorough analysis of holographic p-wave superfluid states [24,54] so as to see how the a-function may be sensitive to the phase structure of the underlying theory. One may also consider the a-function in other setups exhibiting phase transitions, such as the holographic superconductor [30,31] or round black holes [55].…”

“…Observe in particular that φ exhibits some oscillatory behavior. This is reminiscent of the Josephson oscillators by the charged scalar in the holographic superconductor [30,31].…”

AdS Black Holes with a Bouncing Interior

“…A further phenomenon that appears in these works are bounces between different Kasner 'epochs', see e.g. [14,16,21,25,[27][28][29]. This is again familiar from much earlier work, most famously the chaotic bounces of the 'mixmaster' universe [30].…”

“…A recent body of work has demonstrated that a common feature of (minisuperspace) holographic interiors is the emergence of Kasner scaling towards the singularity [11,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”