We prepare an excited finite temperature state in N=4 SYM by means
of a Euclidean path integral with a relevant deformation. The deformation
explicitly breaks imaginary-time translations along the thermal circle whilst
preserving its periodicity. We then study how the state relaxes to thermal
equilibrium in real time. Computations are performed using real-time AdS/CFT,
by constructing novel mixed-signature black holes in numerical relativity
corresponding to Schwinger-Keldysh boundary conditions. These correspond to
deformed cigar geometries in the Euclidean, glued to a pair of dynamical
spacetimes in the Lorentzian.
The maximal extension of the Lorentzian black hole exhibits a `causal
shadow', a bulk region which is spacelike separated from both boundaries. We
show that causal shadows are generic in path-integral prepared states where
imaginary-time translations along the thermal circle are broken.Comment: 22 pages, 12 figures V2: references adde