  We explore the implications of stable gravitational orbits around an AdS
black hole for the boundary conformal field theory. The orbits are long-lived
states that eventually decay due to gravitational radiation and tunneling. They
appear as narrow resonances in the heavy-light OPE when the spectrum becomes
effectively continuous due to the presence of the black hole horizon.
Alternatively, they can be identified with quasi-normal modes with small
imaginary part in the thermal two-point function. The two pictures are related
via the eigenstate thermalisation hypothesis. When the decay effects can be
neglected the orbits appear as a discrete family of double-twist operators. We
investigate the connection between orbits, quasi-normal modes, and double-twist
operators in detail. Using the corrected Bohr-Sommerfeld formula for
quasi-normal modes, we compute the anomalous dimension of double-twist
operators. We compare our results to the prediction of the light-cone
bootstrap, finding perfect agreement where the results overlap. We also compute
the orbit decay time due to scalar radiation and compare it to the tunneling
rate. Perturbatively in spin, in the light-cone bootstrap framework
double-twist operators appear as a small fraction of the Hilbert space which
violate the eigenstate thermalization hypothesis, a phenomenon known as
many-body scars. Nonperturbatively in spin, the double-twist operators become
long-lived states that eventually thermalize. We briefly discuss the connection
between perturbative scars in holographic theories and known examples of scars
in the condensed matter literature.
