  The stress tensor sector of a heavy-heavy-light-light scalar correlator in
CFTs with a large central charge and a large gap is defined by the exchange of
multi-stress tensor operators. The Regge limit of this correlator is determined
by the phase shift of a highly energetic particle propagating in a dual black
hole background. Assuming Einstein gravity in the bulk, the phase shift is
known perturbatively to all orders in the ratio of the heavy scaling dimension
over the central charge. In the CFT, the order counts the number of stress
tensors in the multi-stress tensor operator. By Fourier transforming the
correlator to position space, the multi-stress tensor contributions to the
leading and next-to-leading singularities in the Regge limit are found to all
orders in four dimensions. The leading singularity at each order agrees with
known results obtained by considering a particle in a dual shockwave
background. Moreover, the leading and next-to-leading singularities due to
double- and triple-stress tensors with minimal twist are known from lightcone
bootstrap and agree with the results derived from the phase shift.
