  In this work, a derivation and implementation of the relativistic
time-dependent configuration interaction singles (RTDCIS) method is presented.
Various observables for krypton and xenon atoms obtained by RTDCIS are compared
with experimental data and alternative relativistic calculations. This includes
energies of occupied orbitals in the Dirac-Fock ground state, Rydberg state
energies, Fano resonances and photoionization cross sections. Diagrammatic
many-body perturbation theory, based on the relativistic random phase
approximation, is used as a benchmark with excellent agreement between RTDCIS
reported at the Tamm-Dancoff level. Results from RTDCIS are computed in the
length gauge, here the negative energy states can be omitted with acceptable
loss of accuracy. A complex absorbing potential, that is used to remove
photoelectrons far from the ion, is implemented as a scalar potential and
validated for RTDCIS. The RTDCIS methodology presented here opens for future
studies of strong-field processes, such as attosecond transient absorption and
high-order harmonic generation, with electron and hole spin dynamics and other
relativistic effects described by first principle via the Dirac equation.
