Strong-Field Gravity Tests with the Double Pulsar is a pretty big deal! 16 years of precision timing including "timing parallax" via VLBI has provided a dataset for which analysis requires (and tests) several GR effects simultaneously.
Among everything else it provides, I think this paper can be a rich source of Stack Exchange questions and answer.
Continued timing observations of the double pulsar PSR J0737–3039A/B, which consists of two active radio pulsars (A and B) that orbit each other with a period of 2.45 h in a mildly eccentric (e=0.088) binary system, have led to large improvements in the measurement of relativistic effects in this system. With a 16-yr data span, the results enable precision tests of theories of gravity for strongly self-gravitating bodies and also reveal new relativistic effects that have been expected but are now observed for the first time. These include effects of light propagation in strong gravitational fields which are currently not testable by any other method. In particular, we observe the effects of retardation and aberrational light bending that allow determination of the spin direction of the pulsar. In total, we detect seven post-Keplerian parameters in this system, more than for any other known binary pulsar. For some of these effects, the measurement precision is now so high that for the first time we have to take higher-order contributions into account. These include the contribution of the A pulsar’s effective mass loss (due to spin-down) to the observed orbital period decay, a relativistic deformation of the orbit, and the effects of the equation of state of superdense matter on the observed post-Keplerian parameters via relativistic spin-orbit coupling. We discuss the implications of our findings, including those for the moment of inertia of neutron stars, and present the currently most precise test of general relativity’s quadrupolar description of gravitational waves, validating the prediction of general relativity at a level of 1.3 × 10-4 with 95% confidence. We demonstrate the utility of the double pulsar for tests of alternative theories of gravity by focusing on two specific examples and also discuss some implications of the observations for studies of the interstellar medium and models for the formation of the double pulsar system. Finally, we provide context to other types of related experiments and prospects for the future.
Question: Is there a generally accepted set of Post-Keplerian orbital parameters with definitions?
To my knowledge, in a given frame there are six timeless Keplerian orbital elements, the number of which can be associated with the six elements of a state vector in a $1/r$ potential (see Why are there six orbital elements?) plus a seventh parameter being a specific time or epoch.
The abstract says "In total, we detect seven post-Keplerian parameters in this system, more than for any other known binary pulsar." Are these seven present on some pre-existing "official list" of post-Keplerian orbital elements, or is this paper contributing to the establishment of such a list?