Rosetta stone for parametrized tests of gravity

Several model-independent parametrizations of deviations from general relativity have been developed to test Einstein's theory. Although these different parametrizations were developed for different gravitational observables, they ultimately all test the same underlying physics. In this paper, we develop connections between the parametrized post-Newtonian, parametrized post-Keplerian, and the parametrized post-Einsteinian frameworks, developed to carry out tests of general relativity with Solar System, binary pulsar, and gravitational wave observations, respectively. These connections, although only valid under certain assumptions such as energy/momentum conservation, allow us to use knowledge gained from one framework to inform and guide tests using the others. Relating these parametrizations and combining the results from each approach strengthens our tests of general relativity.