Strong-field tests of relativistic gravity and binary pulsars

Observations of pulsars in gravitationally bound binary systems provide a unique opportunity for testing the strong-field regime of relativistic gravity. We present a detailed account of the "parametrized post-Keplerian" (PPK) formalism, a general phenomenological framework designed to extract the maximum possible information from pulsar timing and pulse-structure data. The PPK approach allows dynamical information to be obtained from the data in a theory-independent way, and encoded in a certain number of fitted post-Keplerian parameters. We show that as many as 19 such parameters can be measured, under favorable conditions, giving access to 15 possible tests of relativistic gravity. We isolate and quantify the theoretical content of these tests by deriving, within the framework of generic boost-invariant theories, expressions linking the phenomenological parameters to the inertial masses of the pulsar and its companion, and to the polar angles of the spin axis of the pulsar. The prospects for extracting some of these tests from observations of known or yet-to-be-discovered binary pulsars is quantitatively assessed through numerical simulations. We show that the recently discovered binary pulsar PSR 1534+12 should, with presently available data, give access to two new strong-field tests of relativistic gravity, if the data are analyzed in the phenomenological way emphasized in this paper. Moreover, in the long run, the first-discovered binary pulsar, PSR 1913+16, could give access to three strong-field tests, beyond the presently obtained \. {}-- { \. {}P}₁ test. Finally, we show how, by combining the PPK approach with the predictions of a rather generic class of tensor-biscalar theories, one can bring together tests based on observations of several different pulsars. We illustrate how such a combination of independent tests can lead to very tight quantitative constraints on possible strong-field deviations from the correct theory of gravity.