Tests of Conservation Laws in Post-Newtonian Gravity with Binary Pulsars

General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider nonconservative ones with a parameterized post-Newtonian parameter, ζ2. A nonzero ζ2 induces a self-acceleration for the center of mass of an eccentric binary pulsar system, which contributes to the second time derivative of the pulsar spin frequency, . In our work, using Will's method, we provide an improved analysis with four well-timed, carefully chosen binary pulsars. In addition, we extend Will's method and derive the effect of on the third time derivative of the spin frequency, . For PSR B1913+16, the constraint from is even tighter than that from . We combine multiple pulsars with Bayesian inference, and obtain the upper limit, at the 95% confidence level, assuming a flat prior in . It improves the existing bound by a factor of 3. Moreover, we propose an analytical timing formalism for . Our simulated times of arrival with simplified assumptions show the capability of binary pulsars in limiting ζ2, and useful clues are extracted for real-data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737−3039A, can yield more constraining limits than .