Tests of conservation laws in post-Newtonian gravity with binary pulsars

Abstract

General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider non-conservative ones with a parameterized post-Newtonian (PPN) parameter, ${\zeta }_2$. A non-zero ${\zeta }_2$ 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, $\ddot{\nu }$. In our work, using the method in Will (1992), we provide an improved analysis with four well-timed, carefully-chosen binary pulsars. In addition, we extend Will's method and derive ${\zeta }_2$'s effect on the third time derivative of the spin frequency, $\stackrel{...}{\nu }$. For PSR B1913+16, the constraint from $\stackrel{...}{\nu }$ is even tighter than that from $\ddot{\nu }$. We combine multiple pulsars with Bayesian inference, and obtain an upper limit, $\left|{\zeta }_2\right|<1.3\times 10^{-5}$ at 95% confidence level, assuming a flat prior in ${\log }_{10}\left|{\zeta }_2\right|$. It improves the existing bound by a factor of three. Moreover, we propose an analytical timing formalism for ${\zeta }_2$. Our simulated times of arrival with simplified assumptions show binary pulsars' capability in limiting ${\zeta }_2$, and useful clues are extracted for real data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737$-$3039A, $\stackrel{...}{\nu }$ can yield more constraining limits than $\ddot{\nu }$.

Comments: 14 pages, 5 figures, 4 tables; accepted by ApJ