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The gravitational strong equivalence principle (SEP) is a cornerstone of thegeneral theory of relativity (GR). The extreme difference in binding energybetween neutron stars and white dwarfs allows for precision tests of the SEPvia the technique of pulsar timing.  To date, the best limit on the validity of SEP under strong-field conditionswas obtained with a unique pulsar in a triple stellar system, PSR J0337+1715.We report here on an improvement of this test using an independent data setacquired over 6 years with the Nan\c cay radio telescope (NRT). Theimprovements arise from a uniformly sampled data set, a theoretical analysis,and a treatment that fixes some short-comings in the previously publishedresults, leading to better precision and reliability of the test.  In contrast to the previously published test, we use a different long-termtiming data set, developed a new timing model and an independent numericalintegration of the motion of the system, and determined the masses and orbitalparameters with a different methodology that treats the parameter $\Delta$,describing a possible strong-field SEP violation, identically to all otherparameters.  We obtain a violation parameter $\Delta = (+0.5 \pm 1.8) \times 10^{-6}$ at95\% confidence level, which is compatible with and improves upon the previousstudy by 30\%. This result is statistics-limited and avoids limitation bysystematics as previously encountered. We find evidence for red noise in thepulsar spin frequency, which is responsible for up to 10\% of the reporteduncertainty. We use the improved limit on SEP violation to place constraints ona class of well-studied scalar-tensor theories, in particular we find$\omega_{\rm BD} > 140\,000$ for the Brans-Dicke parameter. The conservativelimits presented here fully take into account current uncertainties in theequation for state of neutron-star matter.

An improved test of the strong equivalence principle with the pulsar in a triple star system