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We design a direct test of the local position invariance (LPI) in thepost-Newtonian gravity, using the timing observation of the triple pulsar, PSRJ0337+1715. The test takes advantage of the large gravitational accelerationexerted by the outer white dwarf to the inner neutron star -- white dwarfbinary. Using machine-precision three-body simulations and dedicatedMarkov-chain Monte Carlo (MCMC) techniques with various sampling strategies andnoise realizations, we estimate that the Whitehead's parameter could havealready been limited to $|\xi| \lesssim 0.4$ (95\% CL), with the publishedtiming data spanning from January 2012 to May 2013. The constraint is stillorders of magnitude looser than the best limit, yet it is able to independentlyfalsify Whitehead's gravity theory where $\xi=1$. In addition, the new test isimmune to extra assumptions and involves full dynamics of a three-body systemwith a strongly self-gravitating neutron star.

An independent test on the local position invariance of gravity with the triple pulsar PSR J0337+1715