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The Standard-Model Extension provides a framework to systematicallyinvestigate possible violation of the Lorentz symmetry. Concerning gravity, thelinearized version was extensively examined. We here cast the first set ofexperimental bounds on the nonlinear terms in the field equation from theanisotropic cubic curvature couplings. These terms introduce body-dependentaccelerations for self-gravitating objects, thus violating the gravitationalweak equivalence principle (GWEP). Novel phenomena, that are absent in thelinearized gravity, remain experimentally unexplored. We constrain them withprecise binary-orbit measurements from pulsar timing, wherein the high densityand large compactness of neutron stars are crucial for the test. It is thefirst study that seeks GWEP-violating signals in a fully anisotropic frameworkwith Lorentz violation.

Testing the Gravitational Weak Equivalence Principle in the Standard-Model Extension with Binary Pulsars