New Limits on the Strong Equivalence Principle from Two Long-period Circular-orbit Binary Pulsars

Following a brief review of the principles of the strong equivalence principle (SEP) and tests for its violation in the strong and weak gravitational field regimes, we present preliminary results of new tests using two long-period binary pulsars: J0407+1607 and J2016+1947. PSR J0407+1607 is in a 669day orbit around a > ∼ 0.2M ̄ companion, while J2016+1947 is in a 635-day orbit around a > ∼ 0.3M ̄ companion. The small eccentricities of both orbits (e ∼ 10) mean that these systems reduce previous limits on SEP violation by more than a factor of 4. 1. Equivalence Principles and Gravitational Self-energy The principle of equivalence between gravitational force and acceleration is a common feature to all viable theories of gravity. The Strong Equivalence Principle (SEP), however, is unique to Einstein’s general theory of relativity (GR). Unlike the weak equivalence principle (which dates back to Galileo’s demonstration that all matter free falls in the same way) and the Einstein equivalence principle from special relativity (which states that the result of a non-gravitational experiment is independent of rest-frame velocity and location), the SEP states that free fall of a body is completely independent of its gravitational self energy. Before examining how the SEP can be tested, let us first review the gravitational self energy, 2, which is a useful quantity for distinguishing between strong or weak gravitational fields. Expressed in terms of the rest-mass energy of a body of mass M and size R, 2 = −GM/Rc2. For most bodies, 2 is vanishingly small. For example 2human ∼ −10−26, 2Earth ∼ −5 × 10−10 and even 2 ̄ = −2 × 10−6. Only for compact objects does 2 become significant and we enter the “strongfield” regime. For a white dwarf 2WD ∼ −10−4, for a neutron star 2NS ∼ −0.3 and for a non-rotating black hole, 2BH = −0.5.