Although most of the presently known binary pulsar systems can be adequately timed using Kepler’s laws, there are a number which require an additional set of “postKeplerian” (PK) parameters which have a distinct functional form for a given relativistic theory of gravity. In general relativity (GR) the PK formalism gives the relativistic advance of periastron
the time dilation and gravitational redshift parameter the rate of orbital decay due to gravitational radiation and the two Shapiro delay parameters and which describe the delay in the pulses around superior conjunction where the pulsar radiation traverses the gravitational well of its companion. In the above expressions, all masses are in solar units, , , and . Some combinations, or all, of the PK parameters have now been measured for a number of binary pulsar systems. Further PK parameters due to aberration and relativistic deformation [80] are not listed here but may soon be important for the double pulsar [185].The key point in the PK definitions is that, given the precisely measured Keplerian parameters, the only two unknowns are the masses of the pulsar and its companion, and . Hence, from a measurement of just two PK parameters (e.g., and ) one can solve for the two masses and, using Equation (11), find the orbital inclination angle . If three (or more) PK parameters are measured, the system is “overdetermined” and can be used to test GR (or, more generally, any other theory of gravity) by comparing the third PK parameter with the predicted value based on the masses determined from the other two.

More recently, five PK parameters have been measured for PSRs B1534+12 [298] and J0737 3039A [161]. For PSR B1534+12, the test of GR comes from measurements of , and , where the agreement between theory and observation is within 0.7% [298]. This test will improve in the future as the timing baseline extends and a more significant measurement of can be made. Although a significant measurement of exists, it is known to be contaminated by kinematic effects which depend on the assumed distance to the pulsar [293]. Assuming GR to be correct, the observed and theoretical values can be reconciled to provide a “relativistic measurement” of the distance [288]. Prospects for independent parallax measurements of the distance to this pulsar using radio interferometry await more sensitive telescopes [289].

Less than two years after its discovery, the double pulsar system has already surpassed the three decades of monitoring PSR B1913+16 and over a decade of timing PSR B1534+12 as a precision test of GR. Ongoing precision timing measurements of the double pulsar system should soon provide even more stringent and new tests of GR. Crucial to these measurements will be the timing of the pulsar B, where the observed profile is significantly affected by A’s relativistic wind [198, 216]. A careful decoupling of these profile variations is required to accurately measure TOAs for this pulsar and determine the extent to which the theoryindependent mass ratio can be measured.
The relativistic effects observed in the double pulsar system are so large that corrections to higher postNewtonian order may soon need to be considered. For example, may be measured precisely enough to require terms of second postNewtonian order to be included in the computations [81]. In addition, in contrast to Newtonian physics, GR predicts that the spins of the neutron stars affect their orbital motion via spinorbit coupling. This effect would most clearly be visible as a contribution to the observed in a secular [26] and periodic fashion [337]. For the J07373039 system, the expected contribution is about an order of magnitude larger than for PSR B1913+16 [198]. As the exact value depends on the pulsars’ moment of inertia, a potential measurement of this effect allows the moment of inertia of a neutron star to be determined for the first time [81]. Such a measurement would be invaluable for studies of the neutron star equation of state and our understanding of matter at extreme pressure and densities [168].
The systems discussed above are all double neutron star binaries. A further selfconsistency test of GR has recently been made in the relativistic binary J11416545, where the measurement [25] of , and yield a pulsar mass of and a companion mass of . Since the mass of the companion is some seven standard deviations below the mean neutron star mass (see Figure 28), it is most likely a white dwarf. The observed is consistent, albeit with limited precision, with the predicted value from GR (). Continued timing should reduce the relative error in down to 1% by 2010 [25].

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