68 Tests of General RelativityJ. H. Taylor, for which they received the Nobel Prize in 1993, is a neutron star–neutron
star pair. Pulsars are rapidly rotating (up to 700 times per second], strongly magne-
tized neutron stars with a surface gravity 10^11 stronger than the Earth’s and with
magnetic fields ranging from 10^11 to 10^15 stronger than the Earth’s.
If the magnetic dipole axis does not coincide with the axis of rotation (just as is the
case with Earth), the star would radiate copious amounts of energy along the magnetic
dipole axis. These beams at radio frequencies precess around the axis of rotation like
the searchlights of a beacon. As the beam sweeps past our line of sight, it is observable
as a pulse with the period of the rotation of the star. Hulse, Taylor and collaborators
at Arecibo have demonstrated that pulsars are the extremely stable clocks, the time
variation of the PSR 1913+16 is about 10−^14 on timescales of 6–12 months. The rea-
son for this stability is the intense self-gravity of a neutron star, which makes it almost
undeformable until, in a binary pair, the very last few orbits when the pair coalesce
into one star.
The neutron stars in the binary system PSR 1913+16 rotate, in addition to their
individual spins, also around their common center of mass in a quite eccentric orbit.
One of the binary stars is a pulsar, sweeping in our direction with a period of 59ms,
and the binary period of the system is determined to be 7.751939337h. The radial
velocity curve as a function of time is known, and from this one can deduce the masses
푚 1 and푚 2 of the binary stars to a precision of 0.0005, as well as the parameters of a
Keplerian orbit: the eccentricity and the semi-major axis.
Pulsars lose energy due to its emission of a relativistic wind and electromagnetic
radiation. But the binary system does not behave exactly as expected in Newtonian
astronomy, hence the deviations provide several independent confirmations of gen-
eral relativity. The largest relativistic effect is the apsidal motion of the orbit, which
is analogous to the advance of the perihelion of Mercury. A second effect is the coun-
terpart of the relativistic clock correction for an Earth clock. The light travel time of
signals from the pulsar through the gravitational potential of its companion provides
a further effect.
During the first 17 years of observations the team observed a steadily accumulating
change of orbital phase of the binary system, which must be due to the loss of orbital
rotational energy by the emission ofgravitational radiation. This rate of change can
be calculated since one knows the orbital parameters and the star masses so well.
The calculations based on Einstein’s general relativity agree to within 1% with the
measurements. This was the first observation of gravitational radiation, although it
is indirect, since we as yet have no detector with which to receive such waves. The
result was also an important check on competing gravitational theories, several of
which were ruled out.
To test general relativity in the strong field regime and to search for signals of grav-
itational radiation one requires a massive pulsar spinning in a tight orbit around a
white dwarf. The best example is the pulsar PSR J0348+0432 discovered in 2011,
with a mass of 2. 01 푀⊙spinning at 3.9ms in a 2.46-hr orbit with a low-mass com-
panion,≈ 2 푀⊙. The pulsar is losing energy due to gravitational radiation at a rate in
agreement with Einstein’s general relativity to within 5± 18 %.