138
9 Spherically Symmetric Gravitational Fields
about 0.03
per century. The presently accepted observational value of the precession as determined by radar measurements, about 42.98
per century, agrees with
general relativity to about a part in 10
3 (Will 2014; Wiki ND). The precessions of
other solar system planets have now been measured, as has the precession in both the
Hulse-Taylor system and the double pulsar, which we will discuss below; all agree
with the predictions of general relativity.
The deflection of starlight by the sun is the third classic test. As we noted previously the deflection was first measured for starlight during an eclipse of the sun in
1919, and an agreement of about 30% with theory was found (Von Kluber 1960).
More recently radio sources have been used for the test, so that much more accurate
and dependable results have been obtained. The agreement is now better than about
a part in 10
3 (Kenyon 1990; Will 2014).
A further basic solar system test has been added to the three classic tests; light
or radar signals passing near the sun are delayed by the gravitational field, an effect
which is easily calculable and amounts to some hundreds of microseconds depending
on the geometry of the experiment (Adler 1975). With radar reflected from planets
and signals from planetary probes this effect has been accurately measured by Shapiro
et al., and agrees with theory to better than 1% (Shapiro 1971; Kenyon 1990; Will
2014).
The equivalence principle has been subjected to many diverse tests since 1900,
and the most accurate tests to date indicate that the inertial and gravitational masses
of a body are equal to better than a part in 10
12 (Will 2014). This is impressive, but
there are various plans for space tests of the equivalence principle to an accuracy of
about 10
18 using satellites (Wiki STEP).
Some of the most important tests of general relativity outside the solar system
involve binary pulsar systems. One is PSR1913 + 1916, which is a pulsar in a short
period orbit, about 8 h, around an unseen companion, presumably a neutron star. It
is widely called the Hulse-Taylor system after its discoverers. Because the system is
small the relativistic effects are large. With only timing of the pulsar signals all of
the orbital tests discussed above have been done for the system and are consistent
with general relativity. Most important, the orbit has been observed to decay, which
indicates an energy loss to gravitational radiation, and which agrees with relativity
to within a few percent; we will discuss the process in Chap. 11. This is a most
impressive result, and before the direct detection of waves by LIGO it was the only
observational evidence for gravitational waves (Kenyon 1990; Will 2014). More
recently a binary system of two pulsars, PSR J0737-3039A, has been discovered.
Since it is smaller than the Hulse-Taylor system it promises to provide even more
accurate tests (Burgay 2012).
All of the above tests involve weak gravity, in that the deviation of the metric
components from those of flat space is small, less than about a part in 10
6 for the
solar system. These tests are without question very important, but it is also important
to test the theory for strong gravity, that is where the metric components deviate from
flat space of order unity. We will discuss strong gravity in the next chapter.
9 Spherically Symmetric Gravitational Fields
about 0.03
per century. The presently accepted observational value of the precession as determined by radar measurements, about 42.98
per century, agrees with
general relativity to about a part in 10
3 (Will 2014; Wiki ND). The precessions of
other solar system planets have now been measured, as has the precession in both the
Hulse-Taylor system and the double pulsar, which we will discuss below; all agree
with the predictions of general relativity.
The deflection of starlight by the sun is the third classic test. As we noted previously the deflection was first measured for starlight during an eclipse of the sun in
1919, and an agreement of about 30% with theory was found (Von Kluber 1960).
More recently radio sources have been used for the test, so that much more accurate
and dependable results have been obtained. The agreement is now better than about
a part in 10
3 (Kenyon 1990; Will 2014).
A further basic solar system test has been added to the three classic tests; light
or radar signals passing near the sun are delayed by the gravitational field, an effect
which is easily calculable and amounts to some hundreds of microseconds depending
on the geometry of the experiment (Adler 1975). With radar reflected from planets
and signals from planetary probes this effect has been accurately measured by Shapiro
et al., and agrees with theory to better than 1% (Shapiro 1971; Kenyon 1990; Will
2014).
The equivalence principle has been subjected to many diverse tests since 1900,
and the most accurate tests to date indicate that the inertial and gravitational masses
of a body are equal to better than a part in 10
12 (Will 2014). This is impressive, but
there are various plans for space tests of the equivalence principle to an accuracy of
about 10
18 using satellites (Wiki STEP).
Some of the most important tests of general relativity outside the solar system
involve binary pulsar systems. One is PSR1913 + 1916, which is a pulsar in a short
period orbit, about 8 h, around an unseen companion, presumably a neutron star. It
is widely called the Hulse-Taylor system after its discoverers. Because the system is
small the relativistic effects are large. With only timing of the pulsar signals all of
the orbital tests discussed above have been done for the system and are consistent
with general relativity. Most important, the orbit has been observed to decay, which
indicates an energy loss to gravitational radiation, and which agrees with relativity
to within a few percent; we will discuss the process in Chap. 11. This is a most
impressive result, and before the direct detection of waves by LIGO it was the only
observational evidence for gravitational waves (Kenyon 1990; Will 2014). More
recently a binary system of two pulsars, PSR J0737-3039A, has been discovered.
Since it is smaller than the Hulse-Taylor system it promises to provide even more
accurate tests (Burgay 2012).
All of the above tests involve weak gravity, in that the deviation of the metric
components from those of flat space is small, less than about a part in 10
6 for the
solar system. These tests are without question very important, but it is also important
to test the theory for strong gravity, that is where the metric components deviate from
flat space of order unity. We will discuss strong gravity in the next chapter.