The parametrized post-Newtonian (PPN) formalism was
developed [150] to provide a uniform description of the
weak-gravitational-field limit, and to facilitate comparisons of
rival theories in this limit. This formalism requires 10
parameters (,
,
,
,
,
,
,
,
, and
), which are fully described in the article by Will in this
series [147
], and whose physical meanings are nicely summarized in
Table 2 of that article. (Note that
is not the same as the Post-Keplerian pulsar timing parameter
.) Damour and Esposito-Farèse [38
,
36] extended this formalism to include strong-field effects for
generalized tensor-multiscalar gravitational theories. This
allows a better understanding of limits imposed by systems
including pulsars and white dwarfs, for which the amounts of
self-gravitation are very different. Here, for instance,
becomes
, where
describes the ``compactness'' of mass
. The compactness can be written
where
G
is Newton's constant and
is the gravitational self-energy of mass
, about -0.2 for a neutron star (NS) and
for a white dwarf (WD). Pulsar timing has the ability to set
limits on
, which tests for the existence of preferred-frame effects
(violations of Lorentz invariance);
, which, in addition to testing for preferred-frame effects, also
implies non-conservation of momentum if non-zero; and
, which is also a non-conservative parameter. Pulsars can also be
used to set limits on other SEP-violation effects that constrain
combinations of the PPN parameters: the Nordtvedt
(``gravitational Stark'') effect, dipolar gravitational
radiation, and variation of Newton's constant. The current pulsar
timing limits on each of these will be discussed in the next
sections. Table
1
summarizes the PPN and other testable parameters, giving the
best pulsar and solar-system limits.
Table 1:
PPN and other testable parameters, with the best solar-system
and binary pulsar tests. Physical meanings and most of the
solar-system references are taken from the compilations by
Will [147]. References:
, solar system: [51];
, solar system: [118
];
, solar system: [105
];
, solar system: [95], pulsar: [146
];
, solar system: [105,
152
];
, solar system: [152
], pulsar: [146
];
, pulsar: [149
];
, solar system: [15,
152
];
,
, solar system: [45
], pulsar: [146
];
, pulsar: [6
];
, solar system: [45
,
115
,
59
], pulsar: [135
].
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Testing General Relativity with Pulsar Timing
Ingrid H. Stairs http://www.livingreviews.org/lrr-2003-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |