]. Newton formulated what may be considered the earliest such
principle, now called the ``Weak Equivalence Principle'' (WEP).
It states that in an external gravitational field, objects of
different compositions and masses will experience the same
acceleration. The Einstein Equivalence Principle (EEP) includes
this concept as well as those of Lorentz invariance
(non-existence of preferred reference frames) and positional
invariance (non-existence of preferred locations) for
non-gravitational experiments. This principle leads directly to
the conclusion that non-gravitational experiments will have the
same outcomes in inertial and in freely-falling reference frames.
The Strong Equivalence Principle (SEP) adds Lorentz and
positional invariance for gravitational experiments, thus
including experiments on objects with strong self-gravitation. As
GR incorporates the SEP, and other theories of gravity may
violate all or parts of it, it is useful to define a formalism
that allows immediate identifications of such violations.
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 |