3.1 Strong Equivalence Principle: Nordtvedt Testing General Relativity with Pulsar 2.3 Pulsar timing

3 Tests of GR - Equivalence Principle Violations 

Equivalence principles are fundamental to gravitational theory; for full descriptions, see, e.g., [94] or [152Jump To The Next Citation Point In The Article]. 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 (tex2html_wrap_inline2579, tex2html_wrap_inline2581, tex2html_wrap_inline2583, tex2html_wrap_inline2585, tex2html_wrap_inline2587, tex2html_wrap_inline2589, tex2html_wrap_inline2791, tex2html_wrap_inline2591, tex2html_wrap_inline2593, and tex2html_wrap_inline2797), which are fully described in the article by Will in this series [147Jump To The Next Citation Point In The Article], and whose physical meanings are nicely summarized in Table 2 of that article. (Note that tex2html_wrap_inline2579 is not the same as the Post-Keplerian pulsar timing parameter tex2html_wrap_inline2625 .) Damour and Esposito-Farèse [38Jump To The Next Citation Point In The Article, 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, tex2html_wrap_inline2585 becomes tex2html_wrap_inline2805, where tex2html_wrap_inline2807 describes the ``compactness'' of mass tex2html_wrap_inline2809 . The compactness can be written

equation210

where G is Newton's constant and tex2html_wrap_inline2813 is the gravitational self-energy of mass tex2html_wrap_inline2809, about -0.2 for a neutron star (NS) and tex2html_wrap_inline2819 for a white dwarf (WD). Pulsar timing has the ability to set limits on tex2html_wrap_inline2821, which tests for the existence of preferred-frame effects (violations of Lorentz invariance); tex2html_wrap_inline2823, which, in addition to testing for preferred-frame effects, also implies non-conservation of momentum if non-zero; and tex2html_wrap_inline2591, 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.

   table222
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 [147Jump To The Next Citation Point In The Article]. References: tex2html_wrap_inline2579, solar system: [51]; tex2html_wrap_inline2581, solar system: [118Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2583, solar system: [105Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2585, solar system: [95], pulsar: [146Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2587, solar system: [105, 152Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2589, solar system: [152Jump To The Next Citation Point In The Article], pulsar: [146Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2591, pulsar: [149Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2593, solar system: [15, 152Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2595, tex2html_wrap_inline2597, solar system: [45Jump To The Next Citation Point In The Article], pulsar: [146Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2599, pulsar: [6Jump To The Next Citation Point In The Article]; tex2html_wrap_inline2941, solar system: [45Jump To The Next Citation Point In The Article, 115Jump To The Next Citation Point In The Article, 59Jump To The Next Citation Point In The Article], pulsar: [135Jump To The Next Citation Point In The Article].





3.1 Strong Equivalence Principle: Nordtvedt Testing General Relativity with Pulsar 2.3 Pulsar timing

image Testing General Relativity with Pulsar Timing
Ingrid H. Stairs
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