Equivalence principles are fundamental to gravitational theory; for full descriptions, see, e.g., [95] or [149]. 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 (nonexistence of preferred reference frames) and positional invariance (nonexistence of preferred locations) for nongravitational experiments. This principle leads directly to the conclusion that nongravitational experiments will have the same outcomes in inertial and in freelyfalling reference frames. The Strong Equivalence Principle (SEP) adds Lorentz and positional invariance for gravitational experiments, thus including experiments on objects with strong selfgravitation. 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 postNewtonian (PPN) formalism was developed [151] to provide a uniform description of the weakgravitationalfield 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 [150], and whose physical meanings are nicely summarized in Table 2 of that article. (Note that is not the same as the PostKeplerian pulsar timing parameter .) Damour and EspositoFarèse [36, 39] extended this formalism to include strongfield effects for generalized tensormultiscalar gravitational theories. This allows a better understanding of limits imposed by systems including pulsars and white dwarfs, for which the amounts of selfgravitation are very different. Here, for instance, becomes , where describes the “compactness” of mass . The compactness can be written
where is Newton’s constant and is the gravitational selfenergy of mass , about –0.2 for a neutron star (NS) and –10^{–4} for a white dwarf (WD). Pulsar timing has the ability to set limits on , which tests for the existence of preferredframe effects (violations of Lorentz invariance); , which, in addition to testing for preferredframe effects, also implies nonconservation of momentum if nonzero; and , which is also a nonconservative parameter. Pulsars can also be used to set limits on other SEPviolation 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 solarsystem limits.Parameter 
Physical meaning 
Solarsystem test 
Limit 
Pulsar test 
Limit 
Space curvature produced by unit rest mass 
VLBI, light deflection; measures 
3 × 10^{–4} 


Nonlinearity in superposition law for gravity 
Perihelion shift of Mercury; measures 
3 × 10^{–3} 


Preferredlocation effects 
Solar alignment with ecliptic 
4 × 10^{–7} 


Preferredframe effects 
Lunar laser ranging 
10^{–4} 
Ensemble of binary pulsars 
1.4 × 10^{–4}  
Preferredframe effects 
Solar alignment with ecliptic 
4 × 10^{–7} 


Preferredframe effects and nonconservation of momentum 
Perihelion shift of Earth and Mercury 
2 × 10^{–7} 
Ensemble of binary pulsars 
1.5 × 10^{–19}  
Nonconservation of momentum 
Combined PPN limits 
2 × 10^{–2} 


Nonconservation of momentum 

Limit on for PSR B1913+16 
4 × 10^{–5 }  
Nonconservation of momentum 
Lunar acceleration 
10^{–8} 


Nonconservation of momentum 
Not independent 


, 
Gravitational Stark effect 
Lunar laser ranging 
10^{–3} 
Ensemble of binary pulsars 
9 × 10^{–3} 
Pulsar coupling to scalar field 

Dipolar gravitational radiation for PSR B0655+64 
2.7 × 10^{–4 }  
Variation of Newton’s constant 
Laser ranging to the Moon and Mars 
6 × 10^{–12} yr^{–1} 
Changes in Chandrasekhar mass 
4.8 × 10^{–12} yr^{–1}  
http://www.livingreviews.org/lrr20035 
© Max Planck Society and the author(s)
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