4 Tests of GR - 3 Tests of GR - 3.3 Strong Equivalence Principle: Dipolar

3.4 Preferred-location effects: Variation of Newton's constant 

Theories that violate the SEP by allowing for preferred locations (in time as well as space) may permit Newton's constant G to vary. In general, variations in G are expected to occur on the timescale of the age of the Universe, such that tex2html_wrap_inline3269, where tex2html_wrap_inline3271 is the Hubble constant. Three different pulsar-derived tests can be applied to these predictions, as a SEP-violating time-variable G would be expected to alter the properties of neutron stars and white dwarfs, and to affect binary orbits.

3.4.1 Spin tests 

By affecting the gravitational binding of neutron stars, a non-zero tex2html_wrap_inline3275 would reasonably be expected to alter the moment of inertia of the star and hence change its spin on the same timescale [32]. Goldman [54] writes

  equation728

where I is the moment of inertia of the neutron star, about tex2html_wrap_inline3279, and N is the (conserved) total number of baryons in the star. By assuming that this represents the only contribution to the observed tex2html_wrap_inline3133 of PSR B0655+64, in a manner reminiscent of the test of tex2html_wrap_inline2823 described above, Goldman then derives an upper limit of tex2html_wrap_inline3287, depending on the stiffness of the neutron star equation of state. Arzoumanian [5Jump To The Next Citation Point In The Article] applies similar reasoning to PSR J2019+2425 [103], which has a characteristic age of 27 Gyr once the ``Shklovskii'' correction is applied [102]. Again, depending on the equation of state, the upper limits from this pulsar are tex2html_wrap_inline3289  [5Jump To The Next Citation Point In The Article]. These values are similar to those obtained by solar-system experiments such as laser ranging to the Viking Lander on Mars (see, e.g., [115, 59]). Several other millisecond pulsars, once ``Shklovskii'' and Galactic-acceleration corrections are taken into account, have similarly large characteristic ages (see, e.g., [28, 137]).

3.4.2 Orbital decay tests 

The effects on the orbital period of a binary system of a varying G were first considered by Damour, Gibbons, and Taylor [39], who expected

  equation761

Applying this equation to the limit on the deviation from GR of the tex2html_wrap_inline2771 for PSR 1913+16, they found a value of tex2html_wrap_inline3295 . Nordtvedt [106] took into account the effects of tex2html_wrap_inline3275 on neutron-star structure, realizing that the total mass and angular momentum of the binary system would also change. The corrected expression for tex2html_wrap_inline2771 incorporates the compactness parameter tex2html_wrap_inline2807 and is

  equation775

(Note that there is a difference of a factor of -2 in Nordtvedt's definition of tex2html_wrap_inline2807 versus the Damour definition used throughout this article.) Nordtvedt's corrected limit for PSR B1913+16 is therefore slightly weaker. A better limit actually comes from the neutron-star-white-dwarf system PSR B1855+09, with a measured limit on tex2html_wrap_inline2771 of tex2html_wrap_inline3309  [73]. Using Equation (29Popup Equation), this leads to a bound of tex2html_wrap_inline3311, which Arzoumanian [5Jump To The Next Citation Point In The Article] corrects using Equation (30Popup Equation) and an estimate of NS compactness to tex2html_wrap_inline3313 . Prospects for improvement come directly from improvements to the limit on tex2html_wrap_inline2771 . Even though PSR J1012+5307 has a tighter limit on tex2html_wrap_inline2771  [84], its shorter orbital period means that the tex2html_wrap_inline3275 limit it sets is a factor of 2 weaker than obtained with PSR B1855+09.

3.4.3 Changes in the Chandrasekhar mass 

The Chandrasekhar mass, tex2html_wrap_inline3321, is the maximum mass possible for a white dwarf supported against gravitational collapse by electron degeneracy pressure [29]. Its value - about tex2html_wrap_inline3323 - comes directly from Newton's constant: tex2html_wrap_inline3325, where tex2html_wrap_inline3327 is Planck's constant and tex2html_wrap_inline3329 is the neutron mass. All measured and constrained pulsar masses are consistent with a narrow distribution centred very close to tex2html_wrap_inline3321 : tex2html_wrap_inline3333  [136]. Thus, it is reasonable to assume that tex2html_wrap_inline3321 sets the typical neutron star mass, and to check for any changes in the average neutron star mass over the lifetime of the Universe. Thorsett [135Jump To The Next Citation Point In The Article] compiles a list of measured and average masses from 5 double-neutron-star binaries with ages ranging from 0.1 Gyr to 12 or 13 Gyr in the case of the globular-cluster binary B2127+11C. Using a Bayesian analysis, he finds a limit of tex2html_wrap_inline3337 at the 95% confidence level, the strongest limit on record. Figure  5 illustrates the logic applied.

While some cancellation of ``observed'' mass changes might be expected from the changes in neutron-star binding energy (cf. Section  3.4.2 above), these will be smaller than the tex2html_wrap_inline3321 changes by a factor of order the compactness and can be neglected. Also, the claimed variations of the fine structure constant of order tex2html_wrap_inline3341  [140] over the redshift range 0.5 < z < 3.5 could introduce a maximum derivative of tex2html_wrap_inline3345 of about tex2html_wrap_inline3347 and hence cannot influence the Chandrasekhar mass at the same level as the hypothesized changes in G .

  

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Figure 5: Measured neutron star masses as a function of age. The solid lines show predicted changes in the average neutron star mass corresponding to hypothetical variations in G, where tex2html_wrap_inline2619 implies tex2html_wrap_inline3355 . (From [135], used by permission.)

One of the five systems used by Thorsett has since been shown to have a white-dwarf companion [138], but as this is one of the youngest systems, this will not change the results appreciably. The recently discovered PSR J1811-1736 [89Jump To The Next Citation Point In The Article], a double-neutron-star binary, has a characteristic age of only tex2html_wrap_inline3359 and, therefore, will also not significantly strengthen the limit. Ongoing searches for pulsars in globular clusters stand the best chance of discovering old double-neutron-star binaries for which the component masses can eventually be measured.



4 Tests of GR - 3 Tests of GR - 3.3 Strong Equivalence Principle: Dipolar

image Testing General Relativity with Pulsar Timing
Ingrid H. Stairs
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