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Testing the Motion of Strongly Self-Gravitating Bodies with Radio Pulsars

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Equations of Motion in Relativistic Gravity

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 179))

Abstract

Before the 1970s, precision tests for gravity theories were constrained to the weak-field environment of the Solar System. In terms of relativistic equations of motion, the Solar System gave access to the first order corrections to Newtonian dynamics. Testing anything beyond the first post-Newtonian contributions was for a long time out of reach. The discovery of the first binary pulsar by Russell Hulse and Joseph Taylor in the summer of 1974 initiated a completely new field for testing the relativistic dynamics of gravitationally interacting bodies. For the first time the back reaction of gravitational wave emission on the binary motion could be studied. Furthermore, the Hulse-Taylor pulsar provided the first test bed for the orbital dynamics of strongly self-gravitating bodies. To date, there are a number of binary pulsars known which can be utilized to test different aspects of relativistic dynamics. So far GR has passed these tests with flying colors, while many alternative theories, like scalar-tensor gravity, are tightly constraint by now. This article gives an introduction to gravity tests with pulsars, and summarizes some of the most important results. Furthermore, it gives a brief outlook into the future of this exciting field of experimental gravity.

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Notes

  1. 1.

    Gravitational wave damping has also been observed in a double white-dwarf system, which has an orbital period of just 13 min [19]. This experiment combines gravity regimes G1 (note, \(v/c \sim 3 \times 10^{-3}\)) and GW of Fig. 1.

  2. 2.

    The PPN formalism uses 10 parameters to parametrize in a generic way deviations from GR at the post-Newtonian level, within the class of metric gravity theories (see [5] for details).

  3. 3.

    The mono-scalar-tensor theories \(T_1(\alpha _0,\beta _0)\) of [56, 57] have a conformal coupling function \(A(\varphi ) = \alpha _0 (\varphi - \varphi _0) + \beta _0 (\varphi - \varphi _0)^2/2\). The Jordan-Fierz-Brans-Dicke gravity is the sub-class with \(\beta _0 = 0\), and \(\alpha _0^2 = (2\omega _\mathrm{BD} + 3)^{-1}\).

  4. 4.

    Strictly speaking, this is the total mass of the system scaled with an unknown Doppler factor \(D\), i.e. \(M^\mathrm{observed} = D^{-1} M^\mathrm{intrinsic}\) [39]. For typical velocities, \(D - 1\) is expected to be of order \(10^{-4}\), see for instance [64]. In gravity tests based on post-Keplerian parameters, the factor \(D\) drops out and is therefore irrelevant [54].

  5. 5.

    From the Cassini experiment [11] one obtains \(|\alpha _0| < 3 \times 10^{-3}\) (95 % confidence).

  6. 6.

    These numbers are based on the equation of state MPA1 in [82]. Within GR, MPA1 has a maximum neutron-star mass of \(2.46\,M_\odot \), which can also account for the high-mass candidates of [83–85].

  7. 7.

    The first well determined two Solar mass neutron star is PSR J1614\(-\)2230 [90], which is in a wide orbit and therefore does not provide any gravity test.

  8. 8.

    The light-cylinder is defined as the surface where the co-rotating frame reaches the speed of light.

  9. 9.

    It has been suggested to use the orbital period of binary pulsars to test for gravitational waves of considerably longer wavelength [129, 130].

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Acknowledgments

I would like to thank the workshop organizers for their hospitality, and John Antoniadis for carefully reading the manuscript.

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  1. Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121, Bonn, Germany

    Norbert Wex

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  1. ZARM University of Bremen, Bremen, Germany

    Dirk Puetzfeld

  2. ZARM University of Bremen, Bremen, Germany

    Claus Lämmerzahl

  3. Max-Planck-Institut für Gravitationsphysik, Golm, Brandenburg, Germany

    Bernard Schutz

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Wex, N. (2015). Testing the Motion of Strongly Self-Gravitating Bodies with Radio Pulsars. In: Puetzfeld, D., Lämmerzahl, C., Schutz, B. (eds) Equations of Motion in Relativistic Gravity. Fundamental Theories of Physics, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-319-18335-0_20

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