General relativity verified by a triple-star system

Einstein’s theory of gravity — the general theory of relativity — is based on the principle that all objects accelerate identically in an external gravitational field. A triple-star system provides a stringent test of this principle.
Clifford M. Will is in the Department of Physics, University of Florida, Gainesville, Florida 32611, USA.

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All bodies in a given gravitational field are thought to fall with the same acceleration. This idea, known as the equivalence principle, is central to our understanding of gravitational physics. It was promoted by thinkers ranging from the sixth-century scholar John Philoponus to Galileo; it is the founding principle of Albert Einstein’s general theory of relativity, and was famously demonstrated when Apollo astronaut David Scott dropped a hammer and a feather on the Moon and saw that they hit the lunar surface at the same time. For decades, experimentalists have verified the equivalence principle using exquisitely delicate instruments. Now, in a paper in Nature, Archibald et al.1 report the results of a remarkable test of the principle, in which the falling objects are two stellar remnants: a neutron star and a white dwarf.

A spinning neutron star that emits a beam of electromagnetic radiation is known as a pulsar. The emission seems to pulse because it can be seen only when the beam is pointing towards Earth. The pulses are so regular that variations in their observed period can be readily interpreted as being due to the gravitational tug of another astronomical body on the pulsar. Such variations have been used to discover more than 220 binary systems containing a neutron star, and a handful of pulsars that have associated planets (

In 2014, astronomers reported a pulsar that is unusual because it has two stellar companions2 (Fig. 1). The neutron star, weighing 1.4 solar masses, is in a close 1.6-day orbit with a 0.2-solar-mass white dwarf. This pair of objects is itself in a 327-day orbit with a 0.4-solar-mass white dwarf. The inner and outer orbits are nearly circular and exist in almost exactly the same plane.

Figure 1 | Triple-star system. In 2014, astronomers reported a system that contains three stellar remnants: a neutron star and two white dwarfs2. a, The neutron star is in a close 1.6-day orbit with one of the white dwarfs. b, This pair of objects is itself in a 327-day orbit with the other white dwarf. Archibald et al.1 report no evidence of a deformation of the inner orbit, which would be expected if there were a difference between the accelerations of the neutron star and the inner white dwarf towards the outer white dwarf. The results provide support for Einstein’s theory of gravity — the general theory of relativity.

If the neutron star and the inner white dwarf were to fall with different accelerations towards the outer white dwarf, there would be a tiny deformation of the inner orbit. Archibald and colleagues report an analysis of approximately six years of data showing no evidence of such a deformation. The accelerations of the two bodies differ by no more than 2.6 parts per million, in agreement with the equivalence principle.

Tests of this principle have a long heritage. In the late nineteenth century, the Hungarian physicist Roland von Eötvös devoted years to verifying that the accelerations of various laboratory materials in Earth’s gravitational field differ by less than a few parts per billion3. His modern-day successors, the Eöt-Wash group4 in Seattle, Washington, pushed this bound to parts per 1013. And, in 2017, data from the French space mission MICROSCOPE5 moved the goalpost by a further factor of ten.

Given that a typical object in a physics lab consists of a swarm of elementary particles and their associated fields and energies, it is quite extraordinary that the responses of different materials to gravity should be so similar. In Einstein’s unique imagination, there was a reason: gravity is not a force that acts on all of these particles in some fantastically fine-tuned manner, but is simply an effect of space-time geometry. The constituents of matter follow universal paths in a space-time that is curved by massive bodies, such as Earth or the Sun.

But does gravitational energy act in the same way as matter? The small objects used in lab experiments do not contain enough gravitational energy to answer this question, but planets and stars do. With self-gravity in the picture, a concept called the strong equivalence principle comes into play. This principle singles out the general theory of relativity from its competitors. In Einstein’s theory, all bodies — hammers, feathers, planets, neutron stars, white dwarfs and even black holes — fall with the same acceleration. But in most alternative theories of gravity, such as scalar–tensor theories6, the equivalence principle is violated for bodies that have self-gravity.

For almost 50 years, researchers have measured how long it takes for laser pulses to make the round trip from Earth to the Moon and back — a technique known as lunar laser ranging. Analyses of these data7,8 have verified the strong equivalence principle, by showing that the accelerations of the two bodies towards the Sun differ by no more than a few parts per 1013. Because about 5 parts in 1010 of Earth’s mass is gravitational energy9, this result implies that the accelerations of gravitational energy and matter differ by less than a few parts per 104.

Archibald and colleagues’ study breaks new ground because the gravitational energy inside a neutron star can account for as much as 20% of the body’s mass10. The authors’ results therefore imply that the accelerations of gravitational energy and matter differ by no more than a few parts per 105 — a tenfold improvement over the bound from lunar laser ranging.

More importantly, the authors have provided what is known as a strong-field test of general relativity. Unlike the Solar System, for which Einstein’s theory predicts only small deviations from Newton’s theory of gravity, the motion of a neutron star in a gravitational field invokes full general relativity in all its complex glory. Einstein’s theory passes this strong-field test with flying colours.

Because general relativity predicts a null effect, the grading is a simple pass or fail. But for alternative theories, invoking strong-gravity effects substantially complicates the interpretation of the results. Archibald et al. demonstrate this complexity using scalar–tensor theories as an example. For these theories, the interpretation of the results depends on the internal structure assumed for the neutron star and on the values chosen for quantities known as coupling constants. The authors show that their results improve on certain pre-existing constraints on the parameters that govern these theories — some arising from Solar System measurements and some from data on binary systems containing a pulsar. Although the theories are not completely quashed, their hopes for validity have been made that much fainter.

Nature 559, 40-41 (2018)

doi: 10.1038/d41586-018-05549-4
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  1. 1.

    Archibald, A. M. et al. Nature 559, 73–76 (2018).

  2. 2.

    Ransom, S. M. et al. Nature 505, 520–524 (2014).

  3. 3.

    Eötvös, R. V., Pekár, D. & Fekete, E. Ann. Phys. (Leipz.) 373, 11–66 (1922).

  4. 4.

    Wagner, T. A., Schlamminger, S., Gundlach, J. H. & Adelberger, E. G. Class. Quantum Grav. 29, 184002 (2012).

  5. 5.

    Touboul, P. et al. Phys. Rev. Lett. 119, 231101 (2017).

  6. 6.

    Brans, C. & Dicke, R. H. Phys. Rev. 124, 925–935 (1961).

  7. 7.

    Williams, J. G., Turyshev, S. G. & Boggs, D. H. Int. J. Mod. Phys. D 18, 1129–1175 (2009).

  8. 8.

    Hofmann, F., Müller, J. & Biskupek, L. Astron. Astrophys. 522, L5 (2010).

  9. 9.

    Will, C. M. Theory and Experiment in Gravitational Physics, Revised Edition 174 (Cambridge Univ. Press, 1993).

  10. 10.

    Shapiro, S. L. & Teukolsky, S. A. Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects 241 (Wiley, 1986).

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