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6.2 Second-order scalar-tensor gravity and radio pulsars

As discussed in the previous section, observations of strong-field phenomena provide constraints on Brans–Dicke scalar-tensor gravity, which are, however, at most comparable to those of solar system tests. This is true because the fractional deviation of a Brans–Dicke theory from general relativity is of order ω −1 BD, both for weak and strong gravitational fields, and the solar-system tests have superb accuracy. On the other hand, a scalar-tensor theory with a second-order coupling (e.g., the one arising from the action (22View Equation) with the coupling (23View Equation)) allows for large deviations in the strong-field regime, while being consistent with the weak-field limits [39Jump To The Next Citation Point40].

In the case of neutron stars, the second-order scalar-tensor theory described by Damour and Esposito-Farèse [39Jump To The Next Citation Point] leads to a non-perturbative effect known as spontaneous scalarization (similar to the spontaneous magnetization in ferromagnetism). For significantly large negative values of the parameter β0, there is a range of neutron-star masses for which it becomes energetically favorable for the scalar field to acquire high values inside the neutron star and affect its structure significantly compared to the general relativistic predictions. An example of the mass-radius relation for neutron stars in a second-order scalar-tensor theory with β0 = –8 is shown in Figure 13View Image.

The properties and stability of scalarized neutron stars have been studied extensively in the literature [39Jump To The Next Citation Point13970]. For the purposes of tests of strong-field gravity, the coupling of matter with the gravitational field and the external spacetimes of scalar stars are so different compared to their general relativistic counterparts that large negative values of β0 can be firmly excluded with current observations of binary stellar systems that harbor radio pulsars (see Figure 15View Image).

As expected, weak-field tests bound significantly the value of the parameter α0, leaving the parameter β 0 largely unconstrained. Between the binary systems with radio pulsars, the one with the white-dwarf companion provides the most stringent constraints because the large asymmetry between the two compact objects leads to the prediction of strong dipole gravitational radiation that can be excluded observationally. Finally, for large negative values of the parameter β0, the scalarization of the neutron stars makes the predictions of the theory incompatible with observations.

View Image

Figure 16: Contours of constant gravitational redshift measured at infinity for an atomic line originating at the surface of a neutron star in a scalar-tensor gravity theory, for different values of the parameter β0 that measures the relative contribution of the scalar field. The thick curve separates the scalarized stars from their general-relativistic counterparts. The measurements of a redshift of z = 0.35 from a burster [37Jump To The Next Citation Point] and the astrophysical constraint of a baryonic mass of at least 1.4M ⊙ (dashed lines) result in a bound on the parameter β of − β < 9 [43Jump To The Next Citation Point].

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