Abstract
In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppresses the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.
Highlights
In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars
One may ask what happens if the maximum mass of neutron stars turns out to be larger than the current observational value? Comparing the left and right panel of figure 11, we learn that as the maximum mass increases by changing the polytropic parameters, the critical density for the existence of the scalar field decreases. This allows us to state that for a neutron star described by a polytropic equation of state, which is in agreement with the observational maximum mass, the configurations that would collapse and form a black hole cannot support a non-trivial scalar field
We developed an expansion scheme to solve the non-linear equations inside the Vainshtein radius in a system with the cubic Galileon term
Summary
Our starting point is the Einstein-Hilbert action, minimally coupled to a scalar field with the cubic Galileon term with no additional matter included. In models where the cubic Galileon term is associated with the late time acceleration of the Universe, Λ3α−2 is typically given by (1000 km)−3. Varying this action with respect to the metric and the scalar field, we obtain the following equations of motion: ξμν := Mp2. Where the dimensionless integration constant ζ must be determined by boundary conditions This is an algebraic equation for Φ , with solutions. When substituting the scalar field solution into the Einstein equations, one finds that the Galileon contributions are suppressed by powers of 1/α, they can be neglected in the large α limit.
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