Neutron stars in general second order scalar-tensor theory: The case of nonminimal derivative coupling

We consider the sector of Horndeski’s gravity characterized by the coupling between the kinetic scalar field term and the Einstein tensor. We numerically construct neutron star configurations where the external geometry is identical to the Schwarzschild metric but the interior structure is considerably different from standard general relativity. We constrain the only parameter of this model from the requirement that compact configurations exist, and we argue that solutions less compact than neutron stars, such as white dwarfs, are also supported. Therefore, our model provides an explicit modification of general relativity that is astrophysically viable and does not conflict with Solar System tests.

Figure 1

Range of $Q_0^2\eta$ where $F^{\prime }$ is real and where compact solutions exist. Here, ${\rho }_c/P_c$ is dimensionless. The red (blue) shaded area corresponds to $F^{\prime 2}>0$ for $\eta <0$ $(\eta >0)$. Typical solar mass neutron stars lie inside the black rectangle.

Figure 2

The mass-radius relation for various values of $Q_{\infty }$ and $\eta =+1,-1$. The thick black curve is the GR prediction while the dashed one has $Q_{\infty }=0$. The black dots are the points where the solutions cease to exist. Note that, for $\eta >0$, the curves with $Q_{\infty }=0.016$ and $Q_{\infty }=0.032$ do not reach such a point in the chosen range of central pressures.

Figure 3

Lines of constant $Q_{\infty }$ in the $(P_c,Q)$ plan. The legend indicates the value of $Q_{\infty }$. The scalar field is no longer real for $Q>1/(12\pi )$. All curves, except for $Q_{\infty }=0$, reach a maximal value.

Figure 4

Plot of $F^{\prime 2}$ for $\eta >0$ (left) and $\eta <0$ (right). In the case $\eta <0$, $F^{\prime }$ is imaginary close to the origin for small values of $Q_{\infty }^2$, and becomes real for larger values of $r$, while it is always real for $\eta >0$.