Chameleon stars

We consider a gravitating spherically symmetric configuration consisting of a scalar field nonminimally coupled to ordinary matter in the form of a perfect fluid. For this system we find static, regular, asymptotically flat solutions for both relativistic and nonrelativistic cases. It is shown that the presence of the nonminimal interaction leads to substantial changes both in the radial matter distribution of the star and in the star’s total mass. A simple stability test indicates that, for the choice of parameters used in the paper, the solutions are unstable.

Figure 1

The dependence of the function $v({\xi }_1)$ (which is proportional to the total mass $M$) on the value of the coupling parameter $\Lambda$ from (23) at the fixed central value ${\varphi }_0=0.45$ and $\sigma =0.2$. The data are taken from Table .

Figure 2

The dependence of the function $v({\xi }_1)$ on the central value of ${\varphi }_0$ at the fixed ${\overline{\xi }}_1=3.219$ for $n=1.5$ and ${\overline{\xi }}_1=2.657$ for $n=1.0$, and $\sigma =0.2$ for both graphs. The data are taken from Table .

Figure 3

The density $\rho$ and the pressure $p$ of the fluid, the scalar field $\varphi$, the metric functions $e^{\nu }$, $e^{\lambda }$ and the current mass $M$ as functions of the relative invariant radius $\overline{\xi }/{\overline{\xi }}_1$ for $n=1.5$ and $n=1.0$ respectively. To provide the asymptotic flatness of the solutions, i.e. $e^{\nu }$, $e^{\lambda }\to 1$ as $\overline{\xi }\to \infty$, the value of the constant ${\nu }_c$ needed to be chosen as ${\nu }_c\approx -0.958$ for $n=1.5$ and ${\nu }_c\approx -0.822$ for $n=1.0$.

Figure 4

The distributions of the total energy density in units of ${\rho }_c$ from (29) for different the initial values of ${\varphi }_0=0.30$, 0.35, 0.40, 0.45, from top to bottom.

Figure 5

The distributions of the total energy density in units of ${\rho }_c$ from (29) for the different initial values of ${\varphi }_0=0.45$, 0.35, 0.27, from top to bottom.

Figure 6

The dependence of the function $v({\xi }_1)$ on the central value of ${\varphi }_0$ at the fixed ${\overline{\xi }}_1=3.6560$ for $n=1.5$ and ${\overline{\xi }}_1=3.1437$ for $n=1.0$, and $\sigma =0.001$ for both graphs. The data are taken from Table .

Figure 7

The plot of the total energy density, $T_0^0$, in units of ${\rho }_c$ in the nonrelativistic case ($\sigma =0.001$) for different central values of ${\varphi }_0$ from Table . The solid lines correspond to the case of $n=1.5$, the dashed lines to the case of $n=1.0$. The top two sets of curves correspond to the configurations with the scalar field. For comparison, the energy densities of the nonrelativistic configurations without a scalar field $T_0^0={\rho }_c{\theta }^n$ are also shown by the two bottom, less peaked curves.