Gravitational confinement of ghost scalar fields in neutron stars

Abstract

We investigate the effects, stability, and nonlinear dynamics of ghost scalar matter modeled as a field with a negative kinetic term confined within the cores of neutron stars. To this end, we analyze static configurations of the coupled Einstein-Euler-(ghost, complex) Klein-Gordon system and then we perform fully dynamical numerical evolutions of illustrative cases. Our results demonstrate that neutron stars can gravitationally confine a finite amount of ghost matter and support continuous families of equilibrium solutions, indicating that these configurations are not the result of fine tuning. We analyze the properties of the final states and find that the neutron star undergoes a persistent pulse-like oscillatory motion. In particular, we explicitly compute the frequency synchronization between the stellar fluid oscillation modes and those of the ghost scalar sector.

Figures (18)

• Figure 1: Neutron star configurations coexisting with exotic matter. We present the total mass $M_T$ of the configuration as a function of the neutron star radius $R_N$, for two values of the self interaction parameter $\lambda$. The solid line corresponds to neutron stars without exotic nuclei. Gold curves denote families of mixed stars with constant $\rho_0$ and varying $\chi_0$, while dotted black curves denote constant $\chi_0$ and varying $\rho_0$. In most constructed configurations, the ghost matter is confined within the fluid ($R_{99}^N < R_N$); however, for $\lambda = 200$, configurations in which the opposite occurs are also found and are highlighted in yellow. In the large self-interaction regime, configurations belonging to a family with fixed $\rho_0$ show that both $M_T$ and $R_N$ depend on $\chi_0$; nevertheless, their values are nearly indistinguishable from those of the corresponding pure neutron star with the same $\rho_0$.
• Figure 2: Neutron star radius, $R_N$ and phantom nuclei one, $R^{\chi}_{99}$, (see definitions in the text) as functions of value of the phantom field at the center, $\chi_0$. We present two families of mixed configurations with $\lambda = 200$ and fixed $\rho_0$: left panel, $\rho_0 = 1 \times 10^{-4}$; right panel, $\rho_0 = 5 \times 10^{-4}$. The black dotted line indicates the radius of the corresponding neutron star without exotic nuclei for each value of $\rho_0$. In the case $\rho_0 = 1 \times 10^{-4}$, configurations exist in which the fluid component is trapped by the phantom field.
• Figure 3: Total mass and compactness as functions of $\chi_0$ and $\omega$ for mixed configurations with fixed $\lambda$ and $\rho_0$. Dashed lines denote the reference values at $\chi_0 = 0$. For small $\rho_0$, lower $\lambda$ yields significantly larger masses and compactness than the pure neutron star, whereas for $\lambda = 9.4 \times 10^4$ the increase is modest. In families with $\rho_0=7\times 10^{-3}$ for large enough values of $\chi_0$, there exist configurations for which the total mass, $M_T$, becomes smaller than that of the pure neutron star.
• Figure 4: Families of neutron stars configurations coexisting with exotic matter. We present behavior of the total mass $M_T$ of the star vs the central density $\rho_0$ for $\lambda=200$ and fixed values of the phantom scalar field at the center.
• Figure 5: Profiles of $\chi(r)$, and the metric coefficients $\alpha(r), a (r)$, for a configuration with $\rho_0=1.28\times 10^{-3}, \lambda=200$, and several values of the phantom field at the center. The fermionic density, $\rho(r)$, the phantom scalar field density $\rho_{\chi}$ and $\rho_T$ are also shown for the same configurations