Minimal geometric deformation of Yang-Mills-Dirac stellar configurations

The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions that are solutions of the Yang-Mills-Einstein-Dirac coupled field equations on fluid membranes with finite tension. Their solutions characterize MGD Yang-Mills-Dirac stars, whose mass has order of the Chandrasekhar mass, once the range of both the fermionic self-interaction and the Yang-Mills coupling constants is suitably chosen. Physical features of MGD Yang-Mills-Dirac stars are then discussed and their Arnowitt-Deser-Misner masses are derived, as a function of the fermion coupling constant, the finite brane tension, and the Yang-Mills running parameter.

Figure 1

ADM mass of MGD Yang-Mills-Dirac stars as a function of the central value of the spinor field ${\alpha }_1$ component ${\alpha }_{1c}$ for two values $\xi =0.03$ and $\xi =0.1$, and $\tilde{\lambda }=-1$. Two values of the brane tension $\sigma \approx 2.8\times {10}^6{\mathrm{MeV}}^4$ and $\sigma \sim {10}^{12}{\mathrm{MeV}}^4$ are analyzed for the MGD-decoupling parameter value $\zeta =0.1$.

Figure 2

Linear-log plot of the Yang-Mills field $f(x)$ as a function of dimensionless stellar radius $x$ for $\xi =0.03$ and $\xi =0.1$, with the central value of the spinor field ${\alpha }_1$ component, ${\alpha }_{1c}=0.15$, adopted for $\tilde{\lambda }=-1$. The brane tension $\sigma \sim {10}^{12}{\mathrm{MeV}}^4$ is taken, and $\zeta =0.1$ rules the MGD decoupling.

Figure 3

Spinor field components ${\alpha }_1(x)$ and ${\alpha }_2(x)$ as a function of dimensionless radius $x$ for $\xi =0.03$ and $\xi =0.1$, with the central value ${\alpha }_{1c}=0.15$ adopted for $\tilde{\lambda }=-1$. The brane tension $\sigma \sim {10}^{12}{\mathrm{MeV}}^4$ is taken and $\zeta =0.01$ rules the MGD decoupling.

Figure 4

Spinor field components ${\alpha }_1(x)$ and ${\alpha }_2(x)$ as a function of dimensionless radius $x$ for $\xi =0.03$ and $\xi =0.1$, where ${\alpha }_{1c}=0.15$ is adopted for $\tilde{\lambda }=-1$. The brane tension $\sigma \sim {10}^{12}{\mathrm{MeV}}^4$ is taken, and $\zeta =0.1$ rules the MGD decoupling.

Figure 5

Dimensionless total ADM mass $M_{\star \infty }$ of MGD Yang-Mills-Dirac stellar configurations as a function of the energy of the stationary part of the spinor fields $\tilde{E}$. Brane tension values $\sigma \sim {10}^{12}{\mathrm{MeV}}^4$ (black line), $\sigma \sim {10}^9{\mathrm{MeV}}^4$ (gray line), and $\sigma \sim {10}^6{\mathrm{MeV}}^4$ (light gray line) are taken, and $\zeta =0.1$ rules the MGD decoupling.