Abelian and non-Abelian mimetic black holes

TL;DR

The paper studies static black holes in a gauge-field mimetic extension of gravity with a constraint enforcing $F^2 = - \epsilon \mathcal{E}^2$ via an auxiliary field $\lambda$, focusing on Abelian $U(1)$ and non-Abelian $SU(2)$ sectors. It shows that stealth configurations ($\lambda=0$) can coexist with nontrivial gauge hair: in the Abelian case the solution reduces to Schwarzschild with electric hair, while pure magnetic hair is not allowed; in the non-Abelian case the stealth configuration supports genuine hair encoded by the non-Abelian field $\omega(r)$. The SU(2) stealth hair exhibits multiple branches depending on the magnetic parameter $q_m$ and the mimetic scale, a feature absent in standard Einstein–Yang–Mills black holes where magnetic hair is typically fixed. These findings imply potential modifications to black hole thermodynamics, shadows, and gravitational-wave signatures, illustrating a richer phenomenology in mimetic gauge gravity.

Abstract

We investigate black hole solutions in the mimetic extension of the Einstein-Yang-Mills system, in which the Yang-Mills term is constrained to be constant. In the Abelian U(1) case, we find a static spherically symmetric solution that includes the Schwarzschild and Reissner-Nordstrom black holes as special cases. Moreover, we identify a stealth Schwarzschild solution with an electric hair. We show that it is impossible to have magnetic hair in the U(1) gauge case, while, in contrast, the non-Abelian SU(2) stealth solutions can sustain both electric and magnetic hair. Unlike the conventional SU(2) Einstein-Yang-Mills black hole, which requires a unit magnetic parameter to exhibit nontrivial non-Abelian contributions, the stealth mimetic SU(2) solution admits genuinely non-Abelian configurations with arbitrary integer magnetic parameter.

Figures (8)

• Figure 1: The function $h$, given by \ref{['eq: h for U(1)']}, is plotted for $r_g = 2,$$\mathcal{E} = 1$ and $q_m = 1$ (all values here are given in Planck units). Different colors correspond to different values of parameter $c_1$.
• Figure 2: Four distinct numerical solutions for $\omega$ with parameters $q_m = 3$ and $\tilde{\mathcal{E}} = 0.05$. The orange dotted line represents the asymptotic analytical behavior of $\omega$ given by Eq. \ref{['eq: SU2 omega for big tr']}.
• Figure 3: Four distinctive numerical solutions for $\omega$. The orange dotted lines show asymptotic analytical behavior of $\omega$ given by Eq. \ref{['eq: SU2 omega for big tr']}. For the parameters, we have considered $q_m = 1$ and $\tilde{\mathcal{E}} = 0.05$.
• Figure 4: Three distinctive numerical solutions for $\omega$. The orange dotted lines show asymptotic analytical behavior of $\omega$ given by Eq. \ref{['eq: SU2 omega for big tr']}. For the parameters, we have considered $q_m = \tilde{\mathcal{E}} = 1$.
• Figure 5: Two distinct numerical solutions for $\omega$. The orange dotted lines represent the asymptotic analytical behavior of $\omega$ given by Eq. \ref{['eq: SU2 omega for big tr']}. We have set $q_m = 1$ and $\tilde{\mathcal{E}} = 1.2$.