New Non-Abelian Reissner-Nordstr\"{o}m Black Hole Solutions in the Generalized SU(2) Proca Theory And Some Astrophysical Implications

Abstract

The Generalized SU(2) Proca theory is a vector-tensor theory of gravity whose action is invariant under global transformations of the SU(2) group and includes second-order derivative self-interactions of the vector field beyond the massive Yang-Mills theory. We find that the presence of two Lagrangian pieces consisting of four gauge fields minimally coupled to gravity gives rise to an exact Reissner-Nordstr\"{o}m black hole solution endowed with two different non-Abelian effective charges that depend on the specific combination, $\chi = 2\chi_1 + \chi_2$, of the respective coupling constants. After studying the spacetime structure of the black hole, some astrophysical implications of the black hole solutions are investigated. First, joint analysis of observations of the EHT's first images of Sagittarius A$^{\star}$ of our Galaxy set the first serious constraint on the free parameters of the theory beyond the theoretical bounds found. Second, we investigate the accretion properties of spherical steady flows around this class of non-Abelian Reissner-Nordstr\"{o}m black hole. Specifically, we examine the general conditions under which transonic flow is allowed. Analytical solution for critical accretion is found in terms of the coupling constant. In addition, we explore numerically the effect of changing $\chi$ on the radial velocity and mass density, and show how the extremal Reissner-Nordstr\"{o}m and the standard Schwarzschild solutions as limit cases are achieved. Finally, working in the fully relativistic regime, an analytical expression for the critical mass accretion rate of a polytropic fluid onto a black hole is derived. As a main result, we find that the critical accretion rate efficiency can be noticeably improved compared to the Schwarzschild case for a specific region of the parameter space where the non-Abelian charge becomes imaginary.