Accretion dynamics in black holes with spontaneous Lorentz symmetry breaking

We investigate the spherical accretion of various types of fluids onto a Schwarzschild-like black hole solution modified by a Kalb-Ramond field implementing spontaneous Lorentz symmetry violation (LV). The system is analyzed for isothermal fluids characterized by the equation of state $p=\omega\rho$, including ultra-stiff, ultra-relativistic, and radiation fluids. We investigate the effect of the LV parameter $l$ on the fluid density $\rho(r)$, radial velocity $u(r)$, and accretion rate $\dot{M}$. Using a Hamiltonian dynamical systems approach, we examine the behavior near critical points and identify the sonic transitions in each scenario. Our results show that the LV parameter influences the location of critical points, the flow structure, and the accretion rate, with $l>0$ ($l<0$) enhancing (suppressing) the latter. For ultra-stiff fluids, no critical points are found, and the flow remains entirely subsonic. For ultra-relativistic and radiation fluids, transonic solutions exist, with the position of the sonic point depending on the sign of $l$. We also analyze polytropic fluids $p=\mathcal{K} \rho^{\Gamma}$ with $\Gamma=5/3$ and $\Gamma=4/3$, observing similar qualitative behavior, where the sonic transition is affected by both the equation of state and the LV parameter. These findings suggest that Lorentz symmetry breaking can significantly alter accretion dynamics in black hole spacetimes.