Accretion dynamics in black holes with spontaneous Lorentz symmetry breaking

TL;DR

This paper studies how spontaneous Lorentz symmetry breaking, caused by a Kalb-Ramond field, affects the accretion of different fluids onto a modified Schwarzschild black hole, revealing significant changes in flow structure and accretion rates.

Contribution

It introduces a detailed analysis of accretion dynamics in Lorentz-violating black hole spacetimes using a Hamiltonian approach, highlighting the impact of the LV parameter on critical points and flow behavior.

Findings

LV parameter shifts critical point locations

Ultra-stiff fluids lack critical points and stay subsonic

Transonic solutions depend on the sign of LV parameter

Abstract

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.