Accretion dynamics in black holes with spontaneous Lorentz symmetry breaking

TL;DR

This work analyzes spherical accretion onto a Schwarzschild-like black hole in Kalb–Ramond gravity with spontaneous Lorentz symmetry breaking, characterized by the LV parameter $l$ and metric function $A(r)=\frac{1}{1-l}-\frac{2M}{r}$. It combines Michel-type relativistic hydrodynamics with a Hamiltonian dynamical-systems framework to locate sonic (critical) points for isothermal $p=\omega\rho$ and polytropic fluids, revealing how $l$ shifts critical points, sonic transitions, and accretion rates. Key findings include density enhancement for $l>0$ and suppression for $l<0$, the absence of critical points for ultra-stiff fluids, and qualitatively similar transonic behavior for polytropes with critical points depending on $\Gamma$ and $l$; horizons move according to $r_h=2(1-l)M$. The results show that Lorentz symmetry breaking can significantly modify black hole accretion dynamics in strong gravity, motivating extensions to rotating spacetimes and non-spherical, magnetized flows for potential observational constraints.

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 $p=ωρ$, including ultra-stiff, ultra-relativistic, and radiation fluids. We investigate the effect of the LV parameter $l$ on the fluid density $ρ(r)$, 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 $p=\mathcal{K} ρ^Γ$ with $Γ=5/3$ and $Γ=4/3$, 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.

Figures (7)

• Figure 1: The energy density of Eq. \ref{['rhoLV']} for ultra-stiff ($\omega=1$, top left), ultra-relativist ($\omega=1/2$, top right) and radiation ($\omega=1/3)$, bottom) with $l>0$ and $l<0$, as compared to Schwarzschild solution. Here we made $\mathcal{A}_3=\mathcal{A}_4=1$.
• Figure 2: The radial velocity of Eq. \ref{['uLV']} for ultra-stiff ($\omega=1$, top left), ultra-relativist ($\omega=1/2$, top right) and radiation ($\omega=1/3)$, bottom) with $l>0$ and $l<0$, as compared to Schwarzschild solution. Here we made $\mathcal{A}_4=1$.
• Figure 3: The mass accretion rate of Eq. \ref{['MacLV']} for ultra-stiff ($\omega=1$, top left), ultra-relativist ($\omega=1/2$, top right) and radiation ($\omega=1/3)$, bottom) with $l>0$ and $l<0$, as compared to Schwarzschild solution. Here we made $\mathcal{A}_3=\mathcal{A}_4=1$.
• Figure 4: Representation of the phase space of the solution \ref{['KR0']} for ultra-stiff fluid, $\omega=1$, and $l>0$ (left) and $l>0$ (right).
• Figure 5: Representation of the phase space of the solution \ref{['KR0']} for ultra-relativistic fluid, $\omega=1/2$, and $l>0$ (left) and $l>0$ (right). The sound speed value is given by $v^2_s=\omega=1/2$.