Blandford-Znajek Jets and the Total Angular Momentum Evolution of a Black Hole Connected to a Cosmic String

TL;DR

This work investigates how a one-dimensional cosmic string attached to a rotating black hole modifies Blandford-Znajek jet power and the total angular momentum evolution. By deriving how the jet energy flux $\dot{E}_{BZ}$ depends on the string tension $μ$ and incorporating accretion, string energy extraction, and the Bardeen-Petterson effect, the authors show that at fixed magnetic flux $\Phi$ and accretion rate $\dot{M}_{acc}$ the jet power scales as $\dot{E}_{BZ} \propto 1/μ^2$ for large $μ$, with a time-dependent evolution due to string mass loss. They analyze angular momentum transfer from four channels, finding distinct scaling: accretion $\dot{J}_{acc}$ grows weakly with $μ$ (approximately $μ^{0.19}$ to $μ^{0.01}$ depending on regime), BZ torques scale as $μ^{-1}$, string extraction supplies a $μ$-dependent torque, and the Bardeen-Petterson torque scales roughly as $μ^{3.87}$ but remains subdominant in most spin-down scenarios. The paper concludes that large string tensions make spin-down more likely and that jet-orientation and disk alignment with the string could yield observable signatures, offering a possible method to detect cosmic strings through jet physics and accretion dynamics.

Abstract

Rotating black holes with strong magnetic fields lead to an outward energy flux in the form of jets governed by the Blandford-Znajek mechanism. These jets depend on factors such as accretion rate, magnetic flux and the spin of the black hole. When such rotating black holes get attached to a cosmic string, it leads to a further rotational energy extraction, leading to a reduced spin. We consider such a system and investigate the effect this reduced spin has on the jet power and its dependence on the cosmic string tension, $μ$. It is shown that for a constant magnetic flux and accretion rate, the jet energy flux is inversely proportional to $μ^2$. Interestingly, the rate of this energy flux varies with time and is again dependent on $μ$. We also study the total angular momentum evolution of the black hole by considering four major effects: accretion, jets, cosmic string energy extraction and the Bardeen-Petterson effect. Further, we attempt to analyse the condition for the spin-down of a black hole due to these effects and find out that it is possible for both small and large string tensions, with a higher possibility for larger string tensions. Another interesting phenomenon that has been proposed is the alignment of the jet with the cosmic string. Additionally, the Bardeen-Petterson effect also leads to alignment or misalignment of the inner and outer disks depending on the alignment of the string. In this manuscript we propose that these results might have an observable effect and hence could serve as a potential detection method for cosmic strings.

Figures (6)

• Figure 1: Illustration of the Accreting Black Hole - Cosmic String system
• Figure 2: Energy flux vs Time for different string tensions
• Figure 3: $L_{ISCO}$ vs $\mu$ for $\mu \gtrsim \dot{M}_{acc,G}$
• Figure 4: $L_{ISCO}$ vs $\mu$ for $\mu >> \dot{M}_{acc,G}$
• Figure 5: The black hole and its BZ jet aligning with the cosmic string