# General relativistic study of astrophysical jets with internal shocks

## TL;DR

This study investigates the formation of steady internal shocks in relativistic astrophysical jets around black holes, analyzing how jet geometry and energy influence shock development and potential particle acceleration sites.

## Contribution

It introduces models of relativistic jets with different geometries, demonstrating conditions under which internal shocks form and their properties, a novel analysis in the context of black hole jets.

## Key findings

- Non-conical jets can develop multiple sonic points and shocks.
- Shocks are stronger further from the black hole.
- Jets with intermediate energies host shocks without affecting terminal speed.

## Abstract

We explore the possibility of formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry ($\theta=0$) in a Schwarzschild metric. We use two models for the jet geometry, (i) a conical geometry and (ii) a geometry with non-conical cross-section. Jet with conical geometry is smooth flow. While the jet with non-conical cross section undergoes multiple sonic point and even standing shock. The jet shock becomes stronger, as the shock location is situated further from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium is that, these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically, a jet with energy $1.8~c^2$, will achieve a terminal speed of $v_\infty=0.813c$ for jet with any geometry. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is $40\rg$, then in addition, a steady shock will form at $\rsh \sim 7.5\rg$ and compression ratio of $R\sim 2.7$. Moreover, electron-proton jet seems to harbour the strongest shock. We discuss possible consequences of such a scenario.