Relativistic Hydrodynamics 2025, 17 - Relativistic Accretion, Jets & Heavy-Ion Collisions

In the case for stationary axisymmetric solution orbiting a black hole, solutions in which the fluid accretes onto the black hole on time-scale equal to those of dissipative processes are possible. Those solutions divide into three different classes, defined by their geometrical thickness H(r). The solutions use once again the metric for Kerr black holes, and the usual conservation laws for rest mass, energy, momentum and angular momentum, but adds hydrostatic vertical equilibrium to approximate the conservation of vertical momentum to the system.

In general, observations of superliminal jets imply relativistic velocity of some internal pattern of structure within a jet.The two velocities might coincide. The kinematic interpretation is through a radio blob as observer at infinity and a radio blob moving at some velocity along an angle with line of sight. At time t = 0 the blobs are in the same position, emitting a radio signal, repeated at some later time. The transverse velocity is then the ratio between apparent distance and time interval. This gives an apparent velocity between the radio blobs, primarily dependent on the viewing angle. The relativistic speeds are also responsible for the enhancement of the observed radiation intensity according to the law. If the blobs move at similar speeds, this reduces to a Lorentz factor. If the jet flow is confined to a conical jet and the continuity equation holds, at ultrarelativistic speeds and through the geometry of the expansion. In the absence of shocks, the pressure is expressed through rest-mass density. In the twin-exhaust model, two channels of fluid are ejected in opposite directions from a rotating central object. The cross sectional area of the channel is non-constant, adjusting to the varying pressure like a relativistic de Laval nozzle. The stagnation pressure is defined as the pressure of the flow where it has zero velocity. The pressure is only defined through it, and the Lorentz factor. The resulting bulk flow is 1D, but the walls of the jet aren't necessarily parallel and the fluid's momentum can change along with them.

QCD predicts a phase transition from confined hardonic constituents to a plasma of deconfined quarks and gluons at critical energy density. In such situations, heavy-ion collisions are expected to occur within a relativistic fluid. Relativistic collisions have a c.o.m. energy larger than the rest mass of the nuclei, which then defines a Lorentz factor for further use. It usually comes out between 100 and 200. In lab frame, the nuclei would appear heavily contracted. At ultrarelativistic energies, the nuclei are transparent to nucleons, passing through one another. For proper times, fluids in this mode are exposed to cooling and the matter passes through a hadronisation transition, rarefying the fluid that the local TD equilibrium is no longer maintained and the hadrons decouple, and streaming freely. Hydrodynamic approximations break down at this point, and a kinetic theory should be favored. If this scenario is assumed impossible for this fluid, then at 1D, and without gravitational corrections (in flat spacetime) the collisions are primarily expressed through baryon number, energy and momentum, the latter two being conserved. The longitudinal velocity can be chosen for an initial value, and in the boost-invariant case, this flow is called the "Bjorken flow". Its entropy and energy densities decrease with proper time. An expansion into further dimension introduces an additional transverse rapidity, and results in a cylindrically symmetric flow.