Test particle motion around a black hole dressed with a spherically symmetric stationary fluid

Abstract

We investigate the motion of a massive particle around a spherically symmetric black hole surrounded by a stationary and radial inflow of perfect fluid. The background spacetime is modelled as a spherically symmetric solution to the Einstein field equations, where the effect of the fluid on the geometry is treated as a perturbation on the Schwarzschild background. The equation of state for the fluid is assumed to follow the linear relationship $p=w\rho$, where $p$ is the pressure, $\rho$ is the energy density with $w$ being a constant. The stress-energy tensor is treated as a phenomenological model to capture deviations from the vacuum Einstein theory. We allow the parameter $w$ of the equation of state to take both positive and negative values accepting a broad range of scenarios including exotic ones. Specifically, we examine the cases $w=2/3$, $1/3$, $-3/4$ and $-4/3$. For $\rho \ge 0$, the former two cases satisfy all standard energy conditions while the case of $w=-3/4$ violates the strong energy condition and the case of $w=-4/3$ violates all standard energy conditions. By solving the geodesic equations, we visualize the time-like geodesics around the black hole, focusing on the apsis shift of the orbit. To gain further insight into the effects of accretion, we employ the method of osculating orbital elements. Additionally, we analyze the observable effects on spacetime by studying the redshift of the orbiting test particles as an example of possible observables. We show that the difference in the particle orbits due to the matter accretion may be probed by using the redshift observation of stars orbiting around the black hole.

16 pages, 22 figures

References in corpus (19)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Pulsar searches and timing with the SKA
• Sgr A${}^{\ast }$: a laboratory to measure the central black hole and cluster parameters
• Backreaction of accreting matter onto a black hole in the Eddington-Finkelstein coordinates
• Motion of spinning particles around black hole in a dark matter halo
• The correspondence between sonic points of ideal photon gas accretion and photon spheres
• Rotating accretion flows in $D$ dimensions: sonic points, critical points and photon spheres
• Photon surfaces in spherically, planar and hyperbolically symmetric spacetimes of D-dimensions: Sonic point/photon sphere correspondence
• Quintessence versus phantom dark energy: the arbitrating power of current and future observations
• Backreaction of Mass and Angular Momentum Accretion on Black Holes: General Formulation of the Metric Perturbations and Application to the Blandford-Znajek Process
• General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density
• The general static spherical perfect fluid solution with EoS parameter w=-1/5
• Another Approach to Test Gravity around a Black Hole
• Sonic Point and Photon Surface