The model of the black hole enclosed in dust. The flat space case

TL;DR

This paper develops an exact inhomogeneous cosmological model of a black hole embedded in a dust-filled universe with zero spatial curvature, analyzing particle motion and observable velocities.

Contribution

It presents a novel exact solution combining black hole and dust cosmology, including detailed analysis of particle dynamics and velocity profiles.

Findings

The model includes a Schwarzschild-like black hole within a dust universe.

Derived analytical expressions for particle velocities in the cosmological context.

Showed limitations in studying black hole horizons in comoving coordinates.

Abstract

In this work the model is constructed to describe the black hole enclosed in the dust cosmological background in case of zero spatial curvature. This model is based on our exact solution of the class of LTB inhomogeneous solutions. We considered the properties of the model and built the R-T-structure of the resulting space-time. It was shown that central region includes the Schwarzchild-like black hole. We derived the equations of motion of the test particle from the point of view of the observer comoving with cosmological expansion. We found analytical expressions for observable orbital and radial velocities of the particle and plotted the surface profile of the total velocity in this case. In comoving coordinate frame it is impossible to study the questions concerning the black hole horizon but one can observe the local motion of the particles influenced by the cosmological expansion.