An exact solution of the Lemaître--Tolman--Bondi class is investigated as a possible model of the Schwarzschild-like black hole embedded in a non-static dust-filled universe for the three types of spatial curvature. The solution is obtained in comoving coordinates by means of the mass function method. It is shown that the central part of space contains a Schwarzschild-like black hole. The R-T-structure of the resulting spacetime is built. It is shown that the solution includes both the Schwarzschild and Friedmann solutions as its natural limits. The geodesic equations for test particles are analyzed. The particle observable velocities are found. The trajectories of the test particles are built from the point of view of both comoving and distant observers. For the distant observer, the results coincide with the Schwarzschild picture within a second-order accuracy near the symmetry center.
We study linear perturbations about a dust filled Bianchi Type I model with the vorticity set to zero. In comparison to linear perturbations about FLRW models, modes of perturbations about Bianchi type I models are coupled. We find that the tensor that represents the background shear needs to be degenerate in order for the scalar-mode perturbations to decouple from the rest of the flow.
We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime close to the singularity for which we provide heuristic considerations supported by numerical simulations. The present paper is an extension of our earlier publication [1].
In this paper, we have investigated late time acceleration for a spatially flat dust filled Universe in Brans-Dicke theory in the presence of a positive cosmological constant $Λ$ . Expressions for Hubble's constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with the observed values of the the latest 287 high red shift ($ .3 \leq z \leq 1.4$ ) SN Ia supernova data's taken from Union 2.1 compilation to estimate the present values of the matter and dark energy parameters $(Ω_{m})_0$ and $(Ω_Λ)_0$. We have also estimated the p…
We examine the implementation of Buchert's and Green & Wald's averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert's averaging scheme gives a faithful way of interpreting the large-scale expansion of space, and explicit terms that precisely quantify deviations from the behaviour expected from the Friedmann equations of homogeneous and isotropic cosmological models. The Green & Wald formalism, on the other hand, does not appear to yield any information about the large-scale properties of a…
Recently Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] formulated a novel Einstein-Gauss-Bonnet gravity in which the Gauss-Bonnet coupling has been rescaled as $α/(D-4)$ and the $4D$ theory is defined as the limit $D \rightarrow 4$, which preserves the number degrees of freedom thereby free from the Ostrogradsky instability. We present exact spherically symmetric nonstatic null dust solutions in the novel 4D Einstein-Gauss-Bonnet gravity that bypasses the Lovelock theorem. Our solution represents radiating black holes and regains, in the limit $α\rightarrow 0$, the famous Vaidya black h…
It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is "exotic"---i.e., violates a number of energy conditions. For this reason, it is impossible to construct {static} wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman's solution describes the collapsing dust ball; the inner space--…
We show that the mass function method makes it much easier to obtain the exact solutions of Einstein equations. The known solutions for empty space and for the universe filled with dust-like matter are considered from the point of view of the method and new exact solutions are obtained. Generalized solutions for the Schwarzschild type black holes are considered. It is shown that such black holes always contain non-baryonic matter. New exact solution for the black hole embedded into dust matter cosmological background is obtained.
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant. Schwarzschild, Friedmann and Einstein-de Sitter solutions (as well as all of their fusion with each other) are special cases of the found general solution. A method of generating an infinite number of Tolman's like solutions has been found. Exact solutions has been found for the spherically symmetric gravitational field of perfect dust clouds in the expanding Universe f…
We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions $f(R)$, $F(R)$ and $τ_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic ($f >0$), parabolic ($f=0$) and elliptic ($f < 0$) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the …
We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.
We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150-370 Mpc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation. We use the mechanical approach. Therefore, the peculiar velocities of the inhomogeneities as well as the fluctuations of the other perfect fluids can be considered nonrelativistic. Such fluids are said to be coupled because they are concentrated around the inhomogeneities. We investigate the conditions under which the physical Galileon field, i.e. compatible wi…
We construct exact initial data for closed cosmological models filled with regularly arranged black holes in the presence of $Λ$. The intrinsic geometry of the 3-dimensional space described by this data is a sum of simple closed-form expressions, while the extrinsic curvature is just proportional to $Λ$. We determine the mass of each of the black holes in this space by performing a limiting procedure around the location of each of the black holes, and then compare the result to an appropriate slice through the Schwarzschild-de Sitter spacetime. The consequences of the inhomogeneity of this mod…
We show that the physical conditions which induce the Thakurta metric, recently studied by Bœhm {\it et al.} in the context of time-dependent black hole masses, correspond to a single accreting black hole in the entire Universe filled with isotropic non-interacting dust. In such a case, the physics of black hole accretion is not local but tied to the properties of the whole Universe. We show that radiation, primordial black holes or particle dark matter cannot produce the specific energy flux required for supporting the mass growth of Thakurta black holes. In particular, this solution does not…
The evolution of the universe is studied in exactly solvable dynamical quantum model with the Robertson-Walker metric. It is shown that the equation of motion which describes the expansion or contraction of the universe can be represented in the form of the law of conservation of zero total energy for a particle with arbitrary mass being an analogue of the universe. The analogue particle moves in the potential well under the action of the internal force produced by the curvature of space, matter, and pressures of classical and quantum gravitational sources. At a definite stage of the evolution…
