Tolman-Bondi Solution Research Articles

Growth rate of spherical voids with non-comoving dark matter and baryons

We present numerical solutions to Einstein’s equations describing large spherical cosmic voids constituted by two components: dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous background compatible with the ΛCDM concordance model. We compute numerically the evolution of such configurations in the dark matter frame, with a hypothetical homogeneous distribution of baryons, but respecting the values dictated by the concordance model for the average baryon-to-dark matter density ratio. We reproduce the well-known formation of overdensities at the edge of the void and recover the Lemaître–Tolman–Bondi solutions in the comoving limit of our simulations. We compute the average growth factor of matter fluctuations and find that it departs significantly from the linear perturbative prescription even in the comoving case, where the non-linearity of inhomogeneities has an impact.

Possible Wormholes in a Friedmann Universe

We study the properties of evolving wormholes able to exist in a closed Friedmann dust-filled universe and described by a particular branch of the well-known Lemaître–Tolman–Bondi solution to the Einstein equations and its generalization with a nonzero cosmological constant and an electromagnetic field. Most of the results are obtained with pure dust solutions. It is shown, in particular, that the lifetime of wormhole throats is much shorter than that of the whole wormhole region in the universe (which coincides with the lifetime of the universe as a whole), and that the density of matter near the boundary of the wormhole region is a few times smaller than the mean density of matter in the universe. Explicit examples of wormhole solutions and the corresponding numerical estimates are presented. The traversability of the wormhole under study is shown by a numerical analysis of radial null geodesics.

Some unusual wormholes in general relativity.

In this short review, we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaître-Tolman-Bondi solution. They connect two copies of a closed Friedmann world filled with dust, or two otherwise distant parts of the same Friedmann world. Third, these are wormholes obtained in six-dimensional GR, whose one entrance is located in 'our' asymptotically flat world with very small extra dimensions while the other 'end' belongs to a universe with large extra dimensions and therefore different physical properties. The possible observable features of such wormholes are briefly discussed. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

A study of important solutions in Chern–Simons modified gravity

In this manuscript, we have presented the compatible solutions under the framework of dynamical and non-dynamical Chern–Simons modified gravity. By taking an open choice of external field as a function of angular parameter $$\theta $$ , we obtained Godel-type solutions of non-dynamical Chern–Simons modified gravity. It is mentioned that a vacuum Godel-type solution exists in this theory. Non-static spherical symmetric solutions are also described for dynamical Chern–Simons modified gravity by considering external field as a function of radial parameter r. Later, results are similar to those of well-known Tolman–Bondi solutions found in the context of general relativity. It is observed that in case of $$\varLambda \rightarrow \kappa p_{0}$$ both parameters A(t, r) and B(t, r) turned to be undefined.

Pressure in Lemaître–Tolman–Bondi solutions and cosmologies

Lemaître–Tolman–Bondi solutions have traditionally been confined to systems with no pressure in which the gravity is due to massive dust, but the solutions are little changed in form if, as in cosmology, the pressure is uniform in space at each comoving time. This allows the equations of cosmology to be deduced in a manner that more closely resembles classical mechanics. It also gives some inhomogeneous solutions with growing condensations and black holes. We give criteria by which the sizes of different closed models of the Universe can be compared and discuss conditions for self-closure of inhomogeneous cosmologies with a -term.

Generalization of Tolman–Bondi solution

Generalization of Tolman–Bondi solution

An intrinsic characterization of spherically symmetric spacetimes

We give the necessary and sufficient (local) conditions for a metric tensor to be a nonconformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct application we obtain the ideal labeling of the Schwarzschild, Reissner–Nordström and Lemaître–Tolman–Bondi solutions.

Lemaître–Tolman–Bondi solutions in the Newtonian gauge: from strong to weakfields

Lemaître–Tolman–Bondi (LTB) solutions are used frequently to describe the collapse orexpansion of spherically symmetric inhomogeneous mass distributions in the Universe.These exact solutions are obtained in the synchronous gauge where non-linear dynamics(with respect to the Friedmann–Lemaître–Roberston–Walker (FLRW) background) inducelarge deviations from the FLRW metric. In this paper we show explicitly that this is agauge artefact (for realistic sub-horizon inhomogeneities). We write down the non-lineargauge transformation from synchronous to Newtonian gauge for a general LTB solutionusing the fact that the peculiar velocities are small. In the latter gauge we recoverthe solution in the form of a weakly perturbed FLRW metric that is assumedin standard cosmology. Furthermore we show how to obtain the LTB solutionsdirectly in Newtonian gauge and illustrate how the Newtonian approximationremains valid in the non-linear regime where cosmological perturbation theorybreaks down. Finally we discuss the implications of our results for the backreactionscenario.

Inhomogeneity-induced cosmic acceleration in a dust universe

It is the common consensus that the expansion of a universe always slows down if the gravity provided by the energy sources therein is attractive and accordingly one needs to invoke dark energy as a source of anti-gravity for understanding the cosmic acceleration. To examine this point we find counterexamples for a spherically symmetric dust fluid described by the Lemaître–Tolman–Bondi solution without singularity. Thus, the validity of this naive consensus is indeed doubtful and the effects of inhomogeneities should be restudied. These counter-intuitive examples open a new perspective on the understanding of the evolution of our universe.

Non-linear structure formation and ‘apparent’ acceleration: an investigation

We present an analytically tractable non-linear model of structure formation in a Universewith only dust. The model is a Lemaître–Tolman–Bondi solution (of general relativity) andstructures are shells of different density. We show that the luminosity distance–redshiftrelation has significant corrections at low redshift when the density contrast becomesnon-linear. A minimal effect is a correction in apparent magnitudes of order . We discuss different possibilities that could further enhance this effect and mimic darkenergy.

Spacetimes containing slowly evolving horizons

Slowly evolving horizons are trapping horizons that are "almost" isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the associated mass scales, they also suggest that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes.

Spherical universes with anisotropic pressure

Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, τ, experienced by the dust particles. The general solution contains four arbitrary functions of R—M(R), L(R), E(R) and τ0(R). The solution is described by two quadratures which are, in general, elliptic integrals. It provides a generalization of the Lemaǐtre–Tolman–Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to the Einstein clusters and the significance for gravitational collapse are also discussed.

Evidence for dark matter on different scales from the KLUN galaxy sample

The KLUN (Kinematics of the Local UNiverse) sample of 6600 spiral galaxies is used in studying dark matter on different scales: •The Morphological Type dependence of the zero-point of the Tully-Fisher relation indicates mass to light ratio M/L ≈ 9 − 16 on galactic scales.•Preliminary results from a study of selection effects influencing double galaxies give a larger value M/L ≈ 30 − 50.•Study of the Perseus-Pisces supercluster, using Malmquist bias corrected TF distances and Tolman-Bondi solutions indicates M/L ≈ 200 − 600 for large clusters. Similar results were obtained in our previous work on Virgo galaxies.•Application of a modified version of Sandage-Tammann-Hardy test of the linearity of Hubble law inside the observed hierarchical (fractal) galaxy distribution up to 200 Mpc suggests that either Ω0 is very small (0.01) or the major part of the matter is uniformly distributed dark matter.

On the microwave background anisotropy produced by big voids in open universes

The Tolman-Bondi solution of the Einstein equations is used in order to model the time evolution of the void observed in Bo\"otes. The present density contrast of the central region ($\sim -0.75$) and its radius ($\sim 30h^{-1} \ Mpc$) are fixed, while the density parameter of the Universe, the amplitude of the density contrast inside the void wall, the width of this wall and the distance from the void centre to the Local Group are appropriately varied. The microwave background anisotropy produced by Bo\"otes-like voids is estimated for a significant set of locations. All the voids are placed far from the last scattering surface. It is shown that the anisotropy generated by these voids strongly depends on the density parameter, the wall structure and the void location. The Doppler dipole and quadrupole are subtracted and the residual anisotropy is calculated. In the case of some isolated Bo\"otes-like voids placed at redshifts between 1 and 10 in an open universe with density parameter $\Omega_{0}=0.2$, the residual anisotropy appears to be a few times $10^{-6}$ on scales of a few degrees. This anisotropy is about one order of magnitude greater than previous estimates corresponding to other cases. The anisotropy produced by a distribution of voids is qualitatively studied in the light of this result. Comparisons with previous estimates are discussed.

Inhomogeneous space-time; Its causal structure and possible fractal behaviour

Exact solutions are obtained for a higher-dimensional inhomogeneous space-time with dust as matter content. When the space-time becomes four, our model reduces to the well-known Tolman-Bondi solution. Shell-focussing singularity generally associated with this type of inhomogeneous collapse is discussed. It is observed that naked singularity appears if the degree of inhomogeneity exceeds a critical value, which is slightly larger than the corresponding value in the 4D case. Thus we obtain yet another counterexample of the cosmic-censorship conjecture. With suitable adjustment of the arbitrary functions of integration our space-time can be reduced to the zero-curvature Friedmann-like dust solution. It is further observed that our Friedmann-like solution does not appear to exhibit any fractal behaviour, which agrees with a similar conclusion made by Ribeiro in a recent communication.

On the microwave background anisotropy produced by Great Attractor-like structures

We model the effect on the cosmic microwave background of Great Attractor-like structures located at various distances from us. These structures are described by using the Tolman-Bondi solution of the Einstein equations. Two values of the density parameter, Omega <SUB>0</SUB> = 0.2 and Omega<SUB>0</SUB> = 1, are considered. Physical initial profiles of the energy density and the peculiar velocity lead to both compensated and uncompensated models. Nonlinear gauge-invariant computations give the angular distribution of the microwave background temperature. Angular sizes, amplitudes, and angular temperature profiles of various separable contributions to the total anisotropy are estimated and compared among them. These contributions are produced by the gravitational field, the peculiar velocities of the observer and the emitter, and the temperature fluctuations of the last scattering surface induced by Great Attractor-like structures. Compatibility with observational evidence is analyzed. It is proved that the greatest anisotropies are produced by Great Attractor-like objects located near the last scattering surface. Suitable angular scales for the future detection of these anisotropies are proposed. For fixed proportions of baryon and dark matter, results strongly depend on the value of the density parameter Omega<SUB>0</SUB>; the smallest anisotropies correspond to Omega<SUB>0</SUB> = 1.

The imprints of the Great Attractor and the Virgo cluster on the microwave background

A fully non-linear model based on the Tolman-Bondi solution of the Einstein equations is used to describe the Great Attractor and the Virgo cluster. The background is a Friedmann-Robertson-Walker universe, and the inhomogeneity develops from physically motivated initial profiles of the energy density and the peculiar velocity. Accurate numerical integrations of the field equations of the null geodesics are carried out, and thus the angular temperature distribution of the microwave background produced by the chosen overdensities is found. The observer is located in the Local Group. The quadrupole Q produced by each overdensity is computed and divided into two parts: the relativistic Doppler quadrupole Q D and the reduced quadrupole Q R = Q − Q D

General-relativistic approach to the nonlinear evolution of collisionless matter.

A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian form at different times, can be traced back to the Eulerian picture by solving supplementary first-order differential equations for the relative position vectors of neighboring fluid elements. Similarly to the Zel'dovich approximation, in our approach the evolution of each fluid element is completely determined by the local initial conditions and can be independently followed up to the time when it enters a multistream region. Unlike the Zel'dovich approximation, however, our approach is correct also in three dimensions (except for the possible role of gravitational waves). The accuracy of our numerical procedure is tested by integrating the nonlinear evolution of a spherical perturbation in an otherwise spatially flat Friedmann-Robertson-Walker universe and comparing the results with the exact Tolman-Bondi solution for the same initial profile. An exact solution for the planar symmetric case is also given, which turns out to be locally identical to the Zel'dovich solution.

On the microwave background anisotropies produced by nonlinear voids

view Abstract Citations (36) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Microwave Background Anisotropies Produced by Nonlinear Voids Arnau, J. V. ; Fullana, M. J. ; Monreal, L. ; Saez, D. Abstract The Tolman-Bondi solution of the Einstein equations is used to study the microwave background anisotropy produced by a pressureless spherical cosmological inhomogeneity. Our method improves on previous ones because it does not involve any approximating condition and it allows us to assume the following: (1) a general Friedmann-Robertson-Walker background, (2) an arbitrary relative location of the observer and the inhomogeneity, (3) either an overdense or an underdense inhomogeneity with arbitrary size, (4) an arbitrary initial energy density profile, and (5) an arbitrary amplitude of the density contrast. This general method is applied to compute the anisotropy produced by some nonlinear uncompensated density distributions, which mimic nearby voids. Publication: The Astrophysical Journal Pub Date: January 1993 DOI: 10.1086/172139 Bibcode: 1993ApJ...402..359A Keywords: Anisotropy; Cosmology; Microwaves; Relic Radiation; Universe; Astronomical Models; Computational Astrophysics; Inhomogeneity; Astrophysics; COSMOLOGY: COSMIC MICROWAVE BACKGROUND; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY full text sources ADS |

The general solution for spherical charged dust

The general solution of the Maxwell-Einstein equations for spherical charged dust flow is presented explicitly. The solution is first derived, by a simple geometrical construction, in mass-area (m, r) coordinates, and then transformed to mass-proper time (m, tau ) coordinates. This solution depends on three arbitrary functions of the mass coordinate. This is just what one would expect because, in general, three arbitrary functions are required to determine the evolution of charged dust spheres, namely the initial distributions of the velocity, matter density and charge density. The generalisation to the case of non-zero cosmological constant is also presented. In the special case of neutral dust (and without a cosmological constant) the charged-dust solution reduces to the Tolman-Bondi solution. Several general properties are discussed, as well as two special subclasses-the marginally bound case and the self-similar case.