arXiv subjects

Andrzej Krasiński

Publications and source records attributed to Andrzej Krasiński.

29 records · Page 2Linked to original sources

arXiv2012

Apparent horizons in the quasi-spherical Szekeres models

The notion of an apparent horizon (AH) in a collapsing object can be carried over from the Lema\^ıtre -- Tolman (L--T) to the quasispherical Szekeres models in three ways: 1. Literally by the definition -- the AH is the boundary of the region, in which every bundle of null geodesics has negative expansion scalar. 2. As the locus, at which null lines that are as nearly radial as possible are turned toward decreasing areal radius $R$. These lines are in general nongeodesic. The name "absolute apparent horizon" (AAH) is proposed for this locus. 3. As the boundary of a region, where null \textit{geodesics} are turned toward decreasing $R$. The name "light collapse region" (LCR) is proposed for this region (which is 3-dimensional in every space of constant $t$); its boundary coincides with the AAH. The AH and AAH coincide in the L--T models. In the quasispherical Szekeres models, the AH is different from (but not disjoint with) the AAH. Properties of the AAH and LCR are investigated, and the relations between the AAH and the AH are illustrated with diagrams using an explicit example of a Szekeres metric. It turns out that an observer who is already within the AH is, for some time, not yet within the AAH. Nevertheless, no light signal can be sent through the AH from the inside. The analogue of the AAH for massive particles is also considered.

gr-qc↗

arXiv2012

Geometry and topology of the quasi-plane Szekeres model

This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasi-hyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the $t =$ const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Interpretation of the mass function in the quasi-plane model.

gr-qc↗

arXiv2012

Formation of Gyrs old black holes in the center of galaxies within the Lema\^ıtre--Tolman model

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema\^ıtre--Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass $3.2\cdot 10^{9}M_{\odot}$. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the $Λ$CDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the $Ω_m$ and $Ω_Λ$ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr.

gr-qc↗

arXiv2012

The charged dust solution of Ruban -- matching to Reissner--Nordström and shell crossings

The maximally extended Reissner--Nordström (RN) manifold with $e^2 < m^2$ begs for attaching a material source to it that would preserve the infinite chain of asymptotically flat regions and evolve through the wormhole between the RN singularities. So far, the attempts were discouraging. Here we try one more possible source -- a solution found by Ruban in 1972 that is a charged generalisation of an inhomogeneous Kantowski--Sachs-type dust solution. It can be matched to the RN solution, and the matching surface must stay all the time between the two RN event horizons. However, shell crossings do not allow even half a cycle of oscillation between the maximal and the minimal size.

gr-qc↗

arXiv2011

Cosmological models and misunderstandings about them

Advantages of inhomogeneous cosmological models that are exact solutions of Einstein's equations over linearised perturbations of homogeneous models are presented. Examples of effects that can be described in the inhomogeneous ones are given: the non-repeatable light paths, the observed anisotropies in the cosmic microwave background, the redshift drift and the maximum diameter distance. Criticisms of inhomogeneous models that are based on misunderstandings or fallacious reasonings are pointed out and corrected; these include the "weak singularity", the positivity of deceleration "theorem", the "pathology" of redshift behaviour at the "critical point" and the alleged necessity of the bang time to be constant.

gr-qc↗

arXiv2011

Inhomogeneous cosmological models: exact solutions and their applications

Recently, inhomogeneous generalisations of the Friedmann-Lemaitre-Robertson-Walker cosmological models have gained interest in the astrophysical community and are more often employed to study cosmological phenomena. However, in many papers the inhomogeneous cosmological models are treated as an alternative to the FLRW models. In fact, they are not an alternative, but an exact perturbation of the latter, and are gradually becoming a necessity in modern cosmology. The assumption of homogeneity is just a first approximation introduced to simplify equations. So far this assumption is commonly believed to have worked well, but future and more precise observations will not be properly analysed unless inhomogeneities are taken into account. This paper reviews recent developments in the field and shows the importance of an inhomogeneous framework in the analysis of cosmological observations.

astro-ph.CO↗

arXiv2011

Repeatable light paths in the shearfree normal cosmological models

Conditions for the existence of repeatable light paths (RLPs) in the shearfree normal cosmological models are investigated. It is found that in the conformally nonflat models the only RLPs are radial null geodesics (in the spherical case) and their analogues in the plane- and hyperbolically symmetric cases. In the conformally flat Stephani models, there exist special spherically-, plane- and hyperbolically symmetric subcases, in which all null geodesics are RLPs. They are slightly more general than the Friedmann -- Lema\^ıtre -- Robertson -- Walker (FLRW) models of the corresponding symmetries: their curvature index function $k(t)$ and the scale factor $R(t)$ are expressed through a single function of time. In addition to that, there exist special cases of the Stephani solution in which some of the null geodesics are RLPs. All these special cases are identified.

gr-qc↗

arXiv2011

Redshift propagation equations in the $β' \neq 0$ Szekeres models

The set of differential equations obeyed by the redshift in the general $β' \neq 0$ Szekeres spacetimes is derived. Transversal components of the ray's momentum have to be taken into account, which leads to a set of 3 coupled differential equations. It is shown that in a general Szekeres model, and in a general Lema\^ıtre -- Tolman (L--T) model, generic light rays do not have repeatable paths (RLPs): two rays sent from the same source at different times to the same observer pass through different sequences of intermediate matter particles. The only spacetimes in the Szekeres class in which {\em all} rays are RLPs are the Friedmann models. Among the proper Szekeres models, RLPs exist only in the axially symmetric subcases, and in each one the RLPs are the null geodesics that intersect each $t =$ constant space on the symmetry axis. In the special models with a 3-dimensional symmetry group (L--T among them), the only RLPs are radial geodesics. This shows that RLPs are very special and in the real Universe should not exist. We present several numerical examples which suggest that the rate of change of positions of objects in the sky, for the studied configuration, is $10^{-6} - 10^{-7}$ arc sec per year. With the current accuracy of direction measurement, this drift would become observable after approx. 10 years of monitoring. More precise future observations will be able, in principle, to detect this effect, but there are basic problems with determining the reference direction that does not change.

gr-qc↗

arXiv2010

A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model

Lemaître - Tolman (L--T) toy models with a central observer have been used to study the effect of large scale inhomogeneities on the SN Ia dimming. Claims that a giant void is mandatory to explain away dark energy in this framework are currently dominating. Our aim is to show that L-T models exist that reproduce a few features of the $Λ$CDM model, but do not contain the giant cosmic void. We propose to use two sets of data - the angular diameter distance together with the redshift-space mass-density and the angular diameter distance together with the expansion rate - both defined on the past null cone as functions of the redshift. We assume that these functions are of the same form as in the $Λ$CDM model. Using the Mustapha-Hellaby-Ellis algorithm, we numerically transform these initial data into the usual two L-T arbitrary functions and solve the evolution equation to calculate the mass distribution in spacetime. For both models, we find that the current density profile does not exhibit a giant void, but rather a giant hump. However, this hump is not directly observable, since it is in a spacelike relation to a present observer. The alleged existence of the giant void was a consequence of the L-T models used earlier because their generality was limited a priori by needless simplifying assumptions, like, for example, the bang-time function being constant. Instead, one can feed any mass distribution or expansion rate history on the past light cone as initial data to the L-T evolution equation. When a fully general L-T metric is used, the giant void is not implied.

astro-ph.CO↗

arXiv2007

Can a charged dust ball be sent through the Reissner--Nordström wormhole?

In a previous paper we formulated a set of necessary conditions for the spherically symmetric weakly charged dust to avoid Big Bang/Big Crunch, shell crossing and permanent central singularities. However, we did not discuss the properties of the energy density, some of which are surprising and seem not to have been known up to now. A singularity of infinite energy density does exist -- it is a point singularity situated on the world line of the center of symmetry. The condition that no mass shell collapses to $R = 0$ if it had $R > 0$ initially thus turns out to be still insufficient for avoiding a singularity. Moreover, at the singularity the energy density $ε$ is direction-dependent: $ε\to - \infty$ when we approach the singular point along a $t =$ const hypersurface and $ε\to + \infty$ when we approach that point along the center of symmetry. The appearance of negative-energy-density regions turns out to be inevitable. We discuss various aspects of this property of our configuration. We also show that a permanently pulsating configuration, with the period of pulsation independent of mass, is possible only if there exists a permanent central singularity.

gr-qc↗

arXiv1998

Physics and cosmology in an inhomogeneous Universe

Examples are presented of applications of the Lemaître - Tolman model to problems of astrophysics and gravitation theory. They are: 1. Inferring the spatial distribution of matter by interpretation of observations; 2. Interaction of inhomogeneities in matter distribution with the CMB radiation; 3. Evolution of voids; 4. Singularities; 5. Influence of electromagnetic field on gravitational collapse. This review is meant to demonstrate that the theory is already well-prepared to meet the challenges posed by an inhomogeneous Universe.

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