The idea of black-hole lattices as models for the large-scale structure universe has been under scrutiny several decades, and some properties these systems have elucidated recently in context problem cosmological backreaction. complete, three-dimensional fully relativistic evolution system has, however, never tackled. We explicitly construct first solutions by numerically integrating Einstein's equation case an eight-black-hole lattice with topology S3.

Abstract We consider the question of determining optical drift effects in general relativity, i.e. rate change apparent position, redshift, Jacobi matrix, angular distance and luminosity a distant object as registered by an observer arbitrary spacetime. present fully relativistic covariant approach, which problem is reduced to hierarchy ODE's solved along line sight. The 4-velocities 4-accelerations emitter geometry spacetime sight constitute input data. build on standard geometric optics...

We present the numerical evolution of a family conformally-flat, infinite, expanding cubic black-hole lattices. solve for initial data using an initial-data prescription presented recently, along with new multigrid solver developed this purpose. then apply standard tools relativity to calculate time development dataset and derive quantities cosmological relevance, such as scaling proper lengths. Similarly case S3 lattices, we find that length remains close analytical solution...

The authors develop a new formalism to analyze observations in geometrical optics, and apply it cosmology. This provides uniform approach optical phenomena curved spacetimes and, as an application, the propose definition of parallax distance discuss its application cosmic tomography.

We discuss the continuum limit of initial data for a vacuum, closed cosmological model with black holes as only sources gravitational field. The we consider is an exact solution constraint equations and represents vacuum universe number placed on spatial slice S3 topology considered at moment its largest expansion when are momentary rest. explain how under what conditions Friedmann–Lemaître–Robertson–Walker (FLRW) metric arises contained in goes to infinity. also relation between effective...

The apparent properties of distant objects encode information about the way light they emit propagates to an observer, and therefore curvature underlying spacetime. Measuring relationship between redshift $z$ luminosity distance $D_{\rm L}$ a standard candle, for example, yields on Universe's matter content. In practice, however, in order decode this observer needs make assumption functional form L}(z)$ relation; other words, cosmological model be assumed. work, we use numerical-relativity...

Recently a multidimensional generalization of Isolated Horizon framework has been proposed by Lewandowski and Pawlowski (gr-qc/0410146). Therein the geometric description was easily generalized to higher dimensions structure constraints induced Einstein equations analyzed. In particular, version zeroth law black hole thermodynamics proved. this work we show how IH mechanics can be formulated in dimension--independent fashion derive first BH for arbitrary dimensional IH. We also propose...

The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss progress made study specific subclass cosmologies, black-hole lattice models. particular, illustrate techniques used construction these spacetimes, and examine their resulting physical properties. This includes large-scale dynamics, dressing mass due to interaction between individual black...

A new definition of coarse-grained quantities describing the dust flow in general relativity is proposed. It assigns expansion, shear and vorticity to finite-size comoving domains fluid a covariant, coordinate-independent manner. The are all quasi-local functionals, depending only on geometry boundary considered domain. They can be thought as relativistic generalizations simple volume averages local flat space. procedure based isometric embedding theorem for S2 surfaces thus requires domain...

When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources gravitational field, such as neutron stars or black holes. In this paper I discuss another, less obvious situation, which large relativistic may arise due to a complicated, multiscale structure distribution. present an exact solution with inhomogeneous energy density distribution form hierarchy nested voids and overdensities various sizes, extending...

We discuss the possibility of a dimensional reduction Einstein equations in S3 black-hole lattices. It was reported previous literature that evolution spaces containing curves local, discrete rotational and reflection Symmetry (LDRRS) can be carried out via system ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate this is not case, we show analytically due to presence tensorial quantity which suppressed by symmetry. calculate term analytically, verify...

Astronomical observations reveal hierarchical structures in the Universe, from galaxies, groups of clusters and superclusters, to filaments voids. On largest scales it seems that some kind statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous isotropic solutions Einstein equations, evolution universe is approximated by Friedmann equations. In parallel standard cosmology, field inhomogeneous cosmology backreaction being developed....

In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift, and the proper motion luminous source, in addition to variations redshift viewing angle. These are valid general relativity for any spacetime, they potential interest astrometry precise cosmology. They generalize well-known Etherington’s reciprocity relation angular diameter distance luminosity distance. Similar relation, hold independently spacetime metric,...

The goal of this paper is to express the Bach tensor a four dimensional conformal geometry an arbitrary signature by Cartan normal (CNC) connection. We show that can be identified with Yang-Mills current It follows from result whose CNC connection reducible in appropriate way has degenerate tensor. As example we study case which admits twisting covariantly constant twistor field. This class geometries property known as given Fefferman metric tensors. use our calculate and it proportional...

We discuss a new formalism for light propagation which can be used within the regime of validity geometric optics, but with no limitation on scales interest: from inside Galaxy to ultralarge cosmology. One our main results is that this framework it possible calculate all relevant observables (image magnification, parallax, position drift or proper motion) by simply differentiating photon trajectory respect initial data. then focus observable, we name distance slip: defined as relative...

We present a new method of measuring the mass density along line sight, based on precise measurements variations times arrival (TOAs) electromagnetic signals propagating between two distant regions spacetime. The TOA are measured number slightly displaced pairs points from regions. These due to nonrelativistic geometric effects (R\o{}mer delays and finite distance effects) as well gravitational in light propagation (gravitational ray bending Shapiro delays). show that sufficiently broad...

A framework is developed in which one can write down the constraint equations on a three-dimensional hypersurface of arbitrary signature. It then applied to isolated and dynamical horizons. The derived be used extract physically relevant quantities describing horizon irrespective whether it (null) or at given instant time. Furthermore, small perturbation horizons are considered, finally family an axially symmetric exact solution presented.

A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop BiGONLight Mathematica package, uniquely designed to apply this framework compute optical observables Numerical Relativity. Our package can be used on a wide range scales and redshifts accepts numerical as well analytical input spacetime metric. In paper we focus two cosmological observables, redshift angular diameter distance, specializing our analysis wall...

A new definition of quasi-local angular momentum non-axisymmetric marginally outer trapped surfaces is proposed. It based on conformal decomposition the two-dimensional metric and action group symmetries. The completely general agrees with standard one in axisymmetric surfaces.

Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve reasonable distribution. We argue that this field generated not only galaxy matter, but thin, singular disk as well. The should therefore be considered unphysical.

We present a numerical method for solving Weyl's embedding problem which consists of finding global isometric positively curved and positive-definite spherical 2-metric into the Euclidean three space. The is based on construction introduced by Weingarten was used in Nirenberg's proof conjecture. target results as endpoint an flow R^3 beginning at unit sphere's embedding. employ spectral methods to handle functions surface solve various (non)-linear elliptic PDEs. Possible applications 3+1...

The Einstein-Vlasov equations govern Einstein spacetimes filled with matter which interacts only via gravitation. matter, described by a distribution function on phase space, evolves under the collisionless Boltzmann equation, corresponding to free geodesic motion of particles, while source gravitational field is given stress-energy tensor defined in terms momenta function. As no variational derivation system appears exist literature, we here set out fill this gap. In our approach treat as...

We present a method to compute exact expressions for optical observables static spherically symmetric spacetimes in the framework of bilocal geodesic operator formalism. The are obtained by solving linear deviation equations null geodesics, using spacetime symmetries and associated conserved quantities. solve two different ways: varying geodesics with respect their initial data directly integrating equation deviation. results very general can be applied variety models configurations emitter...

In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion luminous source in addition to variations redshift viewing angle. These are valid general relativity for any spacetime they potential interest astrometry precise cosmology. They generalize well-known Etherington's reciprocity relation angular diameter distance luminosity distance. Similar relation, hold independently metric, positions motions...