Black hole universe with a cosmological constant

We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light performed by a sample of observers slightly displaced with respect to each other and moving with different 4-velocities and 4-accelerations. In our approach, all results of observations can be expressed as functions of the kinematic variables, describing the motions of the observers and the emitting bodies with respect to their local inertial frames, and four linear bilocal geodesic operators, describing the influence of the spacetime geometry on light propagation. The operators are functionals of the curvature tensor along the line of sight. The results are based on the assumption that the regions of emissions and observations are sufficiently small so that the spacetime curvature effects are negligible within each of them, although they are significant for the light propagation between them. The new formulation provides a uniform approach to optical phenomena in curved spacetimes and, as an application, we discuss the problem of a fully relativistic definition of the parallax and position drifts (or proper motions). We then use the results to construct combinations of observables which are completely insensitive to the motion of both the observer and the emitter. These combinations by construction probe the spacetime geometry between the observation and emission regions and in our formalism we may express them as functionals of the Riemann tensor along the line of sight. For short distances one of these combinations depends only on the matter content along the line of sight. This opens up the possibility to measure the matter content of a spacetime in a tomographylike manner irrespective of the motions of the emitter and the observer.Even if A enters the differential equation linearly, the general solution contains a nonlinear dependence.

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“…δ O r A corresponds to the position drift measured with respect to inertially dragged fixed directions. Combining (74) and (73) yields…”

Section: Position Drift Formulamentioning

confidence: 99%

Geometric optics in general relativity using bilocal operators

2019

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“…In order to avoid a highly distorted time slices for the calculation of the surface area, similarly to Refs. [11,16], we calculate the surface area S on the constant proper time slice for the set of observers fixed at grid points. Thus, the area S is given as a function of the proper time τ .…”

Section: Time Evolutionmentioning

confidence: 99%

Gravitational collapse of a massless scalar field in a periodic box

Yoo

Ikeda

Okawa

2019

Class. Quantum Grav.

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Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. We construct the initial data for a Gaussian-like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. It is shown that the expansion law in a late time approaches that of the radiation dominated universe and the matter dominated universe for the small and large initial amplitude cases, respectively. For the large initial amplitude case, the horizon is initially a past outer trapping horizon, whose area decreases with time, and after a certain period of time, it turns to a future outer trapping horizon with the increasing area.

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“…Numerical simulations of spacetime dynamics in cosmological settings have been actively performed in recent years. One main motivation to simulate the cosmological nonlinear dynamics is to quantify the effect of the non-linear small scale inhomogeneity on the global expansion law of the universe [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Another significant motivation comes from primordial black holes [17,18].…”

Section: Introductionmentioning

confidence: 99%