Black-Hole Universe
Irina Galstyan
Abstract
In this contribution, we have constructed new analytical solutions for initial data of the Einstein equations. Such solutions are valuable for gaining a better understanding of prob- lems involving strong gravitational and/or electromagnetic interactions in general relativity.
In this process we have examined an inhomogeneous cosmological model consisting a lattice of regularly arranged, charged black holes with initial data corresponding to the maximum expansion of a cosmological solution. We have also refined the method in such a way that the values of the mass and charge of the sources can be prescribed beforehand subject to certain constraints dictated by the field equations.
Akademisk avhandling f¨ or avl¨ aggande av licentiatexamen vid Stockholms Universitet, Fysikum
December, 2017
Discussion
We studied a physically interesting case of the initial data for a vacuum 3–sphere with black holes. This family of time–symmetric initial data is a counterpart of a closed FLRW model at the moment of its largest expansion in which the homogeneous matter distribution has been re- placed with an arbitrary number of Reissner–Nordstr¨om-like black holes located on a 3–sphere.
This type of initial data for a Schwarszchild–like black holes has been studied extensively in the special case of regular black hole lattices, i.e., arrangements of a fixed number of black holes of equal mass placed in such a way that the resulting initial data has the biggest possible dis- crete group of isometries [48], [67], [6], [25]. We applied this initial data to an exact, analytic inhomogeneous cosmological models containing three, four and eight discrete masses regularly arranged in topological 3–sphere, focusing our attention to the masses, charges and interaction energies by employing exact methods and considering instantaneously static hypersurfaces at the moment of maximum expansion. First, we found that the total net charge is zero for existing solutions. Then we analyzed example models and employed that black holes exist in antipodal pairs. This gives a simple way of obtaining the uncharged lattices discussed in [25].
We have studied time–symmetric initial data for discrete and continuous models and con- structed geometries with cosmological regions connected by Einstein–Rosen bridges. The next step would be to study full evolution of these models. Although, we considered masses that are regularly arranged on the 3–sphere, we believe the formalism we applied allows more compli- cated distributions. In the next, we have discussed and defined different concepts of mass in our models, the “proper mass” and the “bare mass” for each of the black holes. Then we have employed a definition of interaction energy between group of masses in a cosmological model and investigated gravitational consequences of interaction energy. We found that if the group is small compared to the cosmological region scale, the total gravitational mass of the group encodes information about the sum total of the proper mass of each source plus the sum of the pairwise interaction energies between sources.
Finally, the results we obtained are close to the solutions of Lindquist and Wheeler that use a gravitational analogue of the Wigner–Seitz construction [48]. Generally, we believe the frame- work of our constructed models provides a new laboratory for testing ideas about inhomogenety, averaging and backreaction in cosmology. In the presence of electric charges, which is the core of this thesis, the formalism employed here has very recently been considered by [12].
Our work can be regarded as the first step of the study of the evolution of an inhomogeneous model for the Universe, where reflection symmetries play a fundamental role. Less symmetric configurations should then be studied with application to the structure formation problem in cosmology.
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