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Register a new userAre singularities the limits of cosmology?
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Added by
Mariusz P. Dabrowski
Publication date
2014
fields
Physics
and research's language is
English
Authors
Mariusz P. Dabrowski
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We refer to the classic definition of a singularity in Einsteins general relativity (based on geodesic incompletness) as well as to some other criteria to evaluate the nature of singularities in cosmology. We review what different (non-Big-Bang) types of singularities are possible even in the simplest cosmological framework of Friedmann cosmology. We also show that various cosmological singularities may be removed or changed due to the variability of physical constants.
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The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noethers theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the with the Left or Right Painleve Series which describes the expansions.
We investigate Kerr-Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is opposite to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs counter-rotate against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps this counter-rotation is not an accidental oddity particular to Kerr-Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this.
Before atomic timekeeping, clocks were set to the skies. But starting in 1972, radio signals began broadcasting atomic seconds and leap seconds have occasionally been added to that stream of atomic seconds to keep the signals synchronized with the actual rotation of Earth. Such adjustments were considered necessary because Earths rotation is less regular than atomic timekeeping. In January 2012, a United Nations-affiliated organization could permanently break this link by redefining Coordinated Universal Time. To understand the importance of this potential change, its important to understand the history of human timekeeping.
We give an overview of literature related to Jurgen Ehlers pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification encompasses the convergence of one-parametric families of four-dimensional solutions of Einsteins equations of General Relativity to a solution of equations of a Newtonian theory if the inverse of a causality constant goes to zero. As such the corresponding light cones open up and become space-like hypersurfaces of constant absolute time on which Newtonian solutions are found as a limit of the Einsteinian ones. It is explained what it means to not consider the `standard-textbook Newtonian theory of gravitation as a complete theory unlike Einsteins theory of gravitation. In fact, Ehlers Frame theory brings to light a modern viewpoint in which the `standard equations of a self-gravitating Newtonian fluid are Maxwell-type equations. The consequences of Frame theory are presented for Newtonian cosmological dust matter expressed via the spatially projected electric part of the Weyl tensor, and for the formulation of characteristic quasi-Newtonian initial data on the light cone of a Bondi-Sachs metric.
Unless we change direction, we are likely to wind up where we are headed. (Ancient Chinese proverb)
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