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Register a new userThe massless Einstein-Boltzmann system with a conformal-gauge singularity in an FLRW background
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We obtain finite-time existence for the massless Boltzmann equation, with a range of soft cross-sections, in an FLRW background with data given at the initial singularity. In the case of positive cosmological constant we obtain long-time existence in proper-time for small data as a corollary.
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We present higher-dimensional generalizations of the Buchdahl and Janis-Robinson-Winicour transformations which generate static solutions in the Einstein-Maxwell system with a massless scalar field. While the former adds a nontrivial scalar field to a vacuum solution, the latter generates a charged solution from a neutral one with the same scalar field. Applying these transformations to (i) a static solution with an Einstein base manifold, (ii) a multi-center solution, and (iii) a four-dimensional cylindrically symmetric solution, we construct several new exact solutions.
We show that massless solutions to the Einstein-Vlasov system in a Bianchi I space-time with small anisotropy, i.e. small shear and small trace-free part of the spatial energy momentum tensor, tend to a radiation fluid in an Einstein-de Sitter space-time with the anisotropy $Sigma^a_bSigma^b_a$ and $tilde{w}^i_j tilde{w}^j_i$ decaying as $O(t^{-frac12})$.
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
In this paper, we considered the gravitational collapse of a symmetric radiating star consisting of perfect fluid (baryonic) in the background of dark energy (DE) with general equation of state. The effect of DE on the singularity formation has been discussed first separately (only DE present) and then combination of both baryonic and DE interaction. We have also showed that DE components play important role in the formation of Black-Hole(BH). In some cases the collapse of radiating star leads to black hole formation and in other cases it forms Naked-Singularity(or, eternally collapse). The present work is in itself remarkable to describe the effect of dark energy on singularity formation in radiating star.
In this paper we consider a model of Poincare gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einsteins gravitational field and a pair of ``Yang-Mills field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills field without its partner field and the Reissner-Nordstrom type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstrom geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstrom type black-hole.
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