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Register a new userAn interpretation of Robinson-Trautman type N solutions
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The Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant Lambda and the curvature parameter epsilon. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced in a way which depends on epsilon. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds. A particular family of such solutions which can be used to represent snapping or decaying cosmic strings is considered in detail, and its singularity and global structure is presented.
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The evolution of spheroids of matter emitting gravitational waves and null radiation field is studied in the realm of radiative Robinson-Trautman spacetimes. The null radiation field is expected in realistic gravitational collapse, and can be either an incoherent superposition of waves of electromagnetic, neutrino or massless scalar fields. We have constructed the initial data identified as representing the exterior spacetime of uniform and non-uniform spheroids of matter. By imposing that the radiation field is a decreasing function of the retarded time, the Schwarzschild solution is the asymptotic configuration after an intermediate Vaidya phase. The main consequence of the joint emission of gravitational waves and the null radiation field is the enhancement of the amplitude of the emitted gravitational waves. Another important issue we have touched is the mass extraction of the bounded configuration through the emission of both types of radiation.
In our previous paper [Phys. Rev. D 89 (2014) 124029], cited as [1], we attempted to find Robinson-Trautman-type solutions of Einsteins equations representing gyratonic sources (matter field in the form of an aligned null fluid, or particles propagating with the speed of light, with an additional internal spin). Unfortunately, by making a mistake in our calculations, we came to the wrong conclusion that such solutions do not exist. We are now correcting this mistake. In fact, this allows us to explicitly find a new large family of gyratonic solutions in the Robinson-Trautman class of spacetimes in any dimension greater than (or equal to) three. Gyratons thus exist in all twist-free and shear-free geometries, that is both in the expanding Robinson-Trautman and in the non-expanding Kundt classes of spacetimes. We derive, summarize and compare explicit canonical metrics for all such spacetimes in arbitrary dimension.
In this paper we expand upon our previous work [1] by using the entire family of Bianchi type V stiff fluid solutions as seed solutions of the Stephani transformation. Among the new exact solutions generated, we observe a number of important physical phenomena. The most interesting phenomenon is exact solutions with intersecting spikes. Other interesting phenomena are solutions with saddle states and a close-to-FL epoch.
In this paper we present our point of view on correct physical interpretation of the Bel-Robinson tensor within the framework of the standard General Relativity ({bf GR}), i.e., within the framework of the {bf GR} without supplementary elements like arbitrary vector field, distinguished tetrads field or second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the differences of the canonical gravitational energy-momentum calculated in normal coordinates {bf NC(P)}.
[Abridged] If gravitation is to be described by a hybrid metric-Palatini $f(mathcal{R})$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous Godel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of $f(mathcal{R})$ theories, we examine whether they admit Godel-type solutions for well-motivated matter source. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous solutions in $f(mathcal{R})$ theories reduces to the problem of determining solutions of Einsteins field equations with a cosmological constant. Employing this far-reaching result, we determine a general Godel-type whose matter source is a combination of a scalar with an electromagnetic field plus a perfect fluid. This general Godel-type solution contains special solutions in which the essential parameter $m^2$ can be $m^{2} > 0$, $m=0$, and $m^{2} < 0$, covering thus all classes of homogeneous Godel-type spacetimes. This general solution also contains all previously known solution as special cases. The bare existence of these Godel-type solutions makes apparent that hybrid metric-Palatini gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity.
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