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Register a new userRedshift in a six-dimensional classical Kaluza-Klein type model
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Authors
Jacek Syska
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Multidimensional theories still remain attractive from the point of view of better understanding fundamental interactions. In this paper a six-dimensional Kaluza-Klein type model at the classical, Einsteins gravity formulation is considered. The static spherically symmetric solution of the six-dimensional Einstein equations coupled to the Klein-Gordon equation with the massless dilatonic field is presented. As it is horizon free, it is fundamentally different from the four-dimensional Schwarzschild solution. The motion of test particles in such a spherically symmetric configuration is then analyzed. The presence of the dilatonic field has a similar dynamical effect as the existence of additional massive matter. The emphasis is put on some observable quantities like redshifts. It has been suggested that strange features of emission lines from galactic nuclei as well as quasar-galaxy associations may in fact be manifestations of the multidimensionality of the world.
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Multidimensional theories still remain attractive from the point of view of better understanding of fundamental interactions. In this paper we consider a six - dimensional Kaluza -- Klein type model at the classical level. We derive static spherically symmetric solutions to the multidimensional Einstein equations. They are fundamentally different from four - dimensional Schwarzschild solutions: they are horizon free and the presence of massless dilaton field has the same dynamical effect as the existence of additional massive matter in the system. Then we analyse the motion of test particles in such spherically symmetric configurations. The emphasis is put on some observable quantities like redshifts. It is suggested that strange features of emission lines from active galactic nuclei as well as quasar - galaxy associations may in fact be manifestations of multidimensionality of our world.
We perform the 4-dimensional Kaluza-Klein (KK) reduction of the 5-dimensional locally scale invariant Weyl-Dirac gravity. While compactification unavoidably introduces an explicit length scale into the theory, it does it in such a way that the KK radius can be integrated out from the low energy regime, leaving the KK vacuum to still enjoy local scale invariance at the classical level. Imitating a $U(1)timestilde{U}(1)$ gauge theory, the emerging 4D theory is characterized by a kinetic Maxwell-Weyl mixing whose diagonalization procedure is carried out in detail. In particular, we identify the unique linear combination which defines the 4D Weyl vector, and fully classify the 4D scalar sector. The later consists of (using Weyl language) a co-scalar and two in-scalars. The analysis is performed for a general KK $m$-ansatz, parametrized by the power $m$ of the scalar field which factorizes the 4D metric. The no-ghost requirement, for example, is met provided $-frac{1}{2}leq m leq 0$. An $m$-dependent dictionary is then established between the original 5D Brans-Dicke parameter $omega_5$ and the resulting 4D $omega_4$. The critical $omega_5=-frac{4}{3}$ is consistently mapped into critical $omega_4 = -frac{3}{2}$. The KK reduced Maxwell-Weyl kinetic mixing cannot be scaled away as it is mediated by a 4D in-scalar (residing within the 5D Weyl vector). The mixing is explicitly demonstrated within the Einstein frame for the special physically motivated choice of $m=-frac{1}{3}$. For instance, a super critical Brans-Dicke parameter induces a tiny positive contribution to the original (if introduced via the 5-dimensional scalar potential) cosmological constant. Finally, some no-scale quantum cosmological aspects are studied at the universal mini-superspace level.
We study teleparallel gravity in the emph{original} Kaluza-Klein (KK) scenario. Our calculation of the KK reduction of teleparallel gravity indicates that the 5-dimensional torsion scalar $^{(5)}T$ generates the non-Brans-Dicke type effective Lagrangian in 4-dimension due to an additional coupling between the derivative of the scalar field and torsion, but the result is equivalent to that in general relativity. We also discuss the cosmological behavior in the FLRW universe based on the effective teleparallel gravity.
We prove a uniqueness theorem for stationary $D$-dimensional Kaluza-Klein black holes with $D-2$ Killing fields, generating the symmetry group ${mathbb R} times U(1)^{D-3}$. It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints.
We study the shadow of a rotating squashed Kaluza-Klein (KK) black hole and the shadow is found to possess distinct properties from those of usual rotating black holes. It is shown that the shadow for a rotating squashed KK black hole is heavily influenced by the specific angular momentum of photon from the fifth dimension. Especially, as the parameters lie in a certain special range, there is no any shadow for a black hole, which does not emerge for the usual black holes. In the case where the black hole shadow exists, the shadow shape is a perfect black disk and its radius decreases with the rotation parameter of the black hole. Moreover, the change of the shadow radius with extra dimension parameter also depends on the rotation parameter of black hole. Finally, with the latest observation data, we estimate the angular radius of the shadow for the supermassive black hole Sgr $A^{*}$ at the centre of the Milky Way galaxy and the supermassive black hole in $M87$.
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