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Register a new userQuasinormal modes of charged squashed Kaluza-Klein black holes in the G{o}del Universe
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We study the quasinormal modes of scalar perturbation in the background of five-dimensional charged Kaluza-Klein black holes with squashed horizons immersed in the G{o}del universe. Besides the influence due to the compactness of the extra dimension, we disclose the cosmological rotational effect in the wave dynamics. The wave behavior affected by the G{o}del parameter provides an interesting insight into the G{o}del universe.
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We study motions of photons in an unmagnetized cold homogeneous plasma medium in the five-dimensional charged static squashed Kaluza-Klein black hole spacetime. In this case, a photon behaves as a massive particle in a four-dimensional spherically symmetric spacetime. We consider the light deflection by the squashed Kaluza-Klein black hole surrounded by the plasma in a weak-field limit. We derive corrections of the deflection angle to general relativity, which are related to the size of the extra dimension, the charge of the black hole and the ratio between the plasma and the photon frequencies.
We investigate the strong gravitational lensing in a Kaluza-Klein black hole with squashed horizons. We find the size of the extra dimension imprints in the radius of the photon sphere, the deflection angle, the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)times U(1)simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.
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 $M87$.
Applying squashing transformation to Kerr-Godel black hole solutions, we present a new type of a rotating Kaluza-Klein black hole solution to the five-dimensional Einstein-Maxwell theory with a Chern-Simon term. The new solutions generated via the squashing transformation have no closed timelike curve everywhere outside the black hole horizons. At the infinity, the metric asymptotically approaches a twisted S^1 bundle over a four-dimensional Minkowski space-time. One of the remarkable features is that the solution has two independent rotation parameters along an extra dimension associated with the black holes rotation and the Godels rotation. The space-time also admits the existence of two disconnected ergoregions, an inner ergoregion and an outer ergoregion. These two ergoregions can rotate in the opposite direction as well as in the same direction.
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