The shadow of a rotating black hole with nonvanishing gravitomagnetic charge has been studied. It was shown that in addition to the angular momentum of black hole the gravitomagnetic charge term deforms the shape of the black hole shadow. From the numerical results we have obtained that for a given value of the rotation parameter, the presence of a gravitomagnetic charge enlarges the shadow and reduces its deformation with respect to the spacetime without gravitomagnetic charge. Finally we have studied the capture cross section for massive particles by black hole with the nonvanishing gravitomagnetic charge.
In this study, we consider a flat FriedmannRobertson-Walker (FRW) universe in the context of Palatini f (R) theory of gravity. Using the dynamical equivalence between f (R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f (R) Lagrangian we find out the form of f (R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f (R) yield a powerlaw expansion for the scale factor of the universe.
In this paper, in the framework of teleparallel gravity we consider scalar tensor theories of gravity in which scalar fields are nonminimal coupled to torsion scalar. Noether symmetry of the Lagrangian of such a theory for the Friedman-Robertson-Walker spacetime is used to determine the explicit forms for the coupling function and for the potential, and it is shown that both must be power-law forms as a functions of the scalar field. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. It is shown that the equation of state parameter in the present model can cross the phantom divide line for a special case with the coupling function F (φ) = 3 16 φ 2 and for the potential V (φ) = λφ 2 .
Following up on hints of anisotropy in the cosmic microwave background radiation data, we investigate locally rotational symmetric Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and an arbitrary function. We illustrate with families of examples designed to be generalizations of the well-known power-expansion, exponential expansion and Big Rip models in the Friedmann-Robertson-Walker framework. The solutions display surprising variation, a large subset of which features late-time acceleration as is usually ascribed to dark energy (phantom or quintessence), and is consistent with observational data.
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