We study the kinematical and dynamical properties of spacetimes that admit a conformal Killing vector. A 1 + 1 + 2 decomposition of the spacetime is performed using the fluid 4-velocity and a preferred spatial direction. This provides new insights into the behaviour of the acceleration, expansion, shear and vorticity scalars. The energy momentum tensor for an anisotropic fluid with no sheet components is considered and decomposed using the semi-tetrad covariant approach. This makes it possible to generate a set of constraint equations in the new geometrical variables. All the geometrical and thermodynamical quantities are written in terms of the 1 + 1 + 2 decomposition variables. We also find the constraints that must be satisfied by the thermodynamical variables when conformal symmetry exists in a perfect fluid. Noteworthily we show that the conformal factor satisfies a damped wave equation.

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In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the ergoregion. As a result we are able to explicitly write down the 1+1+2 Kerr quantities, and the evolution and propagation equations they satisfy. This formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner; and also to highlight the role of vorticity. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.

In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the horizon. Comparisons are drawn between an observer belonging to the Killing frame and a ZAMO (zero angular momentum observer), a locally non-rotating observer in a zero angular momentum frame, and their resulting geometrical quantities that generate the evolution and propagation equations. This enhances the study of the Kerr geometry as the results are valid in the ergoregion from where energy can be extracted. Using this formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner not present in alternate approaches. We find significant relationships between the properties of shear, vorticity and acceleration. Additionally we observe that in the Killing frame, the gravitational wave is a direct consequence of vorticity and in the ZAMO frame, the gravitational wave is a direct consequence of shear. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach, and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.

In this paper, we consider conformally symmetric generalized Vaidya spacetimes with a composite null dust and null string matter distribution using the semi-tetrad covariant [Formula: see text] decomposition method. The important and novel result that emerges from our analysis is that all the geometric variables related to the time-like and the preferred space-like congruences are completely determined by the conformal vector and conformal factor. This result is unique to the specific matter distribution of the generalized Vaidya configuration. We further show that in the case of the pure null dust (or Vaidya) spacetime, a proper conformal Killing vector cannot be admitted.