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.

中文翻译：

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具有共形对称性的时空半四分体分解

我们研究了允许共形杀伤向量的时空的运动学和动力学特性。使用流体 4 速度和首选空间方向执行时空的 1 + 1 + 2 分解。这提供了对加速度、膨胀、剪切和涡量标量行为的新见解。使用半四元协变方法考虑并分解了无片分量的各向异性流体的能量动量张量。这使得在新的几何变量中生成一组约束方程成为可能。所有几何和热力学量都用 1 + 1 + 2 分解变量表示。我们还找到了当共形对称存在于完美流体中时热力学变量必须满足的约束。