Ever since a new symmetry was found for the imperfect fluid with vorticity, the question of the effect of perturbations on the symmetry itself has been raised. This new symmetry arose when realizing that local four-velocity gauge-like transformations would render the left-hand side of the Einstein equations invariant because the metric tensor would be invariant under this new kind of local transformations. Then the point was raised about the invariance of such a kind of transformations of the stress–energy tensor on the right-hand side of the Einstein equations in curved four-dimensional Lorentz spacetimes. It was verified that these invariances do not work with plain perfect fluid but they do work for imperfect fluids. The imperfect fluid stress–energy tensor will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress–energy tensor itself. This local invariance was also the criteria introduced in order to present a new stress–energy tensor for vorticity as well. New tetrads are at the core of the realization of the existence of this new symmetry because it is through these new tetrads that this new symmetry is realized. It is through the local transformation of these new tetrad vectors that we can prove that the metric tensor is invariant. This new kind of symmetry has its origins in a similar tetrad formulation as to the Einstein–Maxwell spacetimes formalism presented in previous manuscripts. In this paper, we will introduce local perturbations by external agents to the relevant objects in the imperfect fluid geometry. We will demonstrate a theorem that proves that the symmetries under four-velocity gauge-like transformations will be instantaneously broken but at the same time transformed into new symmetries. Because the local orthogonal planes determined by these new tetrads, which happen to be the local planes of symmetry will tilt under local perturbations. There will be a symmetry evolution under perturbations.

自从发现了具有涡度的不完美流体的新对称性以来，人们就提出了扰动对对称性本身的影响的问题。当意识到局部四速度规范变换将使爱因斯坦方程的左侧保持不变时，这种新的对称性就出现了，因为在这种新的局部变换下度量张量将保持不变。然后提出了关于弯曲的四维洛伦兹时空中爱因斯坦方程右侧的应力-能量张量的这种变换的不变性的观点。经证实，这些不变性不适用于普通完美流体，但它们确实适用于不完美流体。当为应力-能量张量本身中包含的几个变量引入附加变换时，不完美的流体应力-能量张量将在局部四速度规式变换下保持不变。这种局部不变性也是引入的标准，以便为涡度提供新的应力-能量张量。新的四分体是实现这种新对称性存在的核心，因为正是通过这些新的四分体来实现这种新的对称性。正是通过这些新的四分体向量的局部变换，我们才能证明度量张量是不变的。这种新的对称性起源于与以前手稿中提出的爱因斯坦-麦克斯韦时空形式主义类似的四分体公式。在本文中，我们将在不完美的流体几何中引入外部代理对相关对象的局部扰动。我们将证明一个定理，证明在四速度规范变换下的对称性会瞬间被打破，但同时会转化为新的对称性。因为由这些新的四分体确定的局部正交平面，恰好是局部对称平面，将在局部扰动下倾斜。扰动下会有对称演化。恰好是局部对称平面将在局部扰动下倾斜。扰动下会有对称演化。恰好是局部对称平面将在局部扰动下倾斜。扰动下会有对称演化。