In this work we employ the time-dependent Karmarkar condition to model dissipative gravitational collapse in the presence of shear which leads to a final static configuration. We believe that this is a first attempt at using the time-dependent Karmarkar condition describing a radiating star with shear in which the collapsing core dissipates energy in the form of a radial heat flux. The final static configuration which is described by an embedding class I spacetime was obtained by Hansraj and Moodly who showed that this solution satisfies all the physical requirements for a static compact object. As the collapse proceeds and the heat flux tends to zero the dynamical core evolves into a static compact core with the exterior spacetime being described by the vacuum Schwarzschild solution.

在这项工作中，我们采用时间相关的Karmarkar条件来模拟在存在剪切力的情况下耗散的重力坍塌，从而导致最终的静态构型。我们相信，这是使用时间相关的Karmarkar条件进行的首次尝试，该条件描述了具有剪切力的辐射星，其中坍塌的核以径向热通量的形式耗散了能量。由嵌入类I时空描述的最终静态配置由Hansraj和Moodly获得，他们证明该解决方案满足了静态紧凑对象的所有物理要求。随着塌陷的进行和热通量趋于零，动态核心演变成静态的紧凑核心，外部时空由真空Schwarzschild解决方案描述。