We show that in the inhomogeneous Lemaître–Tolman–Bondi space–time there are specific regions in which repulsive gravity exists. To find these regions, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. In addition, we analyze the effects of repulsive gravity on the dynamics of the gravitational collapse. In particular, we investigate the collapse in the case of the parabolic solution for the effective scale factor of the Lemaître–Tolman–Bondi metric, corresponding to the marginally bound case. Exploring the corresponding cut-offs at which gravity becomes repulsive, we notice that black holes with dominant repulsive effects are not excluded a priori. Indeed, we demonstrate that the collapse leads, in general, to the formation of a central naked singularity; however, for particular values of the free parameters entering the model, black holes with dominant repulsive gravity can exist. We show that the expected physical process is not modified as the marginally bound condition is dropped out. Moreover, we show that this is true independently of the hypothesis that the energy–momentum tensor is built up in terms of pressureless matter. Further, we demonstrate that geodesic deviations can depend on the sign of the curvature eigenvalues. Finally, we give an astrophysical interpretation of black holes with dominant repulsive gravity. Indeed, we argue that compact objects with dominant repulsive gravity could be interpreted as progenitors of Gamma Ray Bursts.

我们表明，在不均匀的Lemaître–Tolman–Bondi时空中，存在排斥力的特定区域。为了找到这些区域，我们使用基于曲率特征值行为的斥力不变式定义。此外，我们分析了排斥重力对重力坍塌动力学的影响。特别是，我们研究了Lemaître–Tolman–Bondi度量的有效比例因子的抛物线解的崩溃，它对应于边际约束情况。在探究重力排斥的相应截止点时，我们注意到具有主要排斥作用的黑洞并未被先验排除。实际上，我们证明了崩溃通常会导致形成中央裸奇点；但是，对于进入模型的自由参数的特定值，可能存在具有主要排斥重力的黑洞。我们显示出，由于取消了边界约束条件，因此预期的物理过程没有被修改。此外，我们证明了这一事实与假设能量动量张量是根据无压物质建立的假设无关。此外，我们证明了测地线偏差可以取决于曲率特征值的符号。最后，我们对具有排斥力的黑洞进行了天体物理学的解释。的确，我们认为具有主要排斥力的紧凑物体可以解释为伽玛射线爆发的祖先。