In this paper, in the classical framework, the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric are evaluated. The calculated lower bounds via the linear dynamical systems $L_{\frac{\partial }{\partial \theta }}$, $L_{\frac{\partial }{\partial r}}$, and $L_{\frac{\partial }{\partial \varphi }}$ are $-\ln 2+\ln |{(\dot{R}B)}^2-{(R^{\prime })}^2|-2\ln |B|$, $2\ln |\dot{B}|-\ln 2$ and $-\ln 2-2\ln |B|+\ln |({\dot{R}}^2{B}^2-R^{\prime 2}){\sin }^2\theta -B^2{\cos }^2\theta |$ respectively. The sensitivities and the lower sensitivities via $L_{\frac{\partial }{\partial t}}$ are zero are also shown. In the quantum framework, the properties of the Einstein-Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014 are analyzed. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler-DeWitt equation. Forbidding such a combination leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger-like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, the time evolution of the Einstein-Vaz shells is discussed.

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关于广义勒梅特托尔曼邦迪度量：经典敏感性和量子爱因斯坦-瓦兹壳

本文在经典框架中评估了广义 Lemaitre Tolman Bondi 度量的灵敏度下界。通过线性动力系统计算的下界$L_{\frac{\partial }{\partial \theta }}$,$L_{\frac{\partial }{\partial r}}$， 和$L_{\frac{\partial }{\partial \phi }}$是$-因2+因|{（\dot{右}乙）}^2-{（{右}^{\prime }）}^2|-2因|乙|$,$2因|\dot{乙}|-因2$和$-因2-2因|乙|+因|（{\dot{右}}^2{乙}^2-{右}^{\prime 2}）{罪}^2\theta -{乙}^2{\mathrm{因斯}}^2\theta |$分别。灵敏度和较低灵敏度通过$L_{\frac{\partial }{\partial t}}$也显示为零。在量子框架中，分析了爱因斯坦-瓦兹壳层的性质，该壳层是瓦兹在2014年讨论的勒梅特·托尔曼·邦迪引起的量子引力塌缩的最终结果。事实上，瓦兹表明，只有将惠勒-德威特方程的两个独立且完整的解结合起来，才能获得持续塌缩到奇点的效果。禁止这种组合自然会导致量子坍缩期间物质在史瓦西表面上凝结。这样，一个全新的黑洞（BH）框架就出现了。瓦兹的方法也与爱因斯坦 1939 年关于将塌缩粒子定位在薄球壳内的想法一致。在这里，遵循我们中的一个 (CC) 的方法，我们通过类似薛定谔的方法推导出 BH 质量和能谱，进一步支持 Vaz 的结论，即事件视界覆盖的时空奇点不是事件视界覆盖的时空奇点，而是事件视界覆盖的时空奇点。引力塌缩本质上是一个量子物体，一个极其致密的“暗星”。这种“引力原子”不是由任何简并压力支撑，而是由量子引力支撑，就像普通原子由量子力学支撑一样。最后，讨论了爱因斯坦-瓦兹壳的时间演化。