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arXiv 1909.04411gr-qchep-th
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$f(R)$重力的坍缩及$R$匹配方法

Collapse in $f(R)$ gravity and the method of $R$ matching

Sandip Chowdhury, Kunal Pal, Kuntal Pal, Tapobrata Sarkar

摘要:

$f(R)$引力中的坍缩解由于连接条件而受到限制,该连接条件要求Ricci标量及其法向导数在类时坍缩超曲面上连续。这些是通过$R$匹配方法获得的,该方法在$f(R)$崩溃场景中普遍存在。本文研究了带修正项$αR^2$的球对称坍缩问题,并利用$R$ -匹配方法证明了一类新的解.在讨论了这些理论中的剪切与各向异性之间的代数关系的一些数学公式之后,我们考虑了两种度量形式。在第一种情况下,坍缩度量被认为是共同运动半径和时间的可分函数,坍缩是无剪切的;在第二种情况下,考虑了不可分的内部解,它代表了具有非零剪切粘度的引力坍缩.我们到达新的解决方案,表明形成的黑洞或局部裸奇点,同时遵守所有必要的能量条件。可分离的情况下,允许一个简单的解析表达式的能量动量张量,这表明在整个崩溃的压力的积极性,并进一步用于研究的热通量演化的塌缩物质,其解析解在一定的近似下。在我们所考虑的例子中,这些都清楚地强调了修正引力的作用。

英文摘要:

Collapsing solutions in $f(R)$ gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of $R$-matching, which is ubiquitous in $f(R)$ collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term $αR^2$, and use $R$-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.

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