发表机构
Indian Institute of Technology Kanpur; Inter-University Centre for Astronomy and Astrophysics（坎普尔印度理工学院; 大学间天体物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究膜世界中均匀尘埃云球对称坍缩，发现高能区存在反弹，可导致黑洞到白洞转变，并恢复广义相对论极限。
AI 中文摘要
我们研究了Shtanov--Sahni膜世界中三维膜上均匀尘埃云的球对称坍缩，其中额外维度是类时的。在高能区，膜Friedmann方程在物质密度中获得一个负二次项，由临界密度$\rhoc=2\lambda$控制，其中$\lambda$是负膜张力的量级。对于空间闭合的内部，我们精确积分了动力学。尺度因子的每个转折点都位于$\astar=\sqrt{3/4\pi\lambda}$之上，反弹存在当且仅当共动密度满足一个简单条件，并且所有曲率不变量在整个循环中保持在仅由$\lambda$确定的下界之下。共动世界线是测地完备的。然后我们将云跨越共动边界与一个具有无迹有效源的球对称外部匹配，并闭式求解Israel条件。外部是带电Vaidya几何，其质量函数和潮汐电荷由边界半径确定。潮汐电荷为正，与Randall--Sundrum情形符号相反，且外部不能是静态的。当且仅当质量超过$2/(3\sqrt{\pi\lambda})$时，在边界上形成陷获区域，在这种情况下反弹仍发生在边界的非陷获邻域内。对于陷获云，我们通过一个静态楔形连接一个超前和一个延迟的带电Vaidya片，构造了覆盖整个收缩、反弹和再膨胀的外部。匹配度规为$C^{1,1}$类，有效能量条件成立，云通过白洞区域重新出现进入第二个渐近区域。在广义相对论极限$\lambda\to\infty$下，恢复Oppenheimer--Snyder解。
英文摘要
We study the spherical collapse of a homogeneous dust cloud on a three-brane in the Shtanov--Sahni braneworld, in which the extra dimension is timelike. In the high-energy regime the brane Friedmann equation acquires a negative quadratic term in the matter density, controlled by a critical density $\rhoc=2λ$, where $λ$ is the magnitude of the negative brane tension. For a spatially closed interior we integrate the dynamics exactly. Every turning point of the scale factor lies above $\astar=\sqrt{3/4πλ}$, a bounce exists if and only if a simple condition on the comoving density holds, and all curvature invariants stay below bounds fixed by $λ$ alone along the entire cycle. Comoving worldlines are geodesically complete. We then match the cloud across a comoving boundary to a spherically symmetric exterior with a trace-free effective source and solve the Israel conditions in closed form. The exterior is a charged Vaidya geometry whose mass function and tidal charge are fixed by the boundary radius. The tidal charge is positive, opposite in sign to the Randall--Sundrum case, and the exterior cannot be static. A trapped region forms on the boundary if and only if the mass exceeds $2/(3\sqrt{πλ})$, and in that case the bounce still takes place in an untrapped neighbourhood of the boundary. For trapped clouds we construct an exterior over the full contraction, bounce and re-expansion by joining an advanced and a retarded charged Vaidya patch through a static wedge. The matched metric is of class $C^{1,1}$, the effective energy conditions hold, and the cloud re-emerges through a white hole region into a second asymptotic region. In the general relativistic limit $λ\to\infty$ the Oppenheimer--Snyder solution is recovered.
