标题： 修正的Schwarzschild时空在Ricci平坦膜上 显示英文标题

标题： Modified Schwarzschild spacetime in Ricci-flat brane

摘要： 考虑一个关于$1+3+n$维静态时空的假设，其中均匀分布的$n$-膜堆叠在三维旋转对称的空间中，我们找到了爱因斯坦场方程的不同类真空解。通过牛顿极限、克尔施曼标量和朗道-利夫希茨应力-能量伪张量的能动形式，我们分析了这些解。这揭示了一类具有额外维度的史瓦西时空非平凡扩展解的异常物理性质。正的守恒能量与排斥引力和视界上的物理奇异性相关联，而负的守恒能量则意味着引力吸引和裸奇异性。这使史瓦西解处于更广泛的背景下，并为广义相对论提供了新的可能的检验场所。 显示英文摘要

摘要： Considering an ansatz for $1+3+n$ dimensional static spacetime with uniform $n$-branes stacked in three-dimensional rotationally symmetric space, we found different classes of vacuum solutions of Einstein field equations. We analyzed these solutions through the Newtonian limit, Kretschmann scalar, and conserved energy from Landau--Lifshitz stress-energy pseudotensor. This revealed unusual physical properties for a class of solutions with nontrivial extension of the Schwarzschild spacetime with extra dimensions. Positive conserved energy is associated with repulsive gravity and physical singularity on the horizon, while negative conserved energy implies gravitational attraction and naked singularity. This sets the Schwarzschild solution in a broader context and provides new possible testing grounds for general relativity.