标题： 暗洞：比黑洞更好，也有光明的一面（能量会产生引力吗？） 显示英文标题

标题： Darkholes: Nicer than blackholes - with a bright side, too (Does energy produce gravity?)

摘要： 三维空间的几何结构引导寻找一种比具有不受欢迎奇点的黑洞更好的模型。 一个基本的构造在黎曼3维空间中2维球面的4流形上产生一个时空度量，该度量在3维空间的均匀共形变换下保持不变。 当3维空间是欧几里得时，度量简化为德西特的膨胀宇宙度量。 推广得到一个时空度量，该度量保留了德西特度量的“指数膨胀特性”。 一个严格的几何作用原理给出场方程，由于这些方程不遵循爱因斯坦早期将能量和惯性质量与引力质量混淆的观点，因此允许逃避彭罗斯-霍金奇点定理的解。 一个与施瓦茨希尔德黑洞度量渐近的球对称解，在视界和奇点的位置有一个爱因斯坦-罗森“桥”或“隧道”，连接两个渐近欧几里得区域。 在一侧，引力中心吸引，并且是暗的但不是黑的；在另一侧它排斥，并且是亮的。 通过隧道从任一侧到另一侧的旅行和信号传递是可能的。 对该“暗洞”（或“暗洞-亮洞”）的爱因斯坦张量分析表明，并非所有能量都产生引力，将能量称为“负的”，或其与几何的关系称为“奇异的”，是没有根据的。 显示英文摘要

摘要： The geometry of three-dimensional space guides the search for a better model than the blackhole with its unwelcome singularity. An elementary construction produces on the 4-manifold of 2-spheres in a Riemannian 3-space a space-time metric invariant under uniform conformal transformations of the 3-space. When the 3-space is Euclidean, the metric reduces to de Sitter's expanding universe metric. Generalization yields a space-time metric that retains the `exponential expansion property' of the de Sitter metric. A strictly geometric action principle gives field equations which, because they do not adhere to Einstein's early confounding of energy and inertial mass with gravitating mass, admit solutions that escape the Penrose-Hawking singularity theorems. A spherically symmetric solution that is asymptotic to the Schwarzschild blackhole metric has, in place of a horizon and a singularity, an Einstein-Rosen `bridge', or `tunnel', connecting two asymptotically Euclidean regions. On one side the gravitational center attracts, and is dark but not black; on the other side it repels, and is bright. Travel and signaling from either side to the other via the tunnel are possible. Analysis of the Einstein tensor of this `darkhole' (or `darkhole-brighthole') suggests that not all energy produces gravity, and that calling energy `negative', or its relationship to geometry `exotic', is unjustified.