论文标题
具有非最小导数耦合的较高维度标量理论中的静态间距
Static Spacetimes In Higher Dimensional Scalar-Torsion Theories With Non-Minimal Derivative Coupling
论文作者
论文摘要
在本文中，我们考虑了具有非最小衍生耦合的较高维度（$ d \ ge 4 $）标量理论的一类静态空间，并且标量电势打开。该时空与两个表面的产品空间和$（D-2）$ - 维度子手机的一致。在理论中分析运动方程式，我们发现$（d-2）$ - 尺寸submanifold必须接受构造标量为其中之一的恒定三重态结构。这意味着这些运动方程式可以简化为单个高度非线性的普通微分方程，称为主方程。然后，我们表明，在这种情况下，解决方案至少在不是黑洞的原点上裸露的奇异性。在渐近区域中，空间汇聚到通常不是爱因斯坦的恒定标态曲率的空间。我们还使用扰动方法线性化主方程并构建一阶解决方案。最后，我们建立了主方程的局部全球存在分析，然后证明了常规全球解决方案的不存在。
In this paper we consider a class of static spacetimes in higher dimensional ($D \ge 4$) scalar-torsion theories with non-minimal derivative coupling and the scalar potential turned on. The spacetime is conformal to a product space of a two-surface and a $(D-2)$-dimensional submanifold. Analyzing the equations of motion in the theory we find that the $(D-2)$-dimensional submanifold has to admit constant triplet structures in which the torsion scalar is one of them. This implies that these equations of motion can be simplified into a single highly non-linear ordinary differential equation called the master equation. Then, we show that in this case the solution admits at least a naked singularity at the origin which is not a black hole. In the asymptotic region, the spacetimes converge to spaces of constant scalar curvature which are generally not Einstein. We also use perturbative method to linearize the master equation and construct the first order solutions. At the end, we establish the analysis of local-global existences of the master equation and then, prove the non-existence of regular global solutions.
