发表机构
American University of Beirut（贝鲁特美国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究任意时空符号下引力理论中的各向异性畴壁与宇宙学解，确定一类允许一阶表述的标量势，构造各向异性解并恢复Kasner-膨胀子-AdS解。
AI 中文摘要
我们研究了任意时空符号的$D$维引力理论中，与标量场（含标量势）耦合的各向异性畴壁和宇宙学解。我们确定了一类标量势，使得二阶运动方程允许一阶表述。相关的玻色子流允许非平凡的Ricci平坦世界体积，而其Killing旋子实现进一步要求世界体积允许非零平行旋子。五维${\cal N}=2$规范超引力为该构造提供了具体实现，其世界体积几何由其符号决定，并产生pp波、超Kähler和超辛几何。我们进一步构造了一类依赖于单个变量的各向异性解的一般类，各向异性编码在常数无迹矩阵中。当一部分标量场通过其动能项贡献但不进入标量势时，出现一个特殊分支；这些场遵循标量流形上的测地线。作为具体应用，我们恢复了Kasner-膨胀子-AdS解，并表明在适当极限下，它们满足一阶流方程。
英文摘要
We investigate anisotropic domain wall and cosmological solutions in $D$-dimensional gravitational theories of arbitrary spacetime signature coupled to scalar fields with a scalar potential. We identify a class of scalar potentials for which the second-order equations of motion admit a first-order formulation. The associated bosonic flows allow non-trivial Ricci-flat worldvolumes, while their Killing-spinor realization further requires the worldvolume to admit a non-vanishing parallel spinor. Five-dimensional ${\cal N}=2$ gauged supergravity provides a concrete realization of this construction, with the worldvolume geometry determined by its signature and giving rise to pp-wave, hyper-Kähler, and hypersymplectic geometries. We further construct a general class of anisotropic solutions depending on a single variable, with the anisotropy encoded in a constant traceless matrix. A particular branch arises when a subset of scalar fields contribute through their kinetic terms but do not enter the scalar potential; these fields follow geodesics on the scalar manifold. As an explicit application, we recover the Kasner-dilaton-AdS solutions and show that, in the appropriate limit, they satisfy the first-order flow equations.
Comments17 pages
