标题： 关于罗伯特森-沃克宇宙学中的签名转换 显示英文标题

标题： On signature transition in Robertson-Walker cosmologies

摘要： 我们分析了一个引力与自相互作用标量场耦合的经典模型。 我们表明，在这个模型中，对于Robertson-Walker宇宙学，存在空间非平坦情况下从欧几里得到洛伦兹时空的转变解。 然后我们讨论这些爱因斯坦场方程的度规符号改变解存在的条件。 特别是，我们发现存在一个宇宙学常数的上界，并且在度规符号改变的超曲面附近，尺度因子和标量场必须是常数。 此外，我们发现当标量场无质量时，度规符号改变解不存在。 显示英文摘要

摘要： We analyse a classical model of gravitation coupled to a self interacting scalar field. We show that, within the context of this model for Robertson-Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian spacetime. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be constant. Moreover we find that the signature changing solutions do not exist when the scalar field is massless.