标题： 额外维度和可能的时空度规变化 显示英文标题

标题： Extra Dimensions and Possible Space-Time Signature Changes

摘要： 具有稀疏型标量-矢量耦合的爱因斯坦-麦克斯韦-标量方程的精确静态、球对称解，在$D$维引力中包含一连串$n$个里奇平坦内部空间，被考虑，其中麦克斯韦场势有两个非零分量：时间分量，类似库仑的分量和指向一个额外维度的分量。讨论了解的性质和特殊情况，特别是当时空中有视界时的情况。区分了两种类型的视界：传统的黑洞（BH）视界和时空的物理部分改变其符号的视界（后者称为{\it T-地层界面}）。证明了两个定理，一个确定了BH和T视界的存在的条件，另一个表明所研究的系统不能有规则的中心。研究了选定的一族解在球对称扰动下的稳定性。结果表明，只有黑洞解是稳定的，而其他所有解，特别是具有T视界的解都是不稳定的。 显示英文摘要

摘要： Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered, with the Maxwell field potential having two nonzero components: the temporal, Coulomb-like one and the one pointing to one of the extra dimensions. The properties and special cases of the solutions are discussed, in particular, those when there are horizons in the space-time. Two types of horizons are distinguished: the conventional black-hole (BH) ones and those at which the physical section of the space-time changes its signature (the latter are called {\it T-horizons}). Two theorems are proved, one fixing the BH- and T-horizon existence conditions, the other claiming that the system under study cannot have a regular center. The stability of a selected family of solutions under spherically symmetric perturbations is studied. It is shown that only black-hole solutions are stable, while all others, in particular, those with T-horizons are unstable.