We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field $\varphi$ and a self-interaction potential $V\left(\varphi \right)$. The $\varphi$ field can be canonical or phantom, and, accordingly, the theory splits into canonical and phantom sectors. We seek solitonic (stringlike) vacuum solutions of HMPG, that is, completely regular solutions with Minkowski metric far from the symmetry axis, with a possible angular deficit. A transition of the theory to the Einstein conformal frame is used as a tool, and many of the results apply to the general Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories as well as $f\left(R\right)$ theories of gravity. One of these results is a one-to-one correspondence between stringlike solutions in the Einstein and Jordan frames if the conformal factor that connects them is everywhere regular. An algorithm for the construction of stringlike solutions in HMPG and scalar-tensor theories is suggested, and some examples of such solutions are obtained and discussed.

中文翻译：

---

混合Metric-Palatini重力：规则的类似字符串的配置

我们讨论混合度量-帕拉蒂尼重力（HMPG）的静态，圆柱对称真空解决方案，这是最近提出的理论，已被证明可以成功地通过局部观测测试，并在宇宙学上产生一定的进展。我们在其著名的标量张量表示中使用HMPG。后者与广义相对论相吻合，广义相对论包含一个共形耦合的标量场作为引力源$\varphi$ 和自我互动的潜力 $V（\varphi ）$。的$\varphi$场可以是规范的或幻像的，因此，该理论分为规范的和幻像的两个部分。我们寻求HMPG的孤子（弦状）真空解，即完全Minkowski度量远离对称轴且可能存在角度缺陷的完全规则解。该理论向爱因斯坦共形框架的过渡被用作工具，并且许多结果适用于一般的标量张量理论的Bergmann-Wagoner-Nordtvedt类以及$F（\mathrm{[R}）$引力理论。这些结果之一是，如果连接它们的共形因子到处都是规则的，则爱因斯坦框架和约旦框架中的串状解之间是一一对应的。提出了一种基于HMPG和标量张量理论构造字符串解的算法，并获得和讨论了此类解的一些例子。