论文标题
混合度量 - 帕拉蒂尼重力中的宇宙弦乐对象
Cosmic stringlike objects in hybrid metric-Palatini gravity
论文作者
论文摘要
我们考虑了混合度量 - 帕拉蒂尼修饰的重力理论的标量表示中的静态和圆柱对称内部弦型解。作为我们研究的第一步，我们通过沿$ t $和$ z $轴施加洛伦兹的不变性来获得重力场方程，并进一步简化了分析，从而将未知的度量张量组件的数量减少到单个函数$ W^2（r）$。在这种情况下，对于标量场电位的任意形式，可以以精确的闭合参数形式获得字段方程的一般解，而标量字段$ ϕ $则以参数为参数。我们详细考虑了字段方程的几种精确解决方案，对应于无效和恒定的电位，以及表单$ v（ϕ）= v_0x^{3/4} $的幂律电位，其中标量场的行为，公制张量组件和字符串的行为可以在简单的数学形式中描述。我们还使用数值方法研究了具有指数和HIGGS类型标量场电势的字符串模型。通过这种方式，我们在混合度量 - 帕拉蒂重力的背景下获得了一大批新型稳定弦乐溶液，其中基本参数（例如标量场，度量张量组件和弦张力）在基本上取决于标量场的初始值，以及其导数的初始值，以及$ r = 0 $ r = 0 $ rcivearmar ocdular Axis。
We consider static and cylindrically symmetric interior string type solutions in the scalar-tensor representation of the hybrid metric-Palatini modified theory of gravity. As a first step in our study, we obtain the gravitational field equations and further simplify the analysis by imposing Lorentz invariance along the $t$ and $z$ axes, which reduces the number of unknown metric tensor components to a single function $W^2(r)$. In this case, the general solution of the field equations can be obtained, for an arbitrary form of the scalar field potential, in an exact closed parametric form, with the scalar field $ϕ$ taken as a parameter. We consider in detail several exact solutions of the field equations, corresponding to a null and constant potential, and to a power-law potential of the form $V(ϕ)=V_0ϕ^{3/4}$, in which the behaviors of the scalar field, of the metric tensor components and of the string tension can be described in a simple mathematical form. We also investigate the string models with exponential and Higgs type scalar field potentials by using numerical methods. In this way we obtain a large class of novel stable string-like solutions in the context of hybrid metric-Palatini gravity, in which the basic parameters, such as the scalar field, metric tensor components, and string tension, depend essentially on the initial values of the scalar field, and of its derivative, on the $r=0$ circular axis.
