The magnetosphere structure of compact objects is considered in the context of a theory of gravity with dynamical torsion field beyond standard General Relativity (GR) introduced previously in Cirilo-Lombardo and Minotti (2019). To this end, a new spherically symmetric solution is obtained. A particular case physically representing a compact object of pseudoscalar fields (for example, axion field) is analyzed from the magnetosphere dynamics viewpoint using the axially symmetric version of the Grad-Shafranov equation (GSE) previously derived. We explicitly show that, in sharp contrast with the dipole case, the quadrupole case (where we have two well defined toroidal lobes) the energy stored in the magnetosphere increases more than in the pure dipole case, fact that is important to explain the problem of excess energy in mechanics of the pulsars and in the structure of magnetars. In this way we briefly discuss with the same argument as the one presented in Wang et al. (2019), how in our theoretical frame our model can help reinterpret phenomenological and observational results in the case of the X-ray emission of XTE J1810-197.

紧凑物体的磁层结构是在重力理论基础上考虑的，该理论具有动态扭力场，超出了先前在Cirilo-Lombardo和Minotti（2019）中引入的标准广义相对论（GR）。为此，获得了新的球对称解。使用先前导出的Grad-Shafranov方程（GSE）的轴向对称形式，从磁层动力学角度分析了物理上代表伪标量场（例如，轴力场）的紧凑对象的特殊情况。我们明确表明，与偶极子情况形成鲜明对比的是，在四极子情况下（我们有两个明确定义的环形波瓣），磁层中存储的能量比纯偶极子情况下增加更多，这对于解释脉冲星的力学和磁星的结构中的过剩能量问题很重要。这样，我们用与Wang等人提出的观点相同的观点简要讨论。（2019），在XTE J1810-197的X射线发射情况下，我们的模型如何在理论框架中帮助重新解释现象学和观察结果。