标题： 磁致约束的吸积中子星山体在广义相对论中 显示英文标题

标题： Magnetically Confined Mountains on Accreting Neutron Stars in General Relativity

摘要： 广义相对论框架下中子星磁约束山问题的表述被提出，所得方程被数值求解，推广了之前的牛顿计算。 吸积物质的流体磁结构以及随后的星体磁偶极矩的磁埋藏被计算出来。 总体上观察到，相对论修正减少了与山相关的流体磁变形。 磁场线弯曲得比之前计算中的更缓和，偶极矩的屏蔽效应也减少了。 定量上发现，无量纲偶极矩（$m_{\rm d}$）随着吸积质量（$M_{\rm a}$）的变化呈$m_{\rm d} = -3.2\times10^{3}M_{\rm a}/M_\odot + 1.0$的形式，这意味着相比牛顿理论，屏蔽效应大约减少了三倍。 此外，山的特征尺度高度，决定了压力、密度和磁场强度梯度的尺度，对于等温状态方程而言，大约减少了$40\%$。 显示英文摘要

摘要： The general relativistic formulation of the problem of magnetically confined mountains on neutron stars is presented, and the resulting equations are solved numerically, generalising previous Newtonian calculations. The hydromagnetic structure of the accreted matter and the subsequent magnetic burial of the star's magnetic dipole moment are computed. Overall, it is observed that relativistic corrections reduce the hydromagnetic deformation associated with the mountain. The magnetic field lines are curved more gently than in previous calculations, and the screening of the dipole moment is reduced. Quantitatively, it is found that the dimensionless dipole moment ($m_{\rm d}$) depends on the accreted mass ($M_{\rm a}$) as $m_{\rm d} = -3.2\times10^{3}M_{\rm a}/M_\odot + 1.0$, implying approximately three times less screening compared to the Newtonian theory. Additionally, the characteristic scale height of the mountain, governing the gradients of quantities like pressure, density, and magnetic field strength, reduces by approximately $40\%$ for an isothermal equation of state.