  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.
