It was recently shown, that in a class of tensor-multiscalar theories of gravity with a nontrivial target space metric, there exist scalarized neutron star solutions. An important property of these compact objects is that the scalar charge is zero and therefore, the binary pulsar experiments can not impose constraints based on the absence of scalar dipole radiation. Moreover, the structure of the solutions is very complicated. For a fixed central energy density up to three neutron star solutions can exist—one general relativistic and two scalarized—which is quite different from the scalarization in other alternative theories of gravity. In the present paper we address the stability of these solutions using two independent approaches—solving the linearized radial perturbation equations and performing nonlinear simulations in spherical symmetry. The results show that the change of stability occurs at the maximum mass models and all solutions before that point are stable. This leads to the interesting consequence that there exists a stable part of the scalarized branch close to the bifurcation point where the mass of the star increases with the decrease of the central energy density.

中文翻译：

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标量化中子星的非线性演化和非唯一性

最近表明，在一类具有非平凡目标空间度量的张量多标量引力理论中，存在标量化中子星解。这些致密天体的一个重要特性是标量电荷为零，因此双脉冲星实验不能基于没有标量偶极子辐射而施加约束。此外，解决方案的结构非常复杂。对于固定的中心能量密度，最多可以存在三个中子星解——一个是广义相对论的，两个是标量化的——这与其他替代引力理论中的标量化完全不同。在本文中，我们使用两种独立的方法来解决这些解的稳定性——求解线性化径向扰动方程和在球对称中执行非线性模拟。结果表明，稳定性的变化发生在最大质量模型处，并且在该点之前的所有解都是稳定的。这导致了一个有趣的结果，即在靠近分叉点的地方存在一个稳定的标量分支，在那里恒星的质量随着中心能量密度的降低而增加。