I-Love-Q relations: from compact stars to black holes
I-Love-Q relations: from compact stars to black holes
复制标题
我-爱-Q关系：从致密恒星到黑洞
DOI：
10.1088/0264-9381/33/9/095005
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发表时间：
2016
影响因子：
3.5
通讯作者：
N. Yunes
中科院分区：
文献类型：
--
作者：
Kent Yagi;N. Yunes
大多数与致密恒星相关的观测值之间的关系，如中子星或夸克星的质量和半径，通常强烈依赖于它们未知的内部结构。然而，最近发现的I-Love-Q关系（惯性矩、潮汐变形能力和四极矩之间的关系）对这种结构几乎不敏感。这些关系对于广义相对论中无毛定理所示的静止黑洞（BHs）是精确的，主要是因为BHs是具有事件视界的真空解。在本文中，我们迈出了研究I-Love-Q近似关系如何在紧致恒星变成黑洞的极限下变得精确的第一步。为此，我们考虑了致密恒星的玩具模型，即具有各向异性压力的不可压缩恒星，这使我们能够模拟具有不断增加的紧致度的恒星的平衡序列，任意接近BH极限。通过扩展Hartle-Thorne的形式，我们在慢旋转和小潮近似下数值构造了这样一个序列，然后从空间无穷远处度量张量的渐近行为中提取了I-Love-Q三重集。我们发现I-Love-Q关系以非平凡的方式逼近BH极限，四极矩和潮汐变形能力随压实度和各向异性量的增加而变化。通过将麦克劳林椭球推广到各向异性恒星，我们证明了多极矩在牛顿极限下也会随着各向异性的增加而改变符号，因为恒星变长了。我们还分析证明了在强各向异性极限下，当紧致度达到临界黑洞值时，恒星转动惯量达到黑洞极限。然而，当考虑到其他引力理论时，通过一系列各向异性恒星来模拟黑洞极限可能会失败。我们在一个特殊的违反奇偶极子修正理论中计算了标量偶极子电荷和惯性矩，并发现当各向异性恒星序列接近黑洞极限时，这些量并不倾向于它们的黑洞对应量。
The relations between most observables associated with a compact star, such as the mass and radius of a neutron star or a quark star, typically depend strongly on their unknown internal structure. The recently discovered I-Love-Q relations (between the moment of inertia, the tidal deformability and the quadrupole moment) are however approximately insensitive to this structure. These relations become exact for stationary black holes (BHs) in General Relativity as shown by the no-hair theorems, mainly because BHs are vacuum solutions with event horizons. In this paper, we take the first steps toward studying how the approximate I-Love-Q relations become exact in the limit as compact stars become BHs. To do so, we consider a toy model for compact stars, i.e. incompressible stars with anisotropic pressure, which allows us to model an equilibrium sequence of stars with ever increasing compactness that approaches the BH limit arbitrarily closely. We numerically construct such a sequence in the slow-rotation and in the small-tide approximations by extending the Hartle–Thorne formalism, and then extract the I-Love-Q trio from the asymptotic behavior of the metric tensor at spatial infinity. We find that the I-Love-Q relations approach the BH limit in a nontrivial way, with the quadrupole moment and the tidal deformability changing sign as the compactness and the amount of anisotropy are increased. Through a generalization of Maclaurin spheroids to anisotropic stars, we show that the multipole moments also change sign in the Newtonian limit as the amount of anisotropy is increased because the star becomes prolate. We also prove analytically that the stellar moment of inertia reaches the BH limit as the compactness reaches a critical BH value in the strongly anisotropic limit. Modeling the BH limit through a sequence of anisotropic stars, however, can fail when considering other theories of gravity. We calculate the scalar dipole charge and the moment of inertia in a particular parity-violating modified theory and find that these quantities do not tend to their BH counterparts as the anisotropic stellar sequence approaches the BH limit.