I-Love-Q relations: from compact stars to black holes


Kent Yagi, Nicolas Yunes


Classical and Quantum Gravity


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.



How is this information collected?

This collection of Montana State authored publications is collected by the Library to highlight the achievements of Montana State researchers and more fully understand the research output of the University. They use a number of resources to pull together as complete a list as possible and understand that there may be publications that are missed. If you note the omission of a current publication or want to know more about the collection and display of this information email Leila Sterman.