Daniela D. Doneva, Stoytcho S. Yazadjiev, Nikolaos Stergioulas, Kostas D. Kokkotas
The famous I-Love-Q relations connect the normalized neutron star moment of inertia I, quadrupole moment Q and the tidal Love number. The most important property of the I-Love-Q relations is that they are practically independent of the EOS for moderate magnetic fields. Several applications were proposed and one of the most important is braking the degeneracy between the spins and the quadrupole moment of neutron star inspirals, and testing alternative theories of gravity. A big portion of the studies are limited to the slowly rotating case. Even though this is a good approximation for a variety of objects, the extension to rapid rotation is also interesting and important.
We have shown that when considering sequences with fixed rotational frequency the equation of state universality is lost. This choice of the parameter is motivated by the observations – the rotational frequency is one of the very few parameters that can be determined with a good accuracy for a big portion of the observed neutron stars. Later studies show, though, that if one uses the normalized rotational frequency instead, the equation of state universality is preserved even for rapid rotation.
We have further explore the I-Q relations for rapidly rotating neutron stars in different alternative theories of gravity. While the results in some cases, such as scalar-tensor theories, have negligible deviations from pure general relativity, in other cases, such as the f(R) theories, the differences can be large thus providing a potential tool for constraining the strong field regime of gravity. But the overall conclusion is that in many cases the I-Love-Q relations will not be useful for testing the generalized theories of gravity due to the normalization of the quantity. If one uses the unnormalized relations, though, the deviations from pure general relativity can be clearly observed.