Evolution of the spin parameter of accreting compact objects with non-Kerr quadrupole moment

Abstract

There is robust observational evidence supporting the existence of $5-20$ $M_{\odot }$ compact bodies in X-ray binary systems and of $10^5-10^9$ $M_{\odot }$ bodies at the center of many galaxies. All these objects are commonly interpreted as black holes, even is there is no direct evidence that they have an event horizon. A fundamental limit for a black hole in 4-dimensional general relativity is the Kerr bound $|a_{\ast }|\le 1$, where $a_{\ast }$ is the spin parameter. This is just the condition for the existence of the event horizon. The accretion process can spin a black hole up to $a_{\ast }\approx 0.998$ and some super-massive objects in galactic nuclei could be rapidly rotating black holes with spin parameter close to this limit. However, if these super-massive objects are not black holes, the Kerr bound does not hold and the accretion process can spin them up to $a_{\ast }>1$. In this paper, I consider compact bodies with non-Kerr quadrupole moment. I study the evolution of the spin parameter due to accretion and I find its equilibrium value. Future experiments like the gravitational wave detector LISA will be able to test if the super-massive objects at the center of galaxies are the black holes predicted by general relativity. If they are not black holes, some of them may be super-spinning objects with $a_{\ast }>1$.

20 pages, 16 figures. v2: published version with a few typos corrected

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