Abstract
We study the observational properties of a class of exact solutions of Einstein’s field equations describing stationary, axially symmetric, rigidly rotating dust (i.e. non-interacting particles). We ask the question whether such solutions can describe astrophysical rotating dark matter clouds near the center of galaxies and we probe the possibility that they may constitute an alternative to supermassive black holes at the center of galaxies. We show that light emission from accretion disks made of ordinary baryonic matter in this space-time has several differences with respect to the emission of light from similar accretion disks around black holes. The shape of the iron Kalpha line in the reflection spectrum of accretion disks can potentially distinguish this class of solutions from the Kerr metric, but this may not be possible with current X-ray missions.
Highlights
The study of the disk’s reflection spectrum is a promising tool to observationally test the space-time metric around these supermassive objects [9,10,11,12]
We ask the question whether such solutions can describe astrophysical rotating dark matter clouds near the center of galaxies and we probe the possibility that they may constitute an alternative to supermassive black holes at the center of galaxies
The shape of the iron Kα line in the reflection spectrum of accretion disks can potentially distinguish this class of solutions from the Kerr metric, but this may not be possible with current X-ray missions
Summary
The study of the disk’s reflection spectrum is a promising tool to observationally test the space-time metric around these supermassive objects [9,10,11,12]. We focus on rotating non-vacuum solutions as possible candidates for supermassive compact objects. This is an ideal natural continuation of the work presented in Ref. The model is made of three elements: (i) As the matter source that determines the geometry we consider a cloud of rigidly rotating dust (i.e. non-interacting particles). One can think of such a pressureless fluid which does not interact with ordinary particles as describing the central region of a dark matter cloud To this aim, we will focus on an exact solution describing a rigidly rotating dust cloud that was first discussed by Bonnor in Ref. 2, we briefly discuss stationary axially symmetric solutions of Einstein’s field equations and in particular rigidly rotating dust.
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