Can accretion disk properties observationally distinguish black holes from naked singularities?

Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. In the context of stationary and axially symmetrical geometries, a possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around axially-symmetric rotating naked singularities, obtained as solutions of the field equations in the Einstein-massless scalar field theory. A first major difference between rotating naked singularities and Kerr black holes is in the frame dragging effect, the angular velocity of a rotating naked singularity being inversely proportional to its spin parameter. Because of the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities. For specific values of the spin parameter and of the scalar charge, the energy flux from the disk around a rotating naked singularity can exceed by several orders of magnitude the flux from the disk of a Kerr black hole. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation by rotating naked singularities is always higher than the conversion efficiency for black holes, i.e., naked singularities provide a much more efficient mechanism for converting mass into radiation than black holes. Thus, these observational signatures may provide the necessary tools from clearly distinguishing rotating naked singularities from Kerr-type black holes.

Figure 1

Radii of circular equatorial orbits around a black hole ($\gamma =1.00$), and a naked singularity ($\gamma =0.99$, 0.7 and 0.5), with a total mass $M$, as functions of the spin parameter $a_{*}$. The dashed curves show the direct orbits, and the dotted curves represent the retrograde ones. The event horizon/singularity is denoted by a solid curve, while the horizontal dotted-dashed line at $2M$ represents the ergosphere in the equatorial plane.

Figure 2

The function $d^{2}V/d(r/M{)}^2$ versus $r/M$ for a rotating black hole, with ($\gamma =1$), and a naked singularity ($\gamma =0.99$, 0.7, and 0.5), with a total mass $M$. The spin parameter $a_{*}$ is set to 0.99, 0.9, 0.7 and 0, respectively.

Figure 3

The radial profile of $\omega$ near the rotating naked singularity with $\gamma =0.9$, for different spin parameters.

Figure 4

The radial profiles of $\Omega$, ${\Omega }_{\min }$, ${\Omega }_{\max }$ and $\omega$ for black holes with $\gamma =1$ and for the rotating naked singularity with $\gamma =0.99$, 0.9, 0.7, 0.5, 0.4, and 0.2, respectively. The spin parameter $a_{*}$ is set to 0.99, 0.7 and 0, respectively.

Figure 5

The radial profiles of the ratio $\Omega /\omega$ for $\gamma =0.4$ (left-hand panel) and $\gamma =0.2$ (right-hand panel), for different values of the spin parameter.

Figure 6

The energy flux $F(r)$ radiated by the disk around a rotating black hole ($\gamma =1$), and a naked singularity ($\gamma =0.99$, 0.7, 0.5, 0.4 and 0.2), with the total mass $5M_{\odot }$, for different values of the spin parameter $a_{*}$. The mass accretion rate is set to ${10}^{-12}{M}_{\odot }/\mathrm{yr}$.

Figure 7

The temperature distribution on a disk around a rotating black hole ($\gamma =1$), and a naked singularity ($\gamma =0.99$, 0.7, 0.5, 0.4 and 0.2), with the total mass of $5M_{\odot }$, for different values of the spin parameter $a_{*}$. The mass accretion rate is set to ${10}^{-12}{M}_{\odot }/\mathrm{yr}$.

Figure 8

The accretion disk spectra for a rotating black hole ($\gamma =1$), and a naked singularity ($\gamma =0.99$, 0.7, 0.5, 0.4 and 0.2), with the total mass of $5M_{\odot }$, for different values of the spin parameter $a_{*}$. The mass accretion rate is set to ${10}^{-12}{M}_{\odot }/\mathrm{yr}$.

Figure 9

Coordinate-dependent Eddington luminosity as a function of the radial coordinate $r$ for the case of a static naked singularity with total mass $M=5M_{\odot }$, and for different values of $\gamma$.