Can accretion properties distinguish between a naked singularity, wormhole and black hole?

Abstract

We first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page-Thorne model which studies accretion properties exclusively for $r\ge r_{\text{ms}}$ (the minimally stable radius of particle orbits), while the radii of singularity/ throat/ horizon $r<r_{\text{ms}}$. Also, its Page-Thorne efficiency $\epsilon$ is found to increase with decreasing $r_{\text{ms}}$ and also yields $\epsilon =0.0572$ for Schwarzschild black hole (SBH). But in the singular limit $r\to r_s$ (radius of singularity), we have $\epsilon \to 1$ giving rise to $100\%$ efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $\frac{d{\mathcal{L}}_{\infty }}{d\ln r}$ of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $L_{\text{Edd}}^{\infty }$ for BNS could be arbitrarily large at $r\to r_s$ due to the scalar field $\varphi$ that is defined in $(r_s,\infty )$. It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

17 pages, 12 figures

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Cited by in corpus (1)

• Accretion flows around exotic tidal wormholes I. Ray-tracing