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

TL;DR

This paper explores how accretion properties can differentiate between naked singularities, wormholes, and black holes, revealing distinct efficiency and luminosity profiles that could help identify these objects observationally.

Contribution

It introduces a mathematical method to derive these objects from the Jordan frame vacuum Brans I solution and analyzes their accretion characteristics using the Page-Thorne model.

Findings

Accretion efficiency approaches 1 near the singularity, indicating high energy conversion.

Buchdahl naked singularity exhibits higher differential luminosity than Schwarzschild black hole.

Eddington luminosity for BNS can be arbitrarily large due to scalar field effects.

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 $r\geq r_{\text{ms}}$ (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 $r\rightarrow r_{s}$ (radius of singularity), we have $\epsilon\rightarrow 1$ 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 $r\rightarrow r_{s}$ due to the scalar field $\phi$ 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.