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 rge 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 rrightarrow 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 }}{dln {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 rrightarrow 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.
Highlights
L accretion luminosity d L∞ d ln r of Buchdahl naked singularity (BNS) is always substantially larger than that of Schwarzschild black holes (BH) (SBH), while
The two major takeaways from the present investigation are: (1) the possibility of conversion of NS into an everywhere regular asymptotically flat WH solution and vice versa, while both lead to Schwarzschild BH (SBH) as a special cases
To elaborate what we mean, consider vacuum Jordan frame (JF) Brans–Dicke theory in the JF with the scalar field φ playing the role of spin−0 gravity
Summary
To elaborate what we mean, consider vacuum Jordan frame (JF) Brans–Dicke theory in the JF with the scalar field φ playing the role of spin−0 gravity. This coordinates can be extended to cover the full-patch (−∞ < < +∞), which assumes the more familiar form of EBWH [60,61] but we shall not use this form for our purposes Like their JF predecessors, the two EF re-incarnations, BNS and EBWH, are not independent solutions – one can be obtained from the other, to be shown in Sect. The purpose of this paper is to explicitly show how the above famous solutions, Brans I, BNS, EBWH and SBH, are connected with one another and to study the kinematic and emissivity properties of accretion around the last three objects.
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