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

Abstract

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 $$r\ge r_{\text {ms}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>ms</mml:mtext> </mml:msub> </mml:mrow> </mml:math> (the minimally stable radius of particle orbits), while the radii of singularity/throat/horizon $$r&lt;r_{\text {ms}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>ms</mml:mtext> </mml:msub> </mml:mrow> </mml:math> . Also, its Page–Thorne efficiency $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math> is found to increase with decreasing $$r_{\text {ms}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>ms</mml:mtext> </mml:msub> </mml:math> and also yields $$\epsilon =0.0572$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.0572</mml:mn> </mml:mrow> </mml:math> for Schwarzschild black hole (SBH). But in the singular limit $$r\rightarrow r_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> (radius of singularity), we have $$\epsilon \rightarrow 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>→</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> giving rise to $$100 \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>100</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $$\frac{d{\mathcal {L}}_{\infty }}{d\ln {r}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>ln</mml:mo> <mml:mi>r</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $$L_{\text {Edd}}^{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mrow> <mml:mtext>Edd</mml:mtext> </mml:mrow> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:math> for BNS could be arbitrarily large at $$r\rightarrow r_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> due to the scalar field $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> that is defined in $$(r_{s}, \infty )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

Topics & Concepts