旋转Damour-Solodukhin虫洞的吸积盘：新发现的运动学与发射特性

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本文主要探讨了Bueno等人提出的新型旋转Damour-Solodukhin虫洞（RDSWH），即Kerr状虫洞在引力波信号中的回声特性。这个虫洞模型是一种旋转的广义化，与经典的Kerr黑洞(KBH)有相似之处，特别是在其运动学性质上。作者发现，RDSWH的关键参数，如innermost stable circular orbit (ISCO)、marginally stable radius (r_{ms})、效率(ε)以及disk potential (V_{eff})，对于特定的旋转参数λ而言是独立的，这表明它们与给定旋转的KBH具有相同的物理特性。然而，研究指出当λ的值较高，具体在0.1 < λ ≤ 1范围内，特别是当自旋接近极限值a_{\star} = 0.998时，虫洞的发射率特性开始出现差异。这种发射率的多样性可能为观测提供了独特的线索，因为不同λ值下的发光度峰值行为呈现出相反的趋势，这对于理论与实际观测之间的对比分析极具价值。此外，文章还讨论了辐射通量F(r)的最大值Δ_λ，尽管存在变化，但目前的估计值仍然很小，尚处于无法直接观测的水平。这一结果提示着未来可能的技术进步能够探测到这类虫洞的细微差异，从而进一步验证或扩展我们对极端天体物理学的认识。这篇研究不仅深化了我们对旋转虫洞的理解，也强调了在高精度的引力波观测和理论模型之间建立联系的重要性。它为黑洞物理学的研究者提供了一个新的角度来探索黑洞与周围环境的相互作用，尤其是在吸积盘的动态特性方面。

Eur. Phys. J. C (2019) 79:952

https://doi.org/10.1140/epjc/s10052-019-7488-7

Regular Article - Theoretical Physics

Accretion disk around the rotating Damour–Solodukhin wormhole

R. Kh. Karimov

,R.N.Izmailov

1,a

, K. K. Nandi

1,2

Zel’dovich International Center for Astrophysics, Bashkir State Pedagogical University, 3A, October Revolution Street, Ufa 450008, RB, Russia

High Energy Cosmic Ray Research Center, University of North Bengal, Darjeeling, WB 734 013, India

Received: 5 October 2019 / Accepted: 12 November 2019 / Published online: 21 November 2019

Abstract A new rotating generalization of the Damour–

Solodukhin wormhole (RDSWH), called Kerr-like worm-

hole, has recently been proposed and investigated by Bueno

et al. for echoes in the gravitational wave signal. We show a

novel feature of the RDSWH, viz., that the kinematic prop-

erties such as the ISCO or marginally stable radius r

,efﬁ-

ciency  and the disk potential V

eff

are independent of λ

(which means they are identical to their KBH counterparts

for any given spin). Differences however appear in the emis-

sivity properties for higher values 0.1 <λ≤ 1 (say) and for

the extreme spin a



= 0.998. The kinematic and emissivity

are generic properties as variations of the wormhole mass

and the rate of accretion within the model preserve these

properties. Speciﬁcally, the behavior of the luminosity peak

is quite opposite to each other for the two objects, which

could be useful from the viewpoint of observations. Apart

from this, an estimate of the difference Δ

in the maxima of

ﬂux of radiation F(r) shows non-zero values but is too tiny

to be observable at present for λ<10

−3

permitted by the

strong lensing bound. The broad conclusion is that RDSWH

are experimentally indistinguishable from KBH by accretion

characteristics.

1 Introduction

There is a renewed interest in wormholes after it has been

realized that they can mimic post-merger ring-down ini-

tial quasi-normal mode (QNM) spectrum of gravitational

waves. To our knowledge, this possibility of “wormhole

QNM mode” was ﬁrst put forward by Damour and Solo-

dukhin [1], where resonances were trapped in a double-

hump potential associated with what they termed “black

hole foil”. This is an example of a horizonless wormhole

e-mail: izmailov.ramil@gmail.com

more commonly known as the Damour–Solodukhin worm-

hole (DSWH). The DSWH differs from the Schwarzschild

black hole (SBH) by a dimensionless real deviation parame-

ter λ and represents a twice-asymptotically ﬂat regular space-

time connected by a throat. The authors showed that if λ is

so small that the time scale Δt = 2GM ln





is longer

than the observational time scale, the signals emitted by a

source falling into a wormhole will contain the usual QNM

ringing signature of a black hole, in spite of the absence of

a true horizon [1]. Völkel and Kokkotas [2] have recently

shown, using an inverse method, that the knowledge of the

observed QNM spectrum can allow one to also accurately

construct the double hump Pöschl–Teller potential approxi-

mating that of DSWH. Bueno et al. [3] suitably redeﬁned the

static DSWH and further generalized it the into a Kerr-like

wormhole, called here the rotating DSWH or RDSWH for

brevity. They studied its gravitational wave echo properties.

Gravitational deﬂection of relativistic massive particles by

RDSWH has been recently studied by Jusuﬁ et al. [4].

QNM ringing by BHs have been well reviewed, see, e.g.

Bertietal.[5] but ringing by WHs still remained an open

question. A ﬁrst step towards answering the question was

initiated by Cardoso et al. [6,7], who studied the QNM ring-

ing using a wormhole assembled by means of Visser’s cut-

and-paste surgery of two copies of Schwarzschild black holes

(SBH) at a radius close to the horizon [8] (For future perspec-

tives and new directions of research on ultracompact objects

(UCO) including wormholes, see [9]). The authors of [8]

showed that, while the time evolution of the early QNMs

accurately mimic those from SBH horizon, the differences (if

any) would appear only at later times. This work inspired an

investigation in [10], where it has been shown that the mass-

less Ellis–Bronnikov wormhole (EBWH) [11–13], made of

the minimally coupled exotic scalar ﬁeld, can also reproduce

the black hole QNM spectrum in the eikonal limit (large

). Ringing by massive EBWH was studied in [14]. These

developments prompt a natural inquiry as to whether static

DSWH can exhibit mimicking of SBH in other phenomenon

123

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