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Novel Shadows from the Asymmetric Thin-Shell Wormhole

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Novel Shadows from the Asymmetric Thin-Shell Wormhole Physics Letters B 811 (2020) 135930 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Novel shadows from the asymmetric thin-shell wormhole ∗ Xiaobao Wang a, Peng-Cheng Li b,c, Cheng-Yong Zhang d, Minyong Guo b, a School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, PR China b Center for High Energy Physics, Peking University, No. 5 Yiheyuan Rd, Beijing 100871, PR China c Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No. 5 Yiheyuan Rd, Beijing 100871, PR China d Department of Physics and Siyuan Laboratory, Jinan University, Guangzhou 510632, PR China a r t i c l e i n f o a b s t r a c t Article history: For dark compact objects such as black holes or wormholes, the shadow size has long been thought to Received 29 September 2020 be determined by the unstable photon sphere (region). However, by considering the asymmetric thin- Accepted 2 November 2020 shell wormhole (ATSW) model, we find that the impact parameter of the null geodesics is discontinuous Available online 6 November 2020 through the wormhole in general and hence we identify novel shadows whose sizes are dependent of Editor: N. Lambert the photon sphere in the other side of the spacetime. The novel shadows appear in three cases: (A2) The observer’s spacetime contains a photon sphere and the mass parameter is smaller than that of the opposite side; (B1, B2) there’ s no photon sphere no matter which mass parameter is bigger. In particular, comparing with the black hole, the wormhole shadow size is always smaller and their difference is significant in most cases, which provides a potential way to observe wormholes directly through Event Horizon Telescope with better detection capability in the future. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction two distinct Schwarzschild spacetimes whose difference is only the mass parameter [14]. The Generic spherically symmetric dy- The image of M87* taken by Event Horizon Telescope made its namic thin-shell traversable wormholes and their stabilities were debut and revealed the shadow of black holes in April 2019 [1], discussed in [15]. Using the backward ray-tracing method, we care- which has ignited a wave of researches into the shadows of black fully analyze the ingoing null particles that emit from the observer’ holes. As is well-known, the shadow size of a black hole is con- s position in one side and pass through the throat to the opposite sidered to be determined by the unstable photon sphere (region) side of the thin shell. Note that the static observers on both sides other than the event horizon from the earliest work [2,3]. As one of the spacetime are different, thus we first find the impact pa- of the most important predictions of general relativity (GR) be- rameter of the same photon defined in each side is different and sides black holes, wormhole spacetime [4]also contains unstable related by a simple equation. Correspondingly, the turning point photon sphere which also creates shadows which were found to in each side for the same photon becomes different. Considering a be different from the black holes in the size or the oblateness, see physical process that ingoing photons with no turning point would examples in [5–10]. Even though it has been shown a traversable fall into the thin shell and then turn into outgoing in the other wormhole with ordinary matter is not allowed in GR, if there is side, we first find some of them may hit its turning point de- some exotic matter in the universe, it becomes possible [11,12]. fined in this spacetime and then turn back to its birthplace. Thus, Furthermore, if the exotic matter distributes into a thin shell, a we can see the difference between the traversable wormhole and simple model of thin-shell wormhole can be constructed by the black hole from the null geodesic motion. It’s worth noting that for “cut and paste” technique [13,14]. And as far as we know, the a black hole, the light that enters the event horizon never returns, shadow of a asymmetric thin-shell wormhole has not been studied since the event horizon is a “one-way” membrane. before in general. Based on our new finding, we identify novel shadows in ATSW In this letter, we focus on an asymmetric thin-shell wormhole spacetime (see [16]for a similar study). In particular, these novel (ATSW) spacetime, more specially, a static thin shell connecting shadows originate from spacetime asymmetry of both sides con- nected by the throat and their sizes do not depend on the photon sphere, contrary to what we typically think about. Specifically, let’s Corresponding author. * assume we stay in the spacetime M and the radius of the thin E-mail addresses: [email protected] (X. Wang), [email protected] 1 (P.-C. Li), [email protected] (C.-Y. Zhang), [email protected] shell is R. See Fig. 1, the shadow of the wormhole seen by the (M. Guo). static observer is the same with that of the corresponding black https://doi.org/10.1016/j.physletb.2020.135930 0370-2693/© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. X.Wang,P.-C.Li,C.-Y.Zhangetal. Physics Letters B 811 (2020) 135930 b2 = r2/ f (√r) has two real roots for the positive branch of r when b ≥ bc = 3 3M. For b = bc , both roots are equal to r ph = 3M is known as the radius of photon sphere. For b > bc , the roots are ad- dressed as the turning points with the larger root rl > r ph and the = s ph smaller one 2M rh < r < r , where rh is the radius of the event l,s l,s l,s horizon. Also, we introduce a new parameter b ≡ r / f (r ) that will be later used. Moreover, considering a distant static ob- server at (to, ro →∞, π/2, 0), the angular radius of the shadow c left by the photon sphere satisfies sin θ = b /ro and the radius of sh c the shadow is defined by r ≡ ro sin θ = b , as seen in Fig. 2. Next, let’s introduce some necessary background knowledge of thin-shell wormhole using cut-and-paste method, that is, two dis- tinct spacetimes M1,2 with different parameters are glued by a thin shell which forms a new manifold M = M1 ∪ M2, as seen in Fig. 3. We suppose that a spherical thin shell is moving in a spher- ically symmetric spacetime and the metrics on both sides take in Fig. 1. The shadow of thin-shell wormhole for various parameters. There is novel this form shadow for some situations. 2 2 −1 2 2 2 ds =−fi(ri)dt + f (ri)dr + r d , (3) M ≤ ph i i i i i hole when 1 contains the photon sphere R r1 and M1 > M2, where i = 1, 2, and by focusing on the Schwarzschild case we have that is, there is no novel shadow and the throat behaves like an 2Mi fi (r) = 1 − , where Mi are the mass parameters. “event horizon”. However, we find novel shadows in other cases. ri ph When R ≤ r and M2 > M1, the shadow size of the wormhole The local tetrads in the neighborhood of the thin shell of each 1 √ M sh R−2M2 spacetime 1,2 becomes r = 3 3M2 − which is determined by the pho- 1 R 2M1 ton sphere of the opposite side and always smaller than that in − 1 ∂ a ea ≡ f 2 (R) , (4) Schwarzschild √spacetime since the photons with the impact pa- ti i ∂t M i rameter b1 < 3 3M1 would fall into the spacetime 2 and turn a M a ∂ back to 1 which never occurs for black hole.√ In particular, the e ≡ f (R) , (5) ri i size of the shadow can range from zero to 3 3M1, so that for ∂ri some parameters the difference can be large enough to be de- are related by the following Lorentz transformation [17] tected to distinguish the wormhole from the black hole. When ph a a there is no photon sphere in M , that is, R r , surprisingly, e e 1 > 1 t2 = − t1 a (1 2) a , (6) there also exists a novel shadow. For M > M since R is the turn- e e 1 2 r2 r1 ing point for certain null geodesics with the corresponding impact R R where we have defined parameter b1 and the photons with b1 < b1 will go through the thin shell and never turn back, the shadow of the wormhole de- = cosh sinh sh = R () , (7) pends on the thin shell and its radius is r1 . While for sinh cosh f1(R) { } M M2 > M1 and max 2M2, 3M1 < R < 3M2, the side 2 contains with R the photon sphere and some null geodesics with b1 < b1 could M ˙ turn back after arriving at the spacetime 2, thus the critical im- −1 i R √ i = sinh . (8) R−2M2 pact parameter is 3 3M2 − and the novel shadow size is fi(R) √ R 2M1 sh R−2M2 R ˙ r = 3 3M2 which is smaller than b .
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