Chaotic motion around a black hole under minimal length effects
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Regular Article - Theoretical Physics
Chaotic motion around a black hole under minimal length effects Xiaobo Guo1,a , Kangkai Liang3,4,b , Benrong Mu2,c , Peng Wang3,d , Mingtao Yang3,e 1
Mechanical and Electrical Engineering School, Chizhou University, Chizhou 247000, People’s Republic of China Physics Teaching and Research section, College of Medical Technology, Chengdu University of Traditional Chinese Medicine, Chengdu 611137, People’s Republic of China 3 Center for Theoretical Physics, College of Physics, Sichuan University, Chengdu 610064, People’s Republic of China 4 Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
2
Received: 24 March 2020 / Accepted: 9 August 2020 © The Author(s) 2020
Abstract We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
1 Introduction Chaos is now one of the most important ideas to understand various nonlinear phenomena in general relativity. Chaos in geodesic motion can lead to astrophysical applications and provide some important insight into AdS/CFT correspondence. However, the geodesic motion of a point particle in the generic Kerr–Newman black hole spacetime is well known to be integrable [1], which leads to the absence of chaos. So complicated geometries of spacetime or extra forces imposed upon the particle are introduced to study the chaotic geodesic motion of a test particle. Examples of chaotic behavior of geodesic motion of particles in various backgrounds were considered in [2–8] . On the other hand, the geodesic motion of a ring string instead of a point particle has been shown to exhibit chaotic behavior in a Schwarzschild black hole [9]. Later, the chaotic dynamics of ring strings was studied in other black hole backgrounds [10–12]. Among the various indicators for detecting chaos, the Melnikov method is an analytical approach applicable to near a e-mail:
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integrable perturbed systems and has as its main advantages the fact that only knowledge of the unperturbed integrable dynamics is required [13]. The Melnikov method has been used to discuss the chaotic behavior of geodesic motion in black holes perturbed by gravitational waves [14,15], electromagnetic fields [16] and a thin disc [17]. Recently, chaos due to temporal and spatially periodic perturbations in charged AdS black holes has also been investigated via the Melnikov method [18–21]. The existence of a minimal measurable length has been observed in various quantum theories of gravity such as string theory [22–2
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