Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green’s function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-G...Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green’s function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating Bañados-Teitelboim-Zanelli black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.展开更多
In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.
In the framework of the gravity＇s rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically ...In the framework of the gravity＇s rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle＇s energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as TH In 3, which is consistent with Hod＇s conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle＇s energy, even though the area itself depends on the particle＇s energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.展开更多
In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correcti...In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.展开更多
An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal op...An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal operator, has (SI)decomposition if and only if it is similar to D ( 0≤j<N λjS), where D is a diagonaloperator, λj is a positive number, N is a natural number or ∞, and S is the unilateral shift.展开更多
Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner Nordstrom black hole surrounded by a static and spherically symmetric quintessenc...Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner Nordstrom black hole surrounded by a static and spherically symmetric quintessence. We study the variation of quasinormal frequencies with the quintessential state parameter ε, the total angular momentum number ｜k｜, the charge Q, and the overtone number n changes, respectively. Moreover, from the results we obtained, we find that the massless Dirac field damps more slowly due to the presence of quintessence.展开更多
We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole.The objectpicture of the quasinormal ringing has been obtained by the finite difference method.Compared with a Schwarzs...We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole.The objectpicture of the quasinormal ringing has been obtained by the finite difference method.Compared with a Schwarzschildblack hole,the results show that the electromagnetic field damps more slowly for a stringy black hole.展开更多
The quasinormal modes（QNMs） of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative ap...The quasinormal modes（QNMs） of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal（QNM） frequencies.展开更多
We have investigated the quasinormal modes （QNMs） of phantom scalar perturbation in a Reissner Nordstr6m （RN） background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation...We have investigated the quasinormal modes （QNMs） of phantom scalar perturbation in a Reissner Nordstr6m （RN） background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the Q, NMs and the second order thermodynamic phase transition.展开更多
In our previous work [Chin. Phys. Lett. 35（2018） 010410], the quasinormal modes of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the th...In our previous work [Chin. Phys. Lett. 35（2018） 010410], the quasinormal modes of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel–Kramers–Brillouin approximative approach. In this study, we extend the work to the cases of gravitational, electromagnetic and massless Dirac perturbations. The result further confirms that the noncommutative parameter plays an important role for the quasinormal frequencies.展开更多
The massless scalar quasiaormal modes （QNMs） of a stationary axisymmetric Einstein-Maxwell dilato-axioa （EMDA） black hole are calculated numerically using the continued fraction method first proposed by Leaver. Th...The massless scalar quasiaormal modes （QNMs） of a stationary axisymmetric Einstein-Maxwell dilato-axioa （EMDA） black hole are calculated numerically using the continued fraction method first proposed by Leaver. The fundamental quasinormal frequencies （slowly damped QNMs） are obtained and the peculiar behaviours of them are studied. It is shown that these frequencies depend on the dilaton parameter D, the rotational parameter a, the multiple moment l and the azimuthal number m, and have the same values with other authors at the Schwarzschild and Kerr limit.展开更多
We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is fou...We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.展开更多
Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,wh...Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.展开更多
文摘Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green’s function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating Bañados-Teitelboim-Zanelli black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.
基金Foundation item： Supported by the National Nature Science Foundation of China（11071229） Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions（10KJD110004）
文摘In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.
基金Project supported by the National Natural Science Foundation of China (Grant No 10875012)the Natural Science Foundation of Shandong Province of China (Grant No Y2008A33)+1 种基金the Research Projects of Education Bureau of Shandong Province of China(Grant No J08L151)the Doctoral Foundation of Binzhou University, China (Grant No 2007Y02)
文摘In the framework of the gravity＇s rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle＇s energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as TH In 3, which is consistent with Hod＇s conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle＇s energy, even though the area itself depends on the particle＇s energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.
基金Project supported by the National Natural Science Foundation of China (Grant No.10873004)the Key Project of the National Natural Science Foundation of China (Grant No.10935013)+1 种基金the Scientific Research Fund of the Educational Department of Hunan Province of China (Grant No.08B051)the Program for Excellent Talents in Hunan Normal University and the State Key Development Program for Basic Research Program of China (Grant No.2010CB832803)
文摘In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.
文摘An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal operator, has (SI)decomposition if and only if it is similar to D ( 0≤j<N λjS), where D is a diagonaloperator, λj is a positive number, N is a natural number or ∞, and S is the unilateral shift.
基金Supported by the National Natural Science Foundation of China under Grant No. 10573004
文摘Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner Nordstrom black hole surrounded by a static and spherically symmetric quintessence. We study the variation of quasinormal frequencies with the quintessential state parameter ε, the total angular momentum number ｜k｜, the charge Q, and the overtone number n changes, respectively. Moreover, from the results we obtained, we find that the massless Dirac field damps more slowly due to the presence of quintessence.
基金National Natural Science Foundation of China under Grant No.10573004
文摘We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole.The objectpicture of the quasinormal ringing has been obtained by the finite difference method.Compared with a Schwarzschildblack hole,the results show that the electromagnetic field damps more slowly for a stringy black hole.
基金Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02
文摘The quasinormal modes（QNMs） of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal（QNM） frequencies.
基金Supported by the National Natural Science Foundation of China under Grant No.10905020the China Postdoctoral Science Foundation under Grant Nos.201003245 and 20090460592
文摘We have investigated the quasinormal modes （QNMs） of phantom scalar perturbation in a Reissner Nordstr6m （RN） background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the Q, NMs and the second order thermodynamic phase transition.
基金Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02
文摘In our previous work [Chin. Phys. Lett. 35（2018） 010410], the quasinormal modes of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel–Kramers–Brillouin approximative approach. In this study, we extend the work to the cases of gravitational, electromagnetic and massless Dirac perturbations. The result further confirms that the noncommutative parameter plays an important role for the quasinormal frequencies.
基金Project supported by the National Natural Science Foundation of China （Grant No 10473004）, the FADEDD （Grant No 200317）, and the SRFDP （Grant No 20040542003）.
文摘The massless scalar quasiaormal modes （QNMs） of a stationary axisymmetric Einstein-Maxwell dilato-axioa （EMDA） black hole are calculated numerically using the continued fraction method first proposed by Leaver. The fundamental quasinormal frequencies （slowly damped QNMs） are obtained and the peculiar behaviours of them are studied. It is shown that these frequencies depend on the dilaton parameter D, the rotational parameter a, the multiple moment l and the azimuthal number m, and have the same values with other authors at the Schwarzschild and Kerr limit.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11647050,11675139 and 51575420the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 16JK1394
文摘We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.
基金Supported by the the Natural Science Foundation of Hunan Province,China (2022J40262)the National Natural Science Foundation of China (12375046,12205254)。
文摘Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.
