In this paper,we investigate the gravitational quasi-normal modes(QNMs)of Horndeski hairy black holes.By using the ordinary finite element method,the relations between the QNMs and the parameters of black holes are mi...In this paper,we investigate the gravitational quasi-normal modes(QNMs)of Horndeski hairy black holes.By using the ordinary finite element method,the relations between the QNMs and the parameters of black holes are minutely shown.Both the oscillating frequency and the decay rate increase with the increase of the scalar charge Q.While the oscillating frequency and the decay rate decrease with the black hole mass M increasing.And the quasi-period of the oscillation decreases when the angular momentum l of the perturbation field increases.However,the decay rate has barely changed for different values of 1.Thus,the numerical results indicate that Horndeski black holes are stable.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
Quasinormal modes （QNMs） for Dirac perturbations off（R） black holes （BHs） are described in this paper, involving two types of f（R） solution： f（R） （Sehwarzschild） BHs and f（R） （Maxwell） BHs. With the f...Quasinormal modes （QNMs） for Dirac perturbations off（R） black holes （BHs） are described in this paper, involving two types of f（R） solution： f（R） （Sehwarzschild） BHs and f（R） （Maxwell） BHs. With the finite difference method, the stability of the f（R） black holes （BHs） is analysed and the threshold range off（R） （Schwarzschild） BHs and f（R） （Maxwell） BHs is defined respectively. The results show that due to the presence of the correction factor Ro, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values [k] on the f（R） BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with ]k[ increasing. Furthermore, under the Dirac perturbation, the stability off（R） solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters （]k], charge Q and mass m） are discussed in massless, and massive cases, by contrast to the classical BHs.展开更多
Quasinormal modes(QNMs)for massless and massive Dirac perturbations of Born-Infeld black holes(BHs)in higher dimensions are investigated.Solving the corresponding master equation in accordance with hypergeometric func...Quasinormal modes(QNMs)for massless and massive Dirac perturbations of Born-Infeld black holes(BHs)in higher dimensions are investigated.Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated.We discuss the relationships between QNM frequencies and spacetime dimensions.Meanwhile,we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field.Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n.This shows that the Born-Infeld BHs become more and more unstable at higher dimensions.Furthermore,the traditional finite difference method is improved,so that it can be used to calculate the massive Dirac field.We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field.Because the number of extra dimensions is related to the string scale,there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.展开更多
In this paper, we describe quasinormal modes（QNMs） for gravitational perturbations of Einstein-GaussBonnet black holes（BHs） in higher dimensional spacetimes, and derive the corresponding parameters of such black h...In this paper, we describe quasinormal modes（QNMs） for gravitational perturbations of Einstein-GaussBonnet black holes（BHs） in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime（flat, de Sitter（d S） and anti-de Sitter（Ad S））. Our attention is concentrated on discussing the（in）stability of Einstein-Gauss-Bonnet Ad S BHs through the temporal evolution of all types of gravitational perturbation fields（tensor, vector and scalar）. It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore,the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet Ad S BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet Ad S BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds.展开更多
文摘In this paper,we investigate the gravitational quasi-normal modes(QNMs)of Horndeski hairy black holes.By using the ordinary finite element method,the relations between the QNMs and the parameters of black holes are minutely shown.Both the oscillating frequency and the decay rate increase with the increase of the scalar charge Q.While the oscillating frequency and the decay rate decrease with the black hole mass M increasing.And the quasi-period of the oscillation decreases when the angular momentum l of the perturbation field increases.However,the decay rate has barely changed for different values of 1.Thus,the numerical results indicate that Horndeski black holes are stable.
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 FAPESP No.2012/08934-0National Natural Science Foundation of China under Grant Nos.11205254,11178018,11375279,11605015+1 种基金the Natural Science Foundation Project of CQ CSTC 2011BB0052the Fundamental Research Funds for the Central Universities 106112016CDJXY300002 and CDJRC10300003
文摘Quasinormal modes （QNMs） for Dirac perturbations off（R） black holes （BHs） are described in this paper, involving two types of f（R） solution： f（R） （Sehwarzschild） BHs and f（R） （Maxwell） BHs. With the finite difference method, the stability of the f（R） black holes （BHs） is analysed and the threshold range off（R） （Schwarzschild） BHs and f（R） （Maxwell） BHs is defined respectively. The results show that due to the presence of the correction factor Ro, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values [k] on the f（R） BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with ]k[ increasing. Furthermore, under the Dirac perturbation, the stability off（R） solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters （]k], charge Q and mass m） are discussed in massless, and massive cases, by contrast to the classical BHs.
基金Supported by Natural Science Foundation Project of Qinghai Office of Science and Technology(2019-ZJ-973Q,2019-ZJ-A10)National Natural Science Foundation of China(11873001)。
文摘Quasinormal modes(QNMs)for massless and massive Dirac perturbations of Born-Infeld black holes(BHs)in higher dimensions are investigated.Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated.We discuss the relationships between QNM frequencies and spacetime dimensions.Meanwhile,we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field.Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n.This shows that the Born-Infeld BHs become more and more unstable at higher dimensions.Furthermore,the traditional finite difference method is improved,so that it can be used to calculate the massive Dirac field.We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field.Because the number of extra dimensions is related to the string scale,there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.
基金Supported by FAPESP(2012/08934-0)National Natural Science Foundation of China(11205254,11178018,11375279,11605015)+1 种基金the Natural Science Foundation Project of CQ CSTC(2011BB0052)the Fundamental Research Funds for the Central Universities(106112016CDJXY300002,106112017CDJXFLX0014,CDJRC10300003)
文摘In this paper, we describe quasinormal modes（QNMs） for gravitational perturbations of Einstein-GaussBonnet black holes（BHs） in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime（flat, de Sitter（d S） and anti-de Sitter（Ad S））. Our attention is concentrated on discussing the（in）stability of Einstein-Gauss-Bonnet Ad S BHs through the temporal evolution of all types of gravitational perturbation fields（tensor, vector and scalar）. It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore,the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet Ad S BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet Ad S BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds.
