Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite diff...Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.展开更多
A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure ...A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 < |D| < |P| such that every subgroup of P with order |D| or 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.展开更多
We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories.In the ringdown stage of the black hole merger,for the prograde orbit,the real part of...We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories.In the ringdown stage of the black hole merger,for the prograde orbit,the real part of the quasinormal modes decreases with an increase in the disformal parameter,and the imaginary part also decreases,except in the Kerr case for a large spin parameter.However,for the retrograde orbit,the real part increases with an increase in the disformal parameter,and the imaginary part always decreases with it.For the approximate final spin,regardless of an equal spin,unequal spin,or generic spin configuration merger,the final black hole spin always increases with an increase in the disformal parameter.Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger,which suggests the differences between these two spacetime structures.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
In this work,we investigate a static and spherically symmetric Bardeen-Kiselev black hole(BH)with the cosmological constant,which is a solution of the Einstein-non-linear Maxwell field equations.We compute the quasino...In this work,we investigate a static and spherically symmetric Bardeen-Kiselev black hole(BH)with the cosmological constant,which is a solution of the Einstein-non-linear Maxwell field equations.We compute the quasinormal frequencies for the Bardeen-Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations.By varying the BH parameters,we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner-Nordström-de Sitter BH surrounded by quintessence(RN-dSQ).Interestingly,it is shown that the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q,the state parameter w and the normalization factor c are varied;however,for the gravitational perturbations,the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied.Therefore,compared with the gravitational perturbations,the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately.Another interesting observation is that,due to the presence of Kiselev quintessence,the electromagnetic perturbations around the Bardeen-Kiselev BH with the cosmological constant damps faster and oscillates slowly;for the gravitational perturbations,the quasinormal mode decays slowly and oscillates slowly.We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen-Kiselev BH with the cosmological constant;it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.展开更多
In this study,we investigate the quasinormal modes(QNMs)of a Lorentz-violating spacetime,factoring in a cosmological constant,within the framework of Einstein-bumblebee gravity.Our findings reveal that the interaction...In this study,we investigate the quasinormal modes(QNMs)of a Lorentz-violating spacetime,factoring in a cosmological constant,within the framework of Einstein-bumblebee gravity.Our findings reveal that the interaction of spacetime with an anisotropic bumblebee field imparts distinct contributions to the axial and polar sectors of the vector perturbations.This subsequently breaks the isospectrality typically observed in vector modes.Numerical evidence strongly indicates isospectral breaking in the vector modes of Einstein-bumblebee black holes:a pronounced breakage in the real part of the frequencies,while the imaginary component seems less affected.This isospectral breaking indicates the existence of two different waveforms in the Ringdown phase of the black hole,which provides a potential signal of quantum gravity observable in current experiments.展开更多
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived an...Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.展开更多
We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits.We find that,for regular black holes with spherical symmetry and a single shape...We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits.We find that,for regular black holes with spherical symmetry and a single shape function,the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.展开更多
Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band,providing more opportunities to test theories of gravity than ground-based detecto...Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band,providing more opportunities to test theories of gravity than ground-based detectors.The study of quasinormal modes(QNMs)and their application in gravity theory testing have been an important aspect in the field of gravitational physics.In this study,we investigate the capability of future space-based gravitational wave detectors,such as LISA,TaiJi,and TianQin,to constrain the dimensionless deviating parameter for Einsteindilaton-Gauss-Bonnet(EdGB)gravity with ringdown signals from the merger of binary black holes.The ringdown signal is modeled by the two strongest QNMs in EdGB gravity.Considering time-delay interferometry,we calculate the signal-to-noise ratio of different space-based detectors for ringdown signals to analyze their capabilities.The Fisher information matrix is employed to analyze the accuracy of parameter estimation,with particular focus on the dimensionless deviating parameter for EdGB gravity.The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter is also studied.We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with a decrease in the dimensionless deviating parameter.LISA and TaiJi offer more advantages in constraining the dimensionless deviating parameter to a more accurate level for massive black holes,whereas TianQin is more suited to less massive black holes.The Bayesian inference method is used to perform parameter estimation on simulated data,which verifies the reliability of the conclusion.展开更多
This study investigates the echoes in axial gravitational perturbations in compact objects.Accordingly,we propose an alternative scheme of the finite difference method implemented in two coordinate systems,where the i...This study investigates the echoes in axial gravitational perturbations in compact objects.Accordingly,we propose an alternative scheme of the finite difference method implemented in two coordinate systems,where the initial conditions are placed on the axis of the tortoise coordinate with appropriate boundary conditions that fully re-spect the causality.The scheme is then employed to study the temporal profiles of the quasinormal oscillations in the Schwarzschild black hole and uniform-density stars.When presented as a two-dimensional evolution profile,the res-ulting ringdown waveforms in the black hole metric are split into reflected and transmitted waves as the initial per-turbations evolve and collide with the peak of the effective potential.Meanwhile,for compact stars,quasinormal os-cillations might be characterized by echoes.Consistent with the causality arguments,the phenomenon is produced by the gravitational waves bouncing between the divergent potential at the star's center and the peak of the effective po-tential.The implications of the present study are also discussed herein.展开更多
We investigate the quasinormal mode and greybody factor of Bardeen black holes with a cloud of strings via the WKB approximation and verify them using the Prony algorithm. We find that the imaginary part of the quasin...We investigate the quasinormal mode and greybody factor of Bardeen black holes with a cloud of strings via the WKB approximation and verify them using the Prony algorithm. We find that the imaginary part of the quasinormal mode spectra is always negative, and the perturbation does not increase with time, indicating that the system is stable under scalar field perturbation. Moreover, the string parameter a has a dramatic impact on the frequency and decay rate of the waveforms. In addition, the greybody factor increases when a and λ increase and when q and l decrease. The parameters λ and l have a significant effect on the tails. In particular, when l=0, a de Sitter phase appears at the tail.展开更多
Recently,a parametrized Schwarzschild metric(PSM)was proposed,in which n=2 to solve the differences of mass of M87*from different observations.We find the axial gravitational quasinormal modes of this metric are unsta...Recently,a parametrized Schwarzschild metric(PSM)was proposed,in which n=2 to solve the differences of mass of M87*from different observations.We find the axial gravitational quasinormal modes of this metric are unstable for n>1.The decay rate of the quasinormal mode of the case n<1 is much smaller than the case n=1,which can be used to differentiate the PSM from a Schwarzschild one.展开更多
The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall par...The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases.Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η,(l, n), ε and Nq, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.展开更多
It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship(SCC).Relevant issues for Reissner-Nordstrom-de Sitter(RN-dS)black holes and Born-...It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship(SCC).Relevant issues for Reissner-Nordstrom-de Sitter(RN-dS)black holes and Born-Infeld-de Sitter black holes have been discussed.In this paper,we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields.It has been argued that SCC can be violated in a near-extremal RN-dS black hole.However,we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de Sitter black hole.Compared with Born-Infeld model,we find that the NLED effect has similar behavior.展开更多
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
基金Supported by King Saud University, Deanship of Scientific Research, College of Science Research Center
文摘Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.
基金supported by National Natural Science Foundation of China (Grant No. 10771132)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200802800011)+1 种基金the Research Grant of Shanghai University, Shanghai Leading Academic Discipline Project (Grant No. J50101)Natural Science Foundation of Anhui Province (Grant No.KJ2008A030)
文摘A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 < |D| < |P| such that every subgroup of P with order |D| or 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.
基金Supported by the National Key Research and Development Program of China(2020YFC2201400)the National Natural Science Foundation of China(12275079,12035005,12275078)。
文摘We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories.In the ringdown stage of the black hole merger,for the prograde orbit,the real part of the quasinormal modes decreases with an increase in the disformal parameter,and the imaginary part also decreases,except in the Kerr case for a large spin parameter.However,for the retrograde orbit,the real part increases with an increase in the disformal parameter,and the imaginary part always decreases with it.For the approximate final spin,regardless of an equal spin,unequal spin,or generic spin configuration merger,the final black hole spin always increases with an increase in the disformal parameter.Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger,which suggests the differences between these two spacetime structures.
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.
基金funded by the Guizhou Provincial Science and Technology Project(Guizhou Scientific Foundation-ZK[2022]General 491)the National Natural Science Foundation of China(Grant No.12265007).
文摘In this work,we investigate a static and spherically symmetric Bardeen-Kiselev black hole(BH)with the cosmological constant,which is a solution of the Einstein-non-linear Maxwell field equations.We compute the quasinormal frequencies for the Bardeen-Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations.By varying the BH parameters,we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner-Nordström-de Sitter BH surrounded by quintessence(RN-dSQ).Interestingly,it is shown that the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q,the state parameter w and the normalization factor c are varied;however,for the gravitational perturbations,the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied.Therefore,compared with the gravitational perturbations,the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately.Another interesting observation is that,due to the presence of Kiselev quintessence,the electromagnetic perturbations around the Bardeen-Kiselev BH with the cosmological constant damps faster and oscillates slowly;for the gravitational perturbations,the quasinormal mode decays slowly and oscillates slowly.We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen-Kiselev BH with the cosmological constant;it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122504,12375046,and 12035005)the Innovative Research Group of Hunan Province(Grant No.2024JJ1006)+1 种基金the Natural Science Foundation of Hunan Province(Grant No.2023JJ30384)Hunan Provincial Major Sci-Tech Program(Grant No.2023ZJ1010)。
文摘In this study,we investigate the quasinormal modes(QNMs)of a Lorentz-violating spacetime,factoring in a cosmological constant,within the framework of Einstein-bumblebee gravity.Our findings reveal that the interaction of spacetime with an anisotropic bumblebee field imparts distinct contributions to the axial and polar sectors of the vector perturbations.This subsequently breaks the isospectrality typically observed in vector modes.Numerical evidence strongly indicates isospectral breaking in the vector modes of Einstein-bumblebee black holes:a pronounced breakage in the real part of the frequencies,while the imaginary component seems less affected.This isospectral breaking indicates the existence of two different waveforms in the Ringdown phase of the black hole,which provides a potential signal of quantum gravity observable in current experiments.
基金Supported by the National Natural Science Foundation of China (Grant No. 10773002)
文摘Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
基金support from the National Natural Science Foundation of China (12175108)。
文摘We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits.We find that,for regular black holes with spherical symmetry and a single shape function,the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.
基金the National Key R&D Program of China(2022YFC2204602)the Natural Science Foundation of China(11925503)。
文摘Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band,providing more opportunities to test theories of gravity than ground-based detectors.The study of quasinormal modes(QNMs)and their application in gravity theory testing have been an important aspect in the field of gravitational physics.In this study,we investigate the capability of future space-based gravitational wave detectors,such as LISA,TaiJi,and TianQin,to constrain the dimensionless deviating parameter for Einsteindilaton-Gauss-Bonnet(EdGB)gravity with ringdown signals from the merger of binary black holes.The ringdown signal is modeled by the two strongest QNMs in EdGB gravity.Considering time-delay interferometry,we calculate the signal-to-noise ratio of different space-based detectors for ringdown signals to analyze their capabilities.The Fisher information matrix is employed to analyze the accuracy of parameter estimation,with particular focus on the dimensionless deviating parameter for EdGB gravity.The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter is also studied.We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with a decrease in the dimensionless deviating parameter.LISA and TaiJi offer more advantages in constraining the dimensionless deviating parameter to a more accurate level for massive black holes,whereas TianQin is more suited to less massive black holes.The Bayesian inference method is used to perform parameter estimation on simulated data,which verifies the reliability of the conclusion.
基金Supported by the National Natural Science Foundation of China(42230207)and the Brazilian Agencies Fundacao de Amparo a Pesquisa do Estado de Sao Paulo(FAPESP),Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro(FAPERJ),Conselho Nacional de Desenvolvimento Cientifico e Tecnologico(CNPq),Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior(CAPES),a part of this work was developed under the project Institutos Nacionais de Ciencias e Tecnologia-Fisica Nuclear e Aplicacoes(INCT/FNA)Proc.No.464898/2014-5support from the Center for Scientific Computing(NCC/GridUNESP)of the Sao Paulo State University(UNESP)。
文摘This study investigates the echoes in axial gravitational perturbations in compact objects.Accordingly,we propose an alternative scheme of the finite difference method implemented in two coordinate systems,where the initial conditions are placed on the axis of the tortoise coordinate with appropriate boundary conditions that fully re-spect the causality.The scheme is then employed to study the temporal profiles of the quasinormal oscillations in the Schwarzschild black hole and uniform-density stars.When presented as a two-dimensional evolution profile,the res-ulting ringdown waveforms in the black hole metric are split into reflected and transmitted waves as the initial per-turbations evolve and collide with the peak of the effective potential.Meanwhile,for compact stars,quasinormal os-cillations might be characterized by echoes.Consistent with the causality arguments,the phenomenon is produced by the gravitational waves bouncing between the divergent potential at the star's center and the peak of the effective po-tential.The implications of the present study are also discussed herein.
基金Supported by the National Natural Science Foundation of China (12275087)the Fundamental Research Funds for the Central Universities
文摘We investigate the quasinormal mode and greybody factor of Bardeen black holes with a cloud of strings via the WKB approximation and verify them using the Prony algorithm. We find that the imaginary part of the quasinormal mode spectra is always negative, and the perturbation does not increase with time, indicating that the system is stable under scalar field perturbation. Moreover, the string parameter a has a dramatic impact on the frequency and decay rate of the waveforms. In addition, the greybody factor increases when a and λ increase and when q and l decrease. The parameters λ and l have a significant effect on the tails. In particular, when l=0, a de Sitter phase appears at the tail.
基金National Natural Science Foundation of China(NNSFC)under contract No.423007the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)with No.G1323523064supported by the National Natural Science Foundation of China(NNSFC)under contract Nos.127506 and 123519。
文摘Recently,a parametrized Schwarzschild metric(PSM)was proposed,in which n=2 to solve the differences of mass of M87*from different observations.We find the axial gravitational quasinormal modes of this metric are unstable for n>1.The decay rate of the quasinormal mode of the case n<1 is much smaller than the case n=1,which can be used to differentiate the PSM from a Schwarzschild one.
基金Supported by the National Nature 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 of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases.Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η,(l, n), ε and Nq, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.
基金NSFC(Grant No.11505119,11005016,11875196 and 11375121)。
文摘It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship(SCC).Relevant issues for Reissner-Nordstrom-de Sitter(RN-dS)black holes and Born-Infeld-de Sitter black holes have been discussed.In this paper,we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields.It has been argued that SCC can be violated in a near-extremal RN-dS black hole.However,we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de Sitter black hole.Compared with Born-Infeld model,we find that the NLED effect has similar behavior.
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.
