Ultra long lived quasinormal modes of neutron stars in massive scalar-tensor gravity
Jose Luis Blázquez-Salcedo, Fech Scen Khoo, Jutta Kunz
备注：
7 pages, 3 figures. v2: Generalisation of the results to generic massive scalar-tensor gravity; improvements in the discussion, figures and references; main results unchanged; matches published version
The spectrum of frequencies and characteristic times that compose the ringdown phase of gravitational waves emitted by neutron stars carries information about the matter content (the equation of state) and the underlying theory of gravity. Typically, modified theories of gravity introduce additional degrees of freedom/fields, such as scalars, which result in new families of modes composing the ringdown spectrum. Simple but physically promising candidates are scalar-tensor theories, which effectively introduce an additional massive scalar field (i.e. an ultra-light boson) that couples non-minimally to gravity, resulting in scalarized neutron stars. Here we present the first calculation of the full ringdown spectrum in such theories. We show that the ringdown spectrum of neutron stars with ultra-light bosons is much richer and fundamentally different from the spectrum in general relativity and that it possesses propagating ultra long lived modes.
Quasinormal modes of a massive Dirac field were calculated for various static black hole backgrounds with the help of the WKB formula. These estimations, however, are rough and valid only for very small values of $μM$, where $M$ and $μ$ are mass of the black hole and field respectively. Thus, no accurate calculations of massive Dirac modes are known even for the Schwarzschild black hole and this is all the more so for the Kerr solution. Here we calculate quasinormal modes of a massive Dirac field in the Kerr background. We have shown that the infinitely long-lived quasinormal modes (quasireson…
Here we show that the phenomenon of arbitrarily long-lived quasinormal modes (called quasiresonances) of a massive scalar field in the vicinity of a black hole is not an artifact of the test field approximation, but takes place also when the (derivative) coupling of a scalar field with the Einstein tensor is taken into consideration. We observe that at large coupling and high multipole numbers, the growing modes appear in the spectrum, which are responsible for the eikonal instability of the field. For small coupling, when the configuration is stable, there appear the purely imaginary quasinor…
Arbitrarily long lived modes, called quasi-resonances, are known to exist in the spectrum of massive fields for a number of black-hole backgrounds at some discrete values of mass of the field. Here we show that these modes also exist in the background of wormholes, unless a wormhole has a constant red-shift function, that is, tideless in the radial direction. The evidence of quasi-resonances is supported by calculations in the frequency and time domains, which are in a good concordance. At large masses of the field, time-domain profiles of the absolute value of the wave function have peculiar …
For a static and spherically symmetric black hole, a photon sphere is composed of circular null geodesics of fixed radius, and plays an important role in observing the black hole. Recently, in an Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and electromagnetic fields, a class of hairy black holes has been found to possess two unstable and one stable circular null geodesics on the equatorial plane, corresponding to three photon spheres outside the event horizon. In this paper, we study quasinormal modes of the scalar field, which are associated with these circula…
Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
Dipartimento di Fisica, Sapienza Università di Roma（罗马大学物理系）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳加尔分校）；School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学培养协会物理科学学院）
We propose accurate calculations of quasinormal modes of black holes in the Einstein-aether theory, which were previously considered in the literature, partially, with insufficient accuracy. We also show that the arbitrarily long-lived modes, quasiresonances, are allowed in the Einstein-aether theory as well and demonstrate that the asymptotic tails, unlike quasinormal frequencies, are indistinguishable from those in the Einstein theory.
Quasinormal modes of rotating black holes with ultralight scalar fields
Beijing Institute of Mathematical Sciences and Applications（北京数学与交叉科学研究院）；St John’s College, Cambridge（剑桥大学圣约翰学院）；DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）
We investigate charged, massive scalar field around static, spherically symmetric black hole immersed into an external asymptotically uniform magnetic field $B$. It is shown that for given multipole number $\ell$ there are $2\ell+1$ numbers of modes due to the Zeeman effect appearing by an interaction of the external magnetic and charged scalar fields introducing an effective mass of the scalar field $μ_{\rm eff}=\sqrt{μ^2-mqB}$ where $m$ is the azimuthal number and $q$ is the charge coupling constant. We calculate threshold value of effective mass in which quasinormal modes are arbitrarily lo…
The purpose of this short communication is to show that the theory of Breit-Wigner resonances can be used as an efficient numerical tool to compute black hole quasinormal modes. For illustration we focus on the Schwarzschild anti-de Sitter (SAdS) spacetime. The resonance method is better suited to small SAdS black holes than the traditional series expansion method, allowing us to confirm that the damping timescale of small SAdS black holes for scalar and gravitational fields is proportional to r_+^(-2l-2), where r_+ is the horizon radius. The proportionality coefficients are in good agreement …
Gravitational perturbations in the geometry of asymptotically flat black hole solution in the deformed Hořava-Lifshitz(HL) gravity are considered and the associated quasinormal mode(QNM) frequencies are evaluated using WKB method. Black holes are found to be stable against small perturbations. We also find a significant deviation in the behavior of QNMs in HL theory for low values of HL parameter $ω$, from that in the standard General Relativity(GR). QNMs are long lived in Hořava theory compared with the usual Schwarzschild black hole case.
We consider the dispersion relation of the shear-diffusion mode in relativistic hydrodynamics, which we generate to high order as a series in spatial momentum q for a holographic model. We demonstrate that the hydrodynamic series can be summed in a way that extends through branch cuts present in the complex q plane, resulting in the accurate description of multiple sheets. Each additional sheet corresponds to the dispersion relation of a different non-hydrodynamic mode. As an example we extract the frequencies of a pair of oscillatory non-hydrodynamic black hole quasinormal modes from the hydr…
We construct quasinormal modes for neutron stars in $R^2$ gravity in the Einstein frame, considering scalar masses in the sub-neV range. In particular, we investigate the fundamental quadrupole fluid f-modes and the dipole fluid F-modes. Employing six equations of state covering matter content with nucleons, hyperons, and quarks, we then propose universal relations for the quadrupole f-modes and dipole F-modes. The dipole F-modes are ultra-long lived and, for the lower scalar masses, their frequencies are inversely proportional to the corresponding Compton wavelength.
In this paper we consider quasi-normal modes of test scalar and electromagnetic fields in the background of a non-Schwarzschild black hole in the Einstein-Weyl gravity. We find the dependence of the modes on the new parameter $p$, which is related to the coupling constant $α$, for different values of the angular parameter $l$ and show that when $l$ is increasing, the frequencies tend to linear dependence on $p$. We have also examined the case of a massive scalar field for which we have shown that the arbitrarily long lived modes (called quasi-resonances) exist in the spectrum.
We study quasinormal modes of static Einstein-Gauss-Bonnet-dilaton black holes. Both axial and polar perturbations are considered and studied from $l=0$ to $l=3$. We emphasize the difference in the spectrum between the Schwarzschild solutions and dilatonic black holes. At large Gauss-Bonnet coupling constant a small secondary branch of black holes is present, when the dilaton coupling is sufficiently strong. The modes of the primary branch can differ from the Schwarzschild modes up to $10\%$. The secondary branch is unstable and possesses long-lived modes. We address the possible effects of th…
We found quasinormal modes, both in time and frequency domains, of the Ernst black holes, that is neutral black holes immersed in an external magnetic field. The Ernst solution reduces to the Schwarzschild solution, when the magnetic field vanishes. It is found that the quasinormal spectrum for massless scalar field in the vicinity of the magnetized black holes acquires an effective "mass" $μ= 2 B m$, where m is the azimuthal number and B is parameter describing the magnetic field. We shall show that in the presence of a magnetic field quasinormal modes are longer lived and have larger oscilla…
Quasinormal modes of black holes were previously calculated in a non-linear electrodynamics and in the Gauss-Bonnet gravity theory. Here we take into consideration both of the above factors and find quasinormal modes of a (massive) scalar field in the background of a black hole in the five-dimensional Einstein-Gauss-Bonnet gravity coupled to a non-linear electrodynamics having Maxwellian weak-field limit. For the non-linear electrodynamics we considered the high frequency (eikonal) regime of oscillations analytically, while for the lower multipoles the higher order WKB analysis with the help o…
Recently an anomalous decay rate of the quasinormal modes of a massive scalar field in Schwarzschild black holes backgrounds was reported in which the longest-lived modes are the ones with higher angular number, for a scalar field mass smaller than a critical value, while that beyond this value the behaviour is inverted. In this work, we extend the study to other asymptotic geometries, such as, Schwarzschild-de Sitter and Schwarzschild-AdS black holes. Mainly, we found that such behaviour and the critical mass are present in the Schwarzschild-de Sitter background. Also, we found that the value…
Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long-lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we …
Cesàro convergence of the high-order WKB method and its applications to black-hole overtones and long-lived modes
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理学院理论物理与天体物理学研究中心）；Institute of Physics, Maria Curie-Skłodowska University（玛丽亚·居里-斯夸多夫斯卡大学物理学院）；Centro de Matemática, Computação e Cognição (CMCC), Universidade Federal do ABC (UFABC)（ABC联邦大学数学、计算与认知中心）
Recently, the anomalous decay rate of quasinormal modes has been studied for some geometries under scalar field perturbations, which occurs when the longest-lived modes are the ones with higher angular number, as well as, the existence of a critical scalar field mass, i.e the value of scalar field mass such that the decay rate does not depend appreciably on the angular number, and beyond which the behaviour of the decay rate is inverted. Here, we consider the propagation of fermionic fields in the background of Schwarzschild de Sitter black holes, and we show that the anomalous decay rate beha…
Ringing Regularity: Gravitational Perturbations and Quasinormal Modes of Einasto-Supported Black Holes
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National Research University TIIAME（TIIAME国立研究大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Tashkent State Technical University（塔什干国立技术大学）；Urgench State University（乌鲁奇州立大学）
The anomalous decay rate of the quasinormal modes occurs when the longest-lived modes are the ones with higher angular number. Such behaviour has been recently studied in different static spacetimes, for uncharged scalar and fermionic perturbations, being observed in both cases. In this work we consider the propagation of charged massive scalar fields in the background of Reissner-Nordström-de Sitter black holes and we mainly study the effect of the scalar field charge in the spectrum of quasinormal frequencies, as well as, its effect on the anomalous decay rate. Mainly, we show that the anoma…
Gravitational quasinormal modes of Dymnikova black holes
University of Hradec Králové（赫拉德茨克拉洛韦大学）；Istanbul University（伊斯坦布尔大学）；National Research University TIIAME（塔什干信息技术与管理系统国立研究大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；Urgench State University（乌尔根奇国立大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Mamun University（马蒙大学）
It has been argued that ultracompact objects, which possess light rings but no horizons, may be unstable against gravitational perturbations. To test this conjecture, we revisit the quasi-black hole solutions, a family of horizonless spacetimes whose limit is the extremal Reissner-Nordström black hole. We find a critical parameter at which the light rings just appear. We then calculate the quasinormal modes of the quasi-black holes. Both the WKB result and the numerical result show that long-live modes survive for the range where light rings exist, indicating that horizonless spacetimes with l…
Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Padé approximants as prescribed in [1] we consider quasinormal modes of a test massless Dirac field in the Einstein-dilaton-Gauss-Bonnet (EdGB) and Einstein-Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new…
Black hole (BH) solution in the conformal Weyl gravity is a generalization of the Schwarzschild spacetime which includes two additional constants appearing when integrating the third order differential equations for gravitational field. One constant looks like the effective cosmological constant providing the de Sitter asymptotic of the solution. The other constant allows one to describe flat rotation of galaxies without introducing of the dark matter. Here we show that the effective "dark matter" term in the metric function drastically changes the asymptotic behavior of the evolution of the w…
We study the waveforms of time signals produced by scalar perturbations in static hairy black holes, in which the perturbations can be governed by a double-peak effective potential. The inner potential peak would give rise to echoes, which provide a powerful tool to test the Kerr hypothesis. The waveforms are constructed in the time and frequency domains, and we find that the late-time waveforms are determined by the long-lived and sub-long-lived quasinormal modes, which are trapped in the potential valley and near the smaller peak, respectively. When the distance between the peaks is signific…
The anomalous decay rate of the quasinormal modes occurs when the longest-lived modes are the ones with higher angular number. Such behaviour has been recently studied in different static spacetimes, for scalar and fermionic perturbations, being observed in both cases. In this work, we extend the existent studies to the charged spacetimes, namely, the Reissner-Nordström, the Reissner-Nordström-de Sitter and the Reissner-Nordström-Anti-de Sitter black holes. We show that the anomalous decay rate behaviour of the scalar field perturbations is present for every charged geometry in the photon sphe…
We derive a quantization formula of Bohr-Sommerfeld type for computing quasinormal frequencies for scalar perturbations in an AdS black hole in the limit of large scalar mass or spatial momentum. We then apply the formula to find poles in retarded Green functions of boundary CFTs on $R^{1,d-1}$ and $RxS^{d-1}$. We find that when the boundary theory is perturbed by an operator of dimension $Δ>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over ΔπT} << {1 \over πT}$. Turning on a large spatial momentum can significantly increase it. For a generic scalar operator …
