WKB Approximation Method Research Articles

Violation of Hod’s conjecture and probing it with optical properties of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity

In this work, the quasinormal modes of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity have been investigated with the help of the Padé averaged higher order WKB approximation method and the validity of Hod’s conjecture has been studied. It is found that the presence of Lorentz symmetry breaking due to the Bumblebee field favours Hod’s conjecture. But in the case of the Gauss–Bonnet term, an increase in the coupling parameter increases the chances of violation of Hod’s conjecture. We further investigated the optical properties of the black hole viz., shadow and emission rate. It is found that a black hole with a lower lifetime favours Hod’s conjecture.

Quasinormal modes, temperatures and greybody factors of black holes in a generalized Rastall gravity theory

We introduce a modification in the energy-momentum conservation violating Rastall’s theory of gravity and obtain a Reissner-Nordström-type black hole solution in spacetime surrounded by a cloud of strings and charge fields. We examine the horizons of the black hole along with the influence of the parameters of the model on it. The scalar quasinormal modes (QNMs) of oscillations of the black hole are also computed using the 6th order WKB approximation method. It is seen that the Rastall parameter β and the newly introduced energy-momentum tensor trace parameter α as well as the charge parameter q and strings field parameter a influence the amplitude and damping of the QNMs. From the metric function, we obtain the temperature of the black hole and study the effects of the four model parameters β, α, q and a on the temperature. We then examine the greybody factors associated with the black hole and the corresponding total absorption cross-section for it. It is seen that the modification we introduced in the Rastall theory has a drastic effect on various properties of the black hole and may lead to interesting outcomes in future when better detection techniques will be available with the LISA and the Einstein Telescope.

Quasinormal modes of black holes in f(Q) gravity

In this work, we have studied the quasinormal modes of a black hole in a model of the type f(Q)=underset{n}{sum }a_{n}left( Q-Q_{0}right) ^{n} in f(Q) gravity by using a recently introduced method known as Bernstein spectral method and confirmed the validity of the method with the help of well known Padé averaged higher order WKB approximation method. Here we have considered scalar perturbation and electromagnetic perturbation in the black hole spacetime and obtained the corresponding quasinormal modes. We see that for a non-vanishing nonmetricity scalar Q_0, quasinormal frequencies in scalar perturbation are greater than those in electromagnetic perturbation scenarios. On the other hand, the damping rate of gravitational waves is higher for electromagnetic perturbation. To confirm the quasinormal mode behaviour, we have also investigated the time domain profiles for both types of perturbations.

Tideless traversable wormholes surrounded by cloud of strings in f(R) gravity

We study the tideless traversable wormholes in the f(R) gravity metric formalism. First we consider three shape functions of wormholes and study their viabilities and structures. The connection between the f(R) gravity model and wormhole shape function has been studied and the dependency of the f(R) gravity model with the shape function is shown. We also obtain a wormhole solution in the f(R) gravity Starobinsky model surrounded by a cloud of strings. In this case, the wormhole shape function depends on both the Starobinsky model parameter and the cloud of strings parameter. The structure and height of the wormhole is highly affected by the cloud of strings parameter, while it is less sensitive to the Starobinsky model parameter. The energy conditions have been studied and we found the ranges of the null energy condition violation for all wormhole structures. The quasinormal modes from these wormhole structures for the scalar and Dirac perturbations are studied using higher order WKB approximation methods. The quasinormal modes for the toy shape functions depend highly on the model parameters. In case of the Starobinsky model's wormhole the quasinormal frequencies and the damping rate increase with an increase in the Starobinsky model parameter in scalar perturbation. Whereas in Dirac perturbation, with an increase in the Starobinsky model parameter the quasinormal frequencies decrease and the damping rate increases. The cloud of strings parameter also impacts prominently and differently the quasinormal modes from the wormhole in the Starobinsky model.

Three-Dimensional Analytical Solutions for Acoustic Transverse Modes in a Cylindrical Duct with Axial Temperature Gradient and Non-Zero Mach Number

Cylindrical ducts with axial mean temperature gradient and mean flows are typical elements in rocket engines, can combustors, and afterburners. Accurate analytical solutions for the acoustic waves of the longitudinal and transverse modes within these ducts can significantly improve the performance of low order acoustic network models for analyses of acoustic behaviours and combustion instabilities in these kinds of ducts. Here, we derive an acoustic wave equation as a function of pressure perturbation based on the linearised Euler equations (LEEs), and the modified WKB approximation method is applied to derive analytical solutions based on very few assumptions. The eigenvalue system is built based on the proposed solutions and applied to predict the resonant frequencies and growth rate for transverse modes. Validations of the proposed solutions are performed by comparing them to the numerical results directly calculated from the LEEs. Good agreements are found between analytical reconstruction and numerical results of three-dimensional transverse modes. The system with both mean temperature profile and mean flow presents a larger absolute value of the growth rate than the condition of either uniform mean temperature or no mean flow.

Quasinormal modes and the correspondence with shadow in black holes with a deficit solid angle and quintessence-like matter

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a 4-dimensional black hole with a deficit solid angle and quintessence-like matter. We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter. The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively. The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter when the multipole number is fixed. The quasinormal modes gotten by these two methods are in good agreement, especially when the multipole number is large. It shows the correspondence between the quasinormal modes in the eikonal limit and shadow.

Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source

Acoustic and entropy waves interacting in a duct with a steady heat source and mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions are obtained by taking advantage of flow invariants and applying a multi-step strategy. The proposed solutions provide first-order corrections to the compact model in the form of integrals of mean flow variables. An eigenvalue system is then built to predict the thermoacoustic modes of a duct containing a distributed heat source or sink. Predictions from the AE solutions agree well with the numerical results of the linearised Euler equations for both frequencies and growth rates, as long as the low-frequency condition is satisfied. The AE solutions are able to accurately reconstruct the acoustic and entropy waves and correct the significant errors in the predicted entropy wave associated with the compact model. The analysis illustrates that the thermoacoustic system needs to account for the entropy wave generated by the interaction of acoustic wave and the distributed steady heat source, especially when density- or entropy-dependent boundary conditions are prescribed at the duct ends. Furthermore, a combination of the AE method and the modified WKB approximation method is discussed for a cooling case. The AE solutions remedy the disadvantage of the WKB solution in the low and very low-frequency domain and facilitate full-frequency theoretical analyses of sound propagation and entropy generation in inhomogeneous duct flow fields.

Quasinormal modes and Hawking radiation sparsity of GUP corrected black holes in bumblebee gravity with topological defects

We have obtained the Generalized Uncertainty Principle (GUP) corrected deSitter and anti-de Sitter black hole solutions in bumblebee gravity with atopological defect. We have calculated the scalar, electromagnetic andgravitational quasinormal modes for the both vanishing and non-vanishingeffective cosmological constant using Padé averaged sixth order WKBapproximation method. Apart from this, the time evolutions for all threeperturbations are studied, and quasinormal modes are calculated using the timedomain profile. We found that the first order and second order GUP parametersα and β, respectively have opposite impacts on the quasinormalmodes. The study also finds that thepresence of a global monopole can decrease the quasinormal frequencies and thedecay rate significantly. On the other hand, Lorentz symmetry violation hasnoticeable impacts on the quasinormal frequencies and the decay rate. Wehave studied the greybody factors, power spectrum and sparsity of the blackhole with the vanishing effective cosmological constant for all the threeperturbations. The presence of Lorentz symmetry breaking and the GUPparameter α decrease, while other GUP parameter β and the presenceof global monopole increase the probability of Hawking radiation to reach thespatial infinity. The presence of Lorentz violation can make the black holesless sparse, while the presence of a global monopole can increase the sparsityof the black holes. Moreover, we have seen that the black hole areaquantization rule is modified by the presence of Lorentz symmetry breaking.

Dispersion properties of a slab waveguide with a graded-index core layer and a nonlinear cladding using the WKB approximation method

Graded-index waveguides deserve investigation because they are more practical than those of step-index profiles. In this communication, a three-layer slab waveguide in which the core film has an exponentially graded refractive index is assumed. In this case, the film and substrate layers merge smoothly to form one layer of refractive index n ( x ) which is equal to n f at the cladding–film boundary and n s deep in the substrate layer. The cladding layer is made of a Kerr-type nonlinear material. An exact solution to such a waveguide structure is not possible. Approximation techniques are usually used in these cases. We employ the WKB approximation method to find an approximate dispersion relation of the proposed waveguide in terms of the asymmetry parameters a , b , and V . The universal dispersion curves are studied in detail. A number of interesting features are observed, such as the lack of a cutoff thickness related to the symmetric waveguide structure of a = 0 . The b -values are all less than one, which corresponds to guided modes.

Quasinormal modes and late-time falloff of Finslerian black holes with cosmological constant

Quasinormal modes of scalar and electromagnetic field perturbations in Finslerian Reissner-Nordstr\"om black holes with a cosmological constant are investigated in this paper. We analyze the fundamental frequencies and dynamical evolution of quasinormal modes using the WKB approximation and finite difference method, respectively. Both approaches show that the periods of oscillation of quasinormal modes increase with higher Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ if the multipole quantum number $l\ensuremath{\ge}2$. Using the Prony method, we show that the results obtained from the finite difference method are consistent with the results obtained from the WKB approximation. Quasinormal modes of Finslerian black holes possess spectrum splitting, which reflects the fact that the spherical symmetry of the Finslerian black holes is broken. The effects of the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ on the late-time tails of scalar and electromagnetic field perturbations are shown. The late-time tails of the Finslerian Reissner-Nordstr\"om black holes possess a power-law falloff. The power-law index has a discontinuous jump, while the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ varies from 0 to nonzero. Such a fact reflects the fact that asymptotic-infinity behaviors of the Finslerian Reissner-Nordstr\"om black holes are different from their counterparts in general relativity.

The Trajectory Nonstability of Charges in LHC Due to Bremsstrahlung

The quasi-classical behavior of a charged particle moving in a magnetic field is derived by the WKB approximation and wave-packet method from the Klein-Gordon equation with the Schwinger radiative term. The lifetime of the wave-packet state is calculated for a constant magnetic field. The finite lifetime of the trajectory is the proof of the nonstationary motion of charges moving in magnetic field.

Quantum gravity evolution in the Hawking radiation of a rotating regular Hayward black hole

In this paper, we study two different phenomena (the Newman-Janis algorithm and the semiclassical Hamilton-Jacobi method) to analyze the Hawking temperature ($T_H$) for massive $4$-dimensional regular Hayward BH with spin parameter. First of all, we compute the rotating regular Hayward black hole solution by taking the Newman-Janis algorithmic rule. We derive the $T_H$ for rotating regular Hayward BH with the help of surface gravity. We have also analyzed the effects of spin parameter $a$ and free parameter $l$ on $T_H$ with the help of graphs. Moreover, we investigate the quantum corrected Hawking temperature ($T'_H$) for rotating regular Hayward black hole. To do so, we utilize the Lagrangian filed equation in the background of GUP within the concept of WKB approximation and semiclassical Hamilton-Jacobi method. The $T'_H$ of rotating regular Hayward BH depends upon correction parameter $\beta$, BH mass $m$, spin parameter $a$, free parameter $l$ and BH radius $r_+$. We also study the graphical behavior of $T'_H$ versus event horizon $r_+$ for rotating regular Hayward BH and check the influences of quantum gravity parameter $\beta$, spin parameter $a$ and free parameter $l$ on the stability of corresponding black hole. Moreover, we study the significance's of logarithmic entropy correction for regular rotating Hayward BH.

Tunneling of hawking radiation for BTZ black hole revisited

We re-examine Hawking radiation for a nonrotating [Formula: see text]-dimensional Bañados–Teitelboim–Zanelli (BTZ) black hole and evaluate the transmission probability of tunneling through the barrier of the event horizon employing the standard method of WKB approximation. Our results are presented for both uncharged and charged cases. We also explore the associated thermodynamics in terms of Hawking temperature and provide estimates of black hole parameters like the surface gravity and entropy.

Any$$\mathbf {\, }l$$-State Energy of the Spinless Salpeter Equation Under the Cornell Potential by the WKB Approximation Method: An Application to Mass Spectra of Mesons

Any$$\mathbf {\, }l$$-State Energy of the Spinless Salpeter Equation Under the Cornell Potential by the WKB Approximation Method: An Application to Mass Spectra of Mesons

Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan potential by WKB and SWKB methods

The energy levels of the Klein–Gordon equation in hyper-radial space under the Deng-Fan potential energy function are studied by the SWKB and WKB approximation methods. We obtained the analytic solution of the energy spectra and the ground state wave function in closed form. Furthermore, we obtained the energy equation corresponding to the Schrodinger equation by invoking the non-relativistic limit. The variations of the non-relativistic N-dimensional energy spectra with the potential parameters and radial quantum number are investigated. The energy levels are degenerate for and increase with the dimensionality number. The ground state wave function and its gradient are continuous at the boundary Our results for the energy spectra are in excellent agreement with the ones obtained by other analytical methods where similar centrifugal approximations were applied.

Study on Tunnelling Radiation in 4 Dimension Black Holes Vector Particles

Recent studies show that the tunnelling radiation of vector particles has been studied successfully by WKB approximation and Hamilton-Jacobi method. In view of this, the main purpose of this paper is to study the Proca equation and the vector particles tunnelling radiation in a 4-dimensional black hole. Finally, the results here show that the temperature of the vector particle is the same as that of the Dirac particle.

Greybody factor for massive fermion emitted by a black hole in de Rham-Gabadadze-Tolley massive gravity theory

The greybody factor of the massive Dirac field around the black hole in the dRGT massive gravity theory is investigated using the rigorous bound and the WKB approximation methods. In both methods, the greybody factor significantly depends on the shape of the potential. If the potential is smaller, there is more probability for the Dirac field to transmit through the black hole, therefore, the greybody factor is higher. Moreover, there exists a critical mass of the Dirac field such that the greybody factor is maximum. By comparing the results from these two methods, we argue that it is useful to use the rigorous bound method for the low potential cases, while using the WKB approximation method for the high potential cases.

Shadow cast and quasinormal modes in f(R) gravity model inspired by Yang–Mills field

In this paper, the null geodesic equations are computed in [Formula: see text] space–time dimensions [Y. Younesizadeh, A. A. Ahmad, A. H. Ahmed, F. Younesizadeh, Ann. Phys. 420, 168246 (2020)] by using the concept of symmetries and Hamilton–Jacobi equation and Carter separable method. With these null geodesics in hand, we evaluate the celestial coordinates (x, y) and the radius [Formula: see text] of the BH shadow and represent it graphically. In addition, we have shown that the peak of this energy slowly shifts to lower frequencies and its height decreases with the increase in the YM magnetic charge ([Formula: see text]) values and decrease in the [Formula: see text] parameter ([Formula: see text]) values. In addition, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. The most important result derived from this study is that the height of this potential increases with increase in the YM magnetic charge ([Formula: see text]) values. Then, we study the quasinormal modes (QNMs) of these 4D black holes. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the YM magnetic charge ([Formula: see text]) values and the [Formula: see text] parameter ([Formula: see text]) values change.

Quasinormal modes and shadows of a new family of Ayón-Beato-García black holes

We obtain a type of Ay\'{o}n-Beato-Garc\'{\i}a (ABG) related black hole solutions with five parameters: the mass $m$, the charge $q$, and three dimensionless parameters $\alpha$, $\beta$ and $\gamma$ associated with nonlinear electrodynamics. We find that this type of black holes is regular under the conditions: $\alpha \gamma \geqslant 6$, $\beta \gamma \geqslant 8$, and $\gamma >0$. Here we focus on the saturated case: $\alpha={6}/{\gamma}$ and $\beta ={8}/{\gamma }$, such that only three parameters $m$, $q$ and $\gamma$ remain, which leads to a new family of ABG black holes. For such a family of black holes, we investigate the influence of the charge $q$ and the parameter $\gamma$ on the horizon radius and the Hawking temperature. In addition, we calculate the quasinormal mode frequencies of massless scalar field perturbations by using the sixth-order WKB approximation method and the unstable circular null geodesic method in the eikonal limit. We also compute the shadow radius for the new family of ABG black holes and use the shadow data of the $M87^{*}$ black hole detected by the Event Horizon Telescope to provide an upper limit on the charge $q$ of the new black holes. Using the shadow data of the $M87^{*}$ black hole, we find that the upper limit of the charge $q$ increases rapidly at first and then slowly but does not exceed the mass of the $M87^{*}$ black hole at last when the parameter $\gamma$ is increasing and going to infinity, and that the data restrict the frequency range of the fundamental mode with $l=1$ to $1.4\times 10^{-6}Hz\sim 1.9\times 10^{-6} Hz$.

High-dimensional Schwarzschild black holes in scalar\u2013tensor\u2013vector gravity theory

We obtain a high-dimensional Schwarzschild black hole solution in the scalar–tensor–vector gravity (STVG), and then analyze the influence of parameter alpha associated with a deviation of the STVG theory from General Relativity on event horizons and Hawking temperature. We calculate the quasinormal mode frequencies of massless scalar field perturbations for the high-dimensional Schwarzschild STVG black hole by using the sixth-order WKB approximation method and the unstable null geodesic method in the eikonal limit. The results show that the increase of parameter alpha makes the scalar waves decay slowly, while the increase of the spacetime dimension makes the scalar waves decay fast. In addition, we study the influence of parameter alpha on the shadow radius of this high-dimensional Schwarzschild STVG black hole and find that the increase of parameter alpha makes the black hole shadow radius increase, but the increase of the spacetime dimension makes the black hole shadow radius decrease. Finally, we investigate the energy emission rate of the high-dimensional Schwarzschild STVG black hole, and find that the increase of parameter alpha makes the evaporation process slow, while the increase of the spacetime dimension makes the process fast.