The high-energy absorption cross section of the Schwarzschild black hole is well approximated, in the eikonal regime, by the sum of two terms: the geometrical cross section of the black hole photon sphere and the contribution of a sinc function involving the geometrical characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on this photon sphere. From a numerical analysis, we show that, beyond the eikonal description, this absorption cross section presents a simple fine structure. We then describe it analytically by using Regge pole techniques and interpret it in geometrical terms. We naturally extend our analysis to arbitrary static spherically symmetric black holes endowed with a photon sphere and we then apply our formalism to Schwarzschild-Tangherlini and Reissner-Nordström black holes. Finally, on the example of the Schwarzschild black hole, we show numerically that a complicated hyperfine structure lying beyond the fine structure can also be observed.
We derive the absorption cross section of a minimally coupled scalar in the Lifshitz black hole obtained from the new massive gravity. The absorption cross section reduces to the horizon area in the low energy and massless limit of s-wave mode propagation, indicating that the Lifshitz black hole also satisfies the universality of low energy absorption cross section for black holes.
In this paper we study the effects of black hole mass on the absorption cross section for a massive scalar field propagating in a 5-dimensional topological Chern-Simons black hole at the low-frequency limit. We consider the two branches of black hole solutions $(α=\pm 1)$ and we show that, if the mass of black hole increase the absorption cross section decreases at the zero-frequency limit for the branch $α=-1$ and for the other branch, $α=1$, the behavior is opposite, if the black hole mass increase the absorption cross section increases. Also we find that beyond a certain frequency value, th…
In this paper we compute the low energy absorption cross-section for minimally coupled massles scalars and spin-$1/2$ particles, into a general spherically symmetric black hole in arbitrary dimensions. The scalars have a cross section equal to the area of the black hole, while the spin-$1/2$ particles give the area measured in a flat spatial metric conformally related to the true metric.
The absorption cross section is studied in the low-frequency region for a propagating scalar field under the warped AdS$_3$ black hole background in the topologically massive gravity. It can be shown that the absorption cross section is significantly deformed by the gravitational Chern-Simons term, which is proportional to the scattering area of black hole with an additional contribution depending on the left-moving and right-moving temperatures. It means that the cross section is larger than the area in spite of the s-wave limit. Finally, we discuss the left-right quasinormal modes for the sc…
The ratio of the low-energy absorption cross section for Dirac fermion to that for minimally coupled scalar is computed when the spacetimes are various types of the higher-dimensional Reissner-Nordström black holes. It is found that the low-energy absorption cross sections for the Dirac fermion always goes to zero in the extremal limit regardless of the detailed geometry of the spacetime. The physical importance of our results is discussed in the context of the brane-world scenarios and string theories.
In terms of the complex angular momentum method, we compute the absorption cross section by analyzing a massless test scalar field around conformally related black holes. At first, we investigate circular null geodesics and thereby prove a precondition for calculating the absorption cross section in the context of conformally related black holes. Then we use the WKB approximation method to derive the analytic expression of Regge frequency and the oscillation part of absorption cross sections. We find that this oscillation part depends on the scale factor of conformal transformations. By taking…
We investigate the low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions. We first construct the exact solutions to the relevant wave equations in the zero-frequency limit. In most cases it is possible to use these solutions to find the transmission coefficients of partial waves in the low-frequency limit. We use these transmission coefficients to calculate the low-frequency absorption cross section in five and six spacetime dimensions. We find that this cross section is dominated by the modes with l=2 in the sph…
In this paper we consider the solution of a black hole with a global monopole in $f(R)$ gravity and apply the partial wave approach to compute the differential scattering cross section and absorption cross section. We show that in the low-frequency limit and at small angles the contribution to the dominant term in the scattering/absorption cross section is modified by the presence of the global monopole and the gravity modification. In such limit, the absorption cross section shows to be proportional to the area of the event horizon.
We consider the absorption problem for a massless scalar field propagating in static and spherically symmetric black holes of arbitrary dimension endowed with a photon sphere. For this wide class of black holes, we show that the fluctuations of the high-energy absorption cross section are totally and very simply described from the properties (dispersion relation and damping) of the waves trapped near the photon sphere and therefore, in the eikonal regime, from the characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on the photon sphere. This is achieved …
We studied in detail the propagation of a massive tachyonic scalar field in the background of a five-dimensional ($5D$) Einstein--Yang--Mills--Born--Infeld--dilaton black string: the massive Klein--Gordon equation was solved, exactly. Next we obtained complete analytical expressions for the greybody factor, absorption cross-section, and decay-rate for the tachyonic scalar field in the geometry under consideration. The behaviors of the obtained results are graphically represented for different values of the theory's free parameters. We also discuss why tachyons should be used instead of ordinar…
Motivated by the brane-world scenarios, we study the absorption problem when the spacetime background is $(4+n)$-dimensional Schwarzschild black hole. We compute the low-energy absorption cross sections for the brane-localized massive scalar, brane-localized massive Dirac fermion, and massive bulk scalar. For the case of brane-localized massive Dirac fermion we introduce the particle's spin in the traditional Dirac form without invoking the Newman-Penrose method. Our direct introduction of spin enables us to compute contributions to the $j$th-level partial absorption cross section from orbital…
In this paper, we obtain a relation between the high-energy absorption cross section and the strong gravitational lensing for a static and spherically symmetric black hole. It provides us a possible way to measure the high-energy absorption cross section for a black hole from strong gravitational lensing through astronomical observation. More importantly, it allows us to compute the total energy emission rate for high-energy particles emitted from the black hole acting as a gravitational lens. It could tell us the range of the frequency, among which the black hole emits the most of its energy …
We discuss the absorption cross section for the minimally-coupled massless scalar field into a stationary and circularly symmetric black hole with nonzero angular velocity in four or higher dimensions. In particular, we show that it equals the horizon area in the zero-frequency limit provided that the solution of the scalar field equation with an incident monochromatic plane wave converges pointwise to a smooth time-independent solution outside the black hole and on the future horizon, with the error term being at most linear in the frequency. We also show that this equality holds for static b…
Following Sanchez's approach we investigate the effect of scalar mass in the absorption and emission problems of 4d Schwarzschild black hole. The absorption cross sections for arbitrary angular momentum of the scalar field are computed numerically in the full range of energy by making use of the analytic near-horizon and asymptotic solutions and their analytic continuations. The scalar mass makes an interesting effect in the low-energy absorption cross section for S-wave. Unlike the massless case, the cross section decreases with increasing energy in the extremely low-energy regime. As a resul…
The absorption section of black holes surrounded by scalar fields is studied with the sinc approximation in the eikonal limit. The effects of the scalar field on the nonlinear Euler-Heisenberg, the magnetic Bardeen and Reissner-Nordstrom BHs are studied in order to obtain information about how the scalar field affects different BHs.
The expression of the impact parameter, in the analysis for classical and semiclassical scattering cross sections for black holes, is obtained with nonlinear electrodynamics (NLED) while the absorption section is studied with the sinc approximation in the eikonal limit considering NLED. As an illustration, we calculate the classical and semiclassical scattering as well as the absorption sections for three black holes under NLED, the regular magnetic Bardeen and Bronnikov black holes and the singular Euler-Heisenberg black hole. All are compared with the sections of their linear electromagnetic…
We consider a d-dimensional spherically symmetric dilatonic R^2 string corrected black hole solution. We study its stability under tensor type gravitational perturbations and compute the absorption cross section for low frequency gravitational waves.
The absorption cross section of rotating black holes in the Randall-Sundrum brane-world scenario for massless scalar waves is obtained via the partial-wave method. A variety of incidence directions with respect to the black hole rotation axis is considered. Special attention is given to near-extreme black holes, in which cases the absorption cross section increases as the tidal charge becomes more negative. It is shown that black holes with different configurations can present capture cross sections/shadows of same size. However, in such cases, the absorption spectra are different mainly for s…
We study scalar perturbations in the background of a Topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that Topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, …
The behavior of a charged scalar field in the RN black hole space time is studied using WKB approximation. In the present work it is assumed that matter waves can get reflected from the event horizon. Using this effect, the Hawking temperature and the absorption cross section for RN black hole placed in a charged scalar field are calculated. The absorption cross section $σ_{abs}$ is found to be inversely proportional to square of the Hawking temperature of the black hole.
We analyze the low frequency absorption cross section of minimally coupled massless scalar fields by different kinds of charged static black holes in string theory, namely the D1-D5 system in d=5 and a four dimensional dyonic four-charged black hole. In each case we show that this cross section always has the form of some parameter of the solution divided by the black hole Hawking temperature. We also verify in each case that, despite its explicit temperature dependence, such quotient is finite in the extremal limit, giving a well defined cross section. We show that this precise explicit tempe…
We study massive charged fermionic perturbations in the background of a charged two-dimensional dilatonic black hole, and we solve the Dirac equation analytically. Then, we compute the reflection and transmission coefficients and the absorption cross section for massive charged fermionic fields, and we show that the absorption cross section vanishes at the low and high frequency limits. However, there is a range of frequencies where the absorption cross section is not null. Furthermore, we study the effect of the mass and electric charge of the fermionic field over the absorption cross section…
We consider effects of non-uniformity of quasi-spherical small black hole horizons on scattering massless spineless particles in the long-wave approximation. Focusing on 4D flat and AdS neutral black hole backgrounds with conformally spherical geometry of the horizon, we observe the notable differences in compare to the scattering process on the spherically-symmetric black holes. In particular, the absorption cross-section becomes dependent on both, polar and azimuthal, spherical angles, projections of the angular momentum do not keep anymore and the angular momentum operator by itself, though…
In this paper we focus on the partial wave method with the aim of exploring the scattering of massless scalar waves due to the noncommutative Schwarzschild black hole via Lorentzian smeared mass distribution. We determine the phase shift analytically in low-frequency limit and we show that the scattering and absorption cross section is modified. Specially, we show that in the low-frequency limit the scattering/absorption cross section has its value decreased when we increase the value of the non-commutativity parameter. In addition, we have confirmed this result by solving the problem numerica…
We have investigated the absorption cross section and the Hawking radiation of electromagnetic field with Weyl correction in the background of a four-dimensional Schwarzschild black hole spacetime. Our results show that the properties of the absorption cross section and the Hawking radiation depend not only on the Weyl correction parameter, but also on the parity of the electromagnetic field, which is quite different from those of the usual electromagnetic field without Weyl correction in the four-dimensional spacetime. With increase of Weyl correction parameter, the absorption probability, th…
In this paper, we study the scattering and absorption sections of the Schwarzschild--anti de Sitter black hole surrounded by quintessence. The critical values of the cosmological constant and the normalization factor are obtained. We describe the event horizons and the extremal condition of the black hole surrounded by quintessence. The effects of quintessence on the classical and semi--classical scattering cross--sections have been estimated. Also, the absorption section is studied with the sinc approximation in the eikonal limit. We consider the quintessence state parameter in the particular…
The nature of scalar wave functions near the horizon of Reissner Nordstrom (RN) extremal and Schwarzschild-de Sitter (SdS) extremal black holes are found using WKB approximation and the effect of reflection of waves from the horizon. The absorption cross section $σ_{abs}$ when RN extremal and SdS extremal black holes placed in a Klein-Gordon field is calculated.
The absorption and emission problems of the brane-localized and bulk scalars are examined when the spacetime is a $(4+n)$-dimensional Reissner-Nordström black hole. Making use of an appropriate analytic continuation, we compute the absorption and emission spectra in the full range of particle's energy. For the case of the brane-localized scalar the presence of the nonzero inner horizon parameter $r_-$ generally enhances the absorptivity and suppresses the emission rate compared to the case of the Schwarzschild phase. The low-energy absorption cross section exactly equals to $4πr_+^2$, two-dime…
We consider planar massless scalar waves impinging upon a Kerr black hole, for general angles of incidence. We compute the absorption cross section via the partial wave approach, and present a gallery of results. In the low-frequency regime, we show that the cross section approaches the horizon area; in the high-frequency regime, we show that the cross section approaches the geodesic capture cross section. In the aligned case, we extend the complex angular momentum method to obtain a `sinc' approximation, which relates the regular high-frequency oscillations in the cross section to the propert…
Basing on the ideas used by Kiselev, we study three black holes surrounded by quintessence and the effects of quintessence on the classical and semiclassical scattering cross-sections. In contrast, the absorption section is studied with the sinc approximation in the eikonal limit. For Schwarzschild, Reissner-Nordström and Bardeen black holes surrounded by quintessence, the values critical of charges and the normalization factor are obtained. We also described the horizons and the extremal condition of the black holes surrounded by quintessence. By setting for the quintessence state parameter i…
We analytically study the scalar perturbation of non-asymptotically flat (NAF) rotating linear dilaton black holes (RLDBHs) in 4-dimensions. We show that both radial and angular wave equations can be solved in terms of the hypergeometric functions. The exact greybody factor (GF), the absorption cross-section (ACS), and the decay rate (DR) for the massless scalar waves are computed for these black holes (BHs). The results obtained for ACS and DR are discussed through graphs.
We investigate null geodesics impinging parallel to the rotation axis of a Kerr-Newman black hole, and show that the absorption cross section for a massless scalar field in the eikonal limit can be described in terms of the photon orbit parameters. We compare our sinc and low-frequency approximations with numerical results, showing that they are in excellent agreement.
In this work, we investigate the scattering of massless plane scalar waves by the high dimensional noncommutative Schwarzschild-Tangherlini black hole. We use the partial wave approach to determine the scattering and absorption cross sections in the incident wavelength range. Our numerical results demonstrate that the bigger the noncommutative parameter, the smaller the maximum value of the related partial absorption cross section, however the tendency is slightly. We also discovered that when the noncommutative parameter is weak, the absorption cross section of the high dimensional black hole…
Motivated by black hole experiments as a consequence of the TeV-scale gravity arising from modern brane-world scenarios, we study the absorption problem for the massive scalars when the spacetime background is a $(4+n)$-dimensional Reissner-Nordström black hole. For analytic computation we adopt the near-extreme condition in the spacetime background. It is shown that the low-energy absorption cross section for the s-wave case holds an universality, {\it i.e.} the absorption cross section equals to the area of the black hole horizon divided by a velocity parameter.
In this paper we aim to investigate the process of massless scalar wave scattering due to a self-dual black hole through the partial wave method. We calculate the phase shift analytically at the low energy limit and we show that the dominant term of the differential cross section at the small angle limit is modified by the presence of parameters related to the polymeric function and minimum area of a self-dual black hole. We also find that the result for the absorption cross section is given by the event horizon area of the self-dual black hole at the low frequency limit. We also show that, co…
We consider the interaction between a plane wave and a (counter-moving) black hole. We show that energy is transferred from the black hole to the wave, giving rise to a negative absorption cross-section. Moving black holes absorb radiation and deposit energy in external radiation. Due to this effect, a black hole hole of mass M moving at relativistic speeds in a cold medium will appear to be surrounded by a bright "ring" of diameter 3\sqrt{3}GM/c^2 and thickness GM/c^2.
In this paper, we have studied QNM modes and absorption cross sections of Born-Infeld-de Sitter black holes. WKB approximation is employed to compute the QNM modes of massless scalar fields. We have also used null geodesics to compute quasi-normal modes in the eikonal approximation. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. Unstable circular null orbits are derived from the effective metric which is obeyed by light rays under the influence of a nonlinear electromagnetic field. Comparison is shown with the QNM of the linear electro…
The effects of the tidal charge of black holes predicted in the Randall-Sundrum brane-world scenario on the electromagnetic cross sections and emission rate is studied. Although quantitatively different, the cross sections and emission rates of such black holes are similar to the ones of Schwarzschild black holes. The increase of the tidal-charge intensity makes the absorption cross sections increase and the interference-fringe widths of the differential scattering cross sections narrow. The electromagnetic emission rate increases initially with the increase of the tidal-charge intensity, but …
Greybody Factors, Absorption Cross Sections and Hawking Radiation of Holonomy-Corrected Schwarzschild Black Holes
University of Hradec Králové（赫拉德茨克拉洛韦大学）；Kimyo International University in Tashkent（塔什干金学院国际大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Ulugh Beg Astronomical Institute（乌鲁伯格天文研究所）；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）
We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle energies E. At high couplings, where the Schwarzschild radius R_S is much greater than the wavelength lambda, we find that the cross section approaches the classical result for a point particle. At intermediate couplings we find oscillations around the classical limit whose precise form depends on the …
We study fermionic perturbations in the background of a two and five-dimensional dilatonic black holes. Then, we compute the reflection and transmission coefficients and the absorption cross section for fermionic fields, and we show numerically that the absorption cross section vanishes in the low and high frequency limit. Also we find that beyond a certain value of the horizon radius $r_0$ the absorption cross section for five-dimensional dilatonic black hole is constant. Besides, we have find that the absorption cross section decreases for higher angular momentum, and it decreases when the m…
In this work, we numerically investigate the scattering and absorption cross section of the massless scalar field from some well-known regular black holes by using the partial wave approach. Our computational results indicate that the larger the parameters, the lower the associated total absorption cross section maxima. When compared to the Schwarzschild black hole, the scattering cross section is enhanced in some regular black hole spacetimes, meanwhile the scattering width is narrow in the forward orientation. Moreover, it is found that the null geodesics of the critical impact parameter and…
Accretion of fields by black holes is a subject of great interest in physics. It is known that accretion plays a fundamental role in active galactic nuclei and in the evolution of black holes. Accretion of fundamental fields is often related to the study of absorption cross section. Basically all black holes for which absorption of fields has been studied so far present singularities. However, even within general relativity, it is possible to construct regular black holes: objects with event horizons but without singularities. Many physically motivated regular black hole solutions have been pr…
