Bounding the greybody factors for Schwarzschild black holes

We study scalar, electromagnetic, axial and polar gravitational perturbations of the fourdimensional Reissner-Nordström-like black holes with a tidal charge in the Randall-Sundrum braneworld in the first approximation when the tidal perturbations are not taken into account. The quasinormal modes of these perturbations have been studied in both normal and eikonal regimes. Calculations have shown that the black holes on the Randall-Sundrum brane are stable against all kinds of perturbations. Moreover, we determine the greybody factor, giving transmission and reflection of the scattered waves through the effective potentials. It has been shown that the scalar perturbative fields are the most favorite to reflect the wave as compared to the other fields. With increasing value of the tidal charge, the ability of the all perturbative potentials to reflect the waves decreases. Our calculations in low-and high-frequency regimes have shown that black holes on the braneworld always have a bigger absorption cross section of massless scalar waves than the Schwarzschild and standard Reissner-Nordström black holes.

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“…At the small values of ω, transmission coefficient is close to zero while the reflection coefficient is close to one [52].…”

Section: Scatteringmentioning

confidence: 86%

Quasinormal frequencies of black hole in the braneworld

et al. 2016

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“…These bounds were originally used as a technical step when studying a specific model for sonoluminescence [11], and since then have also been used to place limits on particle production in analogue spacetimes [12] and resonant cavities [13], to investigate qubit master equations [14], and to motivate further general investigations of one-dimensional scattering theory [15]. Most recently, these bounds have also been applied to the greybody factors of a Schwarzschild black hole [16].…”

Section: Introductionmentioning

confidence: 99%

Transmission probabilities and the Miller–Good transformation

Boonserm¹,

Visser²

2008

J. Phys. A: Math. Theor.

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Transmission through a potential barrier, and the related issue of particle production from a parametric resonance, are topics of considerable general interest in quantum physics. The authors have developed a rather general bound on quantum transmission probabilities, and recently applied it to bounding the greybody factors of a Schwarzschild black hole. In the current article we take a different tack -we use the Miller-Good transformation (which maps an initial Schrodinger equation to a final Schrodinger equation for a different potential) to significantly generalize the previous bound.

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“…These bounds were first developed in [9]. Their further developments can be found in [10]- [13] and their applications can be found in [14]- [19]. For the radial Teukolsky equation in (9), the rigorous bounds on the greybody factors are given by …”

Section: Rigorous Bounds On Greybody Factorsmentioning

confidence: 99%

Rigorous Bounds on Greybody Factors: Scalar Emission of Negative Angular Momentum Modes from Myers-Perry Black Holes

Ngampitipan¹

2016

IJET

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Abstract-When taking into account the quantum effects, a black hole can emit the so-called Hawking radiation. This Hawking radiation propagates in a curved spacetime due to the presence of a black hole. In this paper, the Myers-Perry black hole is considered, which is an uncharged, rotating black hole occurring in higher dimensions. Scalar Hawking radiation emitted from the Myers-Perry black hole is studied. The rigorous bounds on the greybody factors for massless scalar field of negative-angular-momentum modes are also derived.Index Terms-Greybody factor, hawking radiation, myers-perry black hole, rigorous bound. I. INTRODUCTIONThe existence of black holes has been predicted by Einstein's general theory of relativity. The first solutions of the Einstein's field equation were discovered by Karl Schwarzschild. His solutions predicted the presence of Schwarzschild black holes, which are the uncharged, non-rotating black holes. The second type of black hole was obtained by solving the Einstein's field equation in conjunction with Maxwell's equation. This was done by Hans Reissner and Gunnar Nordstrom . Their solutions represented the Reissner-Nordstrom black holes, which are the charged, non-rotating black holes. The third set of solutions of the Einstein's field equation was discovered by Roy Kerr [1]. His solutions described the Kerr black holes, which are the uncharged, rotating black holes. The Kerr solutions were generalized to higher dimensions by Myers and Perry [2], [3]. Their results led to the prediction of Myers-Perry black holes, which are the uncharged, rotating black holes in higher dimensions.When studying the quantum effects of black holes, Stephen Hawking showed that black holes can emit thermal radiation which became known as Hawking radiation [4]. The curvature of spacetime due to the presence of a black hole acts as the gravitational potential barrier. one-dimensional scattering problem in quantum mechanics. The term 'greybody factor' can be defined as the transmission probability.In this paper, the rigorous bounds on the greybody factors for massless scalar field of negative-angular-momentum modes emitted from a Myers-Perry black hole will be derived. II. MYERS-PERRY SPACETIMEThe Myers-Perry spacetime can be described by the metric Here 2 n d is the metric on the unit n-sphere n S which is given byThe solutions of ( ) 0 r  provide the location of the black hole event horizons. In this paper, we focus on massless scalar field emitted from the Myers-Perry black hole. The equation of motion of this scalar field can be described by the Klein-Gordon equationwhere Engineering and Technology, Vol. 8, No. 4, August 2016 sin cos sin sin cos sinwhile the hyper-spherical harmonics satisfywhere  n S is the Laplacian. Then, the radial Teukolskywhere the tortoise coordinate * r is defined byThe relationship between the tortoise coordinate and the ordinary coordinate is plotted as shown in Fig. 1. where 2 2 a raThis Teukolsky potential can be expressed in another form as The potentialVr is plotted as...

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Bounding the greybody factors for Schwarzschild black holes

Cited by 117 publications

References 45 publications

Quasinormal frequencies of black hole in the braneworld

Quasinormal frequencies of black hole in the braneworld

Transmission probabilities and the Miller–Good transformation

Rigorous Bounds on Greybody Factors: Scalar Emission of Negative Angular Momentum Modes from Myers-Perry Black Holes

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