Some general bounds for one-dimensional scattering

Visser, Matt

doi:10.1103/physreva.59.427

Cited by 111 publications

(259 citation statements)

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“…Therefore, in this paper, some rigorous bounds will be placed on greybody factors. 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].…”

Section: Rigorous Bounds On Greybody Factorsmentioning

confidence: 99%

“…Therefore, in this paper, some rigorous bounds will be placed on greybody factors. These bounds were first developed in [9] …”

Section: Rigorous Bounds On Greybody Factorsmentioning

confidence: 99%

“…Therefore, in this paper, some rigorous bounds will be placed on greybody factors. These bounds were first developed in [9] for any positive functions * () hr . In this paper, we choose IACSIT International Journal of Engineering and Technology, Vol.…”

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confidence: 99%

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

Ngampitipan¹,

Boonserm²,

Chatrabhuti³

et al. 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 The 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 shown in Fig. 2 for five and six dimensions which correspond to n =...

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Section: Rigorous Bounds On Greybody Factorsmentioning

confidence: 99%

“…Therefore, in this paper, some rigorous bounds will be placed on greybody factors. These bounds were first developed in [9] …”

Section: Rigorous Bounds On Greybody Factorsmentioning

confidence: 99%

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

Ngampitipan¹,

Boonserm²,

Chatrabhuti³

et al. 2016

IJET

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“…The general and robust bounds on the transmission probability can be found in [4]. They are applied to generic systems [5][6][7] and black hole greybody factors [3,8].…”

Section: The Charged Dilatonic Black Holes In (2 + 1) Dimensionsmentioning

confidence: 99%

“…They are applied to generic systems [5][6][7] and black hole greybody factors [3,8]. The lower bounds on the transmission probabilities are given by [4,[8][9][10] T ≥ sech 2…”

Section: The Charged Dilatonic Black Holes In (2 + 1) Dimensionsmentioning

confidence: 99%

Transmission Probability for Charged Dilatonic Black Holes in Various Dimensions

Ngampitipan¹,

Boonserm²

2014

Proceedings of the 12th Asia Pacific Physics Conference (APPC12)

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A dilaton is a theoretical particle, which results from the Plank mass raised to a dynamical field. In this paper, the rigorous bounds on the transmission probabilities for charged black holes, coupled to a dilaton field in various dimensions, are calculated. The results show that in the absence of the cosmological constant, the black holes in (2 + 1) dimensions have only one event horizon. Moreover, the charges of the black holes can increase the transmission probabilities. However, for the black holes in (3 + 1) dimensions, the charges of the black holes can filter Hawking radiation.

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