A spectral approach to the Dirac equation in the non-extreme Kerr–Newmann metric

Winklmeier, Monika; Yamada, Osanobu

doi:10.1088/1751-8113/42/29/295204

Cited by 11 publications

(29 citation statements)

References 12 publications

(12 reference statements)

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“…This is in agreement with the seminal studies for the Kerr-Newman (1+3)-dimensional solutions carried out in [17,18] and dealt with different tools in e.g. [19,20]. Compare also [24] for the Kerr-NewmanAdS case and [25] for the Kerr-Newman-dS one.…”

Section: Introductionsupporting

confidence: 90%

Quantum properties of the Dirac field on BTZ black hole backgrounds

Belgiorno¹,

Cacciatori²,

Piazza³

et al. 2010

J. Phys. A: Math. Theor.

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Abstract. We consider a Dirac field on a (1 + 2)-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in (1 + 3) dimensions, essential self-adjointness on2 of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass µ of the Dirac field and the cosmological radius l holds true. The very presence of a boundarylike behaviour of r = ∞ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the (1 + 2)-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.

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Section: Introductionsupporting

confidence: 90%

Quantum properties of the Dirac field on BTZ black hole backgrounds

Belgiorno¹,

Cacciatori²,

Piazza³

et al. 2010

J. Phys. A: Math. Theor.

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“…[39]. Therein a result about essential selfadjointness ofĤ which is analogous to theorem 1 is stated for the Kerr-Newman case (cf.…”

Section: Note Addedmentioning

confidence: 90%

“…one has to check if the limit point case occurs both at the event horizon r = r + and at r = ∞. In the former case, it is useful introducing the following reparameterization of the metric in the non-extremal case: 39) where the parameters m, z 2 , a, l are replaced by r + , r − , a, l. One easily finds:…”

Section: It Is Useful To Introducementioning

confidence: 99%

The Dirac equation in Kerr–Newman–Ads black hole background

Belgiorno¹,

Cacciatori²

2010

Journal of Mathematical Physics

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Abstract. We consider the Dirac equation on the Kerr-Newman-AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operatorĤ. Then we show that for a massive Dirac field with mass µ ≥ 1 2l essential selfadjointness ofĤ on C ∞ 0 ((r + , ∞) × S 2 ) 4 is obtained even in presence of the boundary-like behavior of infinity in an asymptotically AdS black hole background. Furthermore qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axi-symmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the non-extremal case.

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“…Theorem 1 in [1]. See also [14] for the Kerr-Newman case. Moreover, one can show by means of variable separation (cf.…”

Section: Essential Selfadjointness Ofĥmentioning

confidence: 98%

“…We can now use (4.10), (3.13) and the relation 14) to express the product in the space of reduced wave functions (i.e. (3.13)):…”

Section: The Dirac Equationmentioning

confidence: 99%

The absence of normalizable time-periodic solutions for the Dirac equation in the Kerr–Newman–dS black hole background

Belgiorno

Cacciatori

2009

J. Phys. A: Math. Theor.

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Abstract. We consider the Dirac equation on the background of a Kerr-Newman-de Sitter black hole. By performing variable separation, we show that there exists no time-periodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previously considered cases, the novelty is represented by the presence, together with a black hole event horizon, of a cosmological (non degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case.

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A spectral approach to the Dirac equation in the non-extreme Kerr–Newmann metric

Cited by 11 publications

References 12 publications

Quantum properties of the Dirac field on BTZ black hole backgrounds

Quantum properties of the Dirac field on BTZ black hole backgrounds

The Dirac equation in Kerr–Newman–Ads black hole background

The absence of normalizable time-periodic solutions for the Dirac equation in the Kerr–Newman–dS black hole background

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