Scalar-field amplitudes in black-hole evaporation

Farley, A. N.; D’Eath, P. D.

doi:10.1016/j.physletb.2004.09.004

Cited by 14 publications

(71 citation statements)

References 33 publications

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“…For example, the field φ (1) in the interior of the space-time may be decomposed as in Eq. (6) of [3]:…”

Section: The Quantum Amplitude For Late-time Datamentioning

confidence: 99%

“…When considering perturbative boundary data for a field of any spin, posed on Σ F in describing a final state resulting from black-hole evaporation, we denote by {a skℓmP } a set of analogous 'Fourier-like' coefficients, where s gives the particle spin, k the frequency, (ℓ, m) the angular quantum numbers, and P = ± 1 the parity (for s = 0 ). For simplicity, we study in this Paper only bosonic perturbations, of spins s = 0, 1, 2, as treated in [2][3][4][6][7][8]. In each case, we found that the quantum amplitude or wave functional is of the semi-classical form, being given by…”

Section: The Quantum Amplitude For Late-time Datamentioning

confidence: 99%

“…This agrees with the result summarized in Eq. (19) of [3], where the calculation of the probability density was based on the contour-integration treatment of [2].…”

Section: Analytic Continuation and The Large-squeezing Limitmentioning

confidence: 99%

“…For a complete specification of the problem (if indeed such a boundary-value problem is well-posed -see below), one further needs to give the Lorentzian propertime interval T which separates Σ I from Σ F , as measured at spatial infinity. In the papers [3,4], as in the present paper, we take the simplest possibility for the matter fields present, namely, a real massless scalar field φ . Then, suitable boundary data on Σ I and on Σ F are expected to be (h ij , φ) I,F .…”

Section: Introductionmentioning

confidence: 99%

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Quantum amplitudes in black-hole evaporation: coherent and squeezed states

Farley

D’Eath

2006

Class. Quantum Grav.

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In earlier papers, the quantum amplitude for processes involving the formation and evaporation of black holes was calculated by means of a complex-time approach. Instead of taking a more familiar approach to black-hole evaporation, we simply followed Feynman's + iε approach in quantum field theory. The Lorentzian time-interval T , measured at spatial infinity between a pair of asymptotically-flat space-like hypersurfaces Σ I and Σ F carrying initial and final boundary data for the gravitational and other fields, is rotated: T → |T | exp(− iδ) , where 0 < δ ≤ π/2 . Classically and quantum-mechanically, this procedure is expected to lead to a well-posed boundary-value problem. Thus, what we have done is to find quantum amplitudes (not just probability densities) relating to a pure state at late times following gravitational collapse of matter to a black hole. Such pure states, arising from gravitational collapse, are then shown to admit a description in terms of coherent and squeezed states. Indeed, this description is not so different from that arising in a well-known context, namely, the highly-squeezed final state of the relic radiation background in inflationary cosmology. For definiteness, we study the simplest model of collapse, based on Einstein gravity with a massless scalar field. Following the complex rotation above, one finds that, in an adiabatic approximation, the resulting quantum amplitude may be expressed in terms of generalised coherent states of the harmonic oscillator. A physical interpretation is given; further, a squeezed-state representation follows.

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“…For example, the field φ (1) in the interior of the space-time may be decomposed as in Eq. (6) of [3]:…”

Section: The Quantum Amplitude For Late-time Datamentioning

confidence: 99%

Section: The Quantum Amplitude For Late-time Datamentioning

confidence: 99%

“…This agrees with the result summarized in Eq. (19) of [3], where the calculation of the probability density was based on the contour-integration treatment of [2].…”

Section: Analytic Continuation and The Large-squeezing Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum amplitudes in black-hole evaporation: coherent and squeezed states

Farley

D’Eath

2006

Class. Quantum Grav.

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“…(i) In their investigation of quantum amplitudes in black-hole evaporation [1], the authors of [2,3] have considered emission of scalar radiation in a black-hole collapse problem, assuming non-spherical perturbations of the scalar field φ on the final surface Σ F , and that the intrinsic three-metric describes an exactly spherically-symmetric spatial gravitational field.…”

Section: Introductionmentioning

confidence: 99%

The Scalar Wave Equation in a Non-Commutative Spherically Symmetric Space-Time

Grezia

Esposito

Miele

2008

Int. J. Geom. Methods Mod. Phys.

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Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity parameter θ. The present paper studies the asymptotic behaviour of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighbourhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler-Poisson-Darboux equation, where the parameter θ affects explicitly the functional form of the source term. Interestingly, for finite values of θ, there is full qualitative agreement with general relativity: the conformal singularity at spacelike infinity reduces in a considerable way the differentiability class of scalar fields at future null infinity. In the physical space-time, this means that the scalar field has an asymptotic behaviour with a fall-off going on rather more slowly than in flat space-time.

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Quantum Amplitudes in Black–Hole Evaporation with Local Supersymmetry

D’Eath

Farley

2014

Fundamental Theories of Physics

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Scalar-field amplitudes in black-hole evaporation

Cited by 14 publications

References 33 publications

Quantum amplitudes in black-hole evaporation: coherent and squeezed states

Quantum amplitudes in black-hole evaporation: coherent and squeezed states

The Scalar Wave Equation in a Non-Commutative Spherically Symmetric Space-Time

Quantum Amplitudes in Black–Hole Evaporation with Local Supersymmetry

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