Supersymmetric Quantum Cosmology

D’Eath, P. D.

doi:10.1017/cbo9780511524424

Cited by 128 publications

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“…Eq. (3.3) is the momentum constraint equation [9,13]. We can now determine the background metric at late times, when the energy-momentum tensor is that of the black-hole radiation, following Vaidya [7].…”

Section: Solution Of Background Field Equationsmentioning

confidence: 99%

Vaidya Space-Time in Black-Hole Evaporation

Farley

D’Eath

2006

Gen Relativ Gravit

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This paper continues earlier work on the quantum evaporation of black holes. This work has been concerned with the calculation and understanding of quantum amplitudes for final data perturbed slightly away from spherical symmetry on a space-like hypersurface Σ F at a late Lorentzian time T . For initial data, we take, for simplicity, sphericallysymmetric asymptotically-flat data for Einstein gravity with a massless scalar field on an initial surface Σ I at time t = 0 . Together, such boundary data give a quantum analogue of classical Einstein/scalar gravitational collapse to a black hole, perhaps starting from a diffuse, early-time configuration. Quantum amplitudes are calculated following Feynman's approach, by first rotating: T → |T | exp(−iθ) into the complex, where 0 < θ ≤ π/2 , then solving the corresponding complex classical boundary-value problem, which is expected to be well-posed provided θ > 0 , and computing its classical Lorentzian action S class and corresponding semi-classical quantum amplitude, proportional to exp(iS class ). For a locally-supersymmetric Lagrangian, describing supergravity coupled to supermatter, any loop corrections will be negligible, provided that the frequencies involved in the boundary data are well below the Planck scale. Finally, the Lorentzian amplitude is recovered by taking the limit θ → 0 + of the semi-classical amplitude. In the black-hole case, by studying the linearised spin-0 or spin-2 classical solutions in the above (slightly complexified) case, for the corresponding classical boundary-value problem with the given perturbative data on Σ F , one can compute an effective energy-momentum tensor < T µν > EF F , which has been averaged over several wavelengths of the radiation, and which describes the averaged extra energy-momentum contribution in the Einstein field equations, due to the perturbations. In general, this averaged extra contribution will be spherically symmetric, being of the form of a null fluid, describing the radiation (of quantum origin) streaming radially outwards. The corresponding space-time metric, in this region containing radially outgoing radiation, is of the Vaidya form. This, in turn, justifies the treatment of the adiabatic radial mode equations, for spins s = 0 and s = 2 , which is used elsewhere in this work.

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Section: Solution Of Background Field Equationsmentioning

confidence: 99%

Vaidya Space-Time in Black-Hole Evaporation

Farley

D’Eath

2006

Gen Relativ Gravit

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“…will also obey differential constraints connected with the local coordinate invariance of the theory and with any other local invariances such as gauge invariance (if appropriate) [12,26]. This follows from the Dirac canonical approach to the quantisation of theories with local or gauge-like invariances [12,26]; the 'differential' Dirac approach is dual to the 'integral' Feynman approach. The most striking results of the Dirac approach arise when the invariance properties include local supersymmetry [12,22,23].…”

Section: The Quantum Amplitude For Bosonic Boundary Datamentioning

confidence: 99%

“…(The natural arena for hyperbolic equations is in the Cauchy evolution problem [10,11].) A simple example of such badly-posed behaviour is given in [5] (see also Sec.2.4 of [12]), which treats the 1-space, 1-time weak-field analogue of the boundary-value problem of the previous paragraph. In this example, there is only a real massless scalar field in flat Minkowski space-time.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, in the locally-supersymmetric case, for a large class of models, the amplitude above turns out to be exactly semi-classical, in a certain sense -see Eq. (2.2) below [12,[22][23][24]. In Sec.3, we discuss the 'background' nearly-spherically-symmetric 4-metric γ µν , needed in a self-consistent treatment of the classical field equations.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Amplitudes in Black-Hole Evaporation: Complex Approach and Spin-0 Amplitude

Farley

D’Eath

2011

Int. J. Mod. Phys. D

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This paper is concerned with the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. We evaluate quantum amplitudes (not just probabilities) for transitions from initial to final states. This quantum description shows that no information is lost in collapse to a black hole. Boundary data for the gravitational field and (in this paper) a scalar field are posed on an initial space-like hypersurface Σ I and a final surface Σ F . These asymptotically-flat 3-surfaces are separated by a Lorentzian propertime interval T (typically very large), as measured at spatial infinity. The boundary-value problem is made well-posed, both classically and quantum-mechanically, by a rotation of T into the lower-half complex plane: T −→ |T | exp(− iθ), with 0 < θ ≤ π/2 . This corresponds to Feynman's + iǫ prescription. We consider the classical boundary-value problem and calculate the second-variation classical Lorentzian action S (2) class as a functional of the boundary data. Following Feynman, the Lorentzian quantum amplitude is recovered in the limit θ −→ 0 + from the well-defined complex-T amplitude. Dirac's canonical approach to the quantisation of constrained systems shows that, for locally-supersymmetric theories of gravity, the amplitude is exactly semi-classical, namely, exp(iS (2) class ) for weak perturbations, apart from delta-functionals of the supersymmetry constraints. We treat such quantum amplitudes for weak scalar-field configurations on Σ F , taking (for simplicity) the weak final gravitational field to be spherically symmetric. The treatment involves adiabatic solutions of the scalar wave equation. This considerably extends work reported in previous papers, by giving explicit expressions for the real and imaginary parts of such quantum amplitudes.

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“…One can therefore derive, in principle, all we know about cosmology from a choice of boundary conditions [6], including formation of structure [7], coupling to matter fields [8], inflationary solutions [9], supersymmetric models [10,11].…”

Section: Hartle-hawking Quantum Statementioning

confidence: 99%

Quantum Cosmology From Three Different Perspectives

Esposito¹

2008

The Eleventh Marcel Grossmann Meeting

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Our review is devoted to three promising research lines in quantum cosmology and the physics of the early universe. The nonperturbative renormalization programme is making encouraging progress that we here assess from the point of view of cosmological applications: Lagrangian and Hamiltonian form of pure gravity with variable G and Λ; power-law inflation for pure gravity; an accelerating universe without dark energy. In perturbative quantum cosmology, on the other hand, diffeomorphism-invariant boundary conditions lead naturally to a singularity-free one-loop wave function of the Universe. Last, but not least, in the braneworld picture one discovers the novel concept of cosmological wave function of the bulk space-time. Its impact on quantum cosmology and singularity avoidance is still, to a large extent, unexplored.

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Supersymmetric Quantum Cosmology

Cited by 128 publications

References 0 publications

Vaidya Space-Time in Black-Hole Evaporation

Vaidya Space-Time in Black-Hole Evaporation

Quantum Amplitudes in Black-Hole Evaporation: Complex Approach and Spin-0 Amplitude

Quantum Cosmology From Three Different Perspectives

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