Classical and quantum shell dynamics, and vacuum decay

Ansoldi, S.; Aurilia, A.; Balbinot, Roberto; Spallucci, Euro

doi:10.1088/0264-9381/14/10/004

Cited by 53 publications

(98 citation statements)

References 31 publications

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“…The analysis of the solutions of the above mentioned quantum equation for the shell radius is performed using a generalization to non-local problems of WKB ideas [11]. The use of WKB ideas in a similar context in General Relativity has been explored in [13,15,16,17]. In [15] expected values of interesting physical parameters are calculated using the WKB ground state.…”

Section: Introductionmentioning

confidence: 99%

Quantum collapse of a small dust shell

et al. 2002

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The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Hájíček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self adjoint momentum operator in the space of the shell motion which is confined to a half line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

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Section: Introductionmentioning

confidence: 99%

Quantum collapse of a small dust shell

et al. 2002

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“…In our picture, the pre-tunnelling state is represented by the x ≡ 0 solution of the junction condition. Although this case might appear rather simple at first sight and one could be tempted to just state that the initial state is, for example, the full M + spacetime (a point of view which has been taken for example in [67]), much more care has to be taken. The main reason is that when x = 0, the brane's world-volume degenerates to a curve.…”

Section: Discussionmentioning

confidence: 99%

“…Thanks to the spherical symmetry, the system of equations (1) can then be reduced to a single equation [67],…”

Section: B Spherical Symmetrymentioning

confidence: 99%

“…This is the content of a consistent literature on the subject [68,69,70,71,72,73,74,75,76] among which we would like to single out the more general, and recent, [77]: the problem is not trivial at all, because of the same subtleties that appear, for instance, in the Hamiltonian formulation of General Relativity. Among the various possible approaches we will closely follow the quantization procedure originally proposed by Farhi, Guth and Guven [16], which has, lately, been followed also in [67] and [78]. For the Lagrangian approach to the classical dynamics we will instead follow the clear and more general exposition of [77].…”

Section: The Effective Action/the Momentummentioning

confidence: 99%

“…stand for the trivial spherically symmetric part). Then, following [67,77], the effective action for the degrees of freedom associated with the radial and time coordinates takes the form…”

Section: The Effective Action/the Momentummentioning

confidence: 99%

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Shell-mediated tunnelling between (anti-)de Sitter vacua

Ansoldi

Sindoni

2007

Phys. Rev. D

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International School for Advanced Studies, SISSA/ISAS via Beirut, 2-4 -I-34014 Miramare, Trieste (TS), ITALY and INFN, Sezione di TriesteWe give an extensive study of the tunnelling between arbitrary (anti-)de Sitter spacetimes separated by an infinitesimally thin relativistic shell in arbitrary spacetime dimensions. In particular, we find analytically an exact expression for the tunnelling amplitude. The detailed spacetime structures that can arise are discussed, together with an effective regularization scheme for before tunnelling configurations.

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Quantum Transitions Between Minkowski and de Sitter Spacetimes

Alwis

Muia

Pasquarella

et al. 2020

Fortschritte der Physik

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Quantum transitions among de Sitter and Minkowski spacetimes through bubble nucleation are revisited using the Hamiltonian formalism. We interpret tunnelling probabilities as relative probabilities: the ratio of the squared wave functionals P=false|normalΨscriptNfalse|2false|normalΨscriptBfalse|2, with ΨscriptB,scriptN solutions of the Wheeler‐DeWitt equation corresponding to the spacetimes scriptN and scriptB, gives the probability of nucleating the state scriptN relative to the probability of having the state scriptB. We find that the transition amplitude from de Sitter to de Sitter for both up‐ and down‐tunnelling agrees with the original result based on Euclidean instanton methods. Expanding on the work of Fischler, Morgan and Polchinski we find that the Minkowski to de Sitter transition is possible as in the original Euclidean approach of Farhi, Guth and Guven. We further generalise existing calculations by computing the wave function away from the turning points for the classical motion of the wall in de Sitter to de Sitter transitions. We address several challenges for the viability of the Minkowski to de Sitter transition, including consistency with detailed balance and AdS/CFT. This sets this transition on firmer grounds but opens further questions. Our arguments also validate the Coleman‐De Luccia formulae in the presence of gravity since it has no issues involving negative eigenmodes and other ambiguities of the Euclidean approach. We briefly discuss the implications of our results for early universe cosmology and the string landscape.

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Classical and quantum shell dynamics, and vacuum decay

Cited by 53 publications

References 31 publications

Quantum collapse of a small dust shell

Quantum collapse of a small dust shell

Shell-mediated tunnelling between (anti-)de Sitter vacua

Quantum Transitions Between Minkowski and de Sitter Spacetimes

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