Hornbostel, Erich M(oritz) von

Katz, Israel J.

doi:10.1093/gmo/9781561592630.article.13358

Cited by 1 publication

(2 citation statements)

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“…The expressions (16a) and (16b) correspond to finite and infinite intervals respectively. Note that this requires us to take C 2 = 0 in (15) and limits the acceptable solutions (15) to Bessel functions of order ν = 1/2 (trigonometric). This result also eliminates unbounded wave functions since for large Z, J ν (W (2) Z) ∼ Z −1/2 so our solutions, which are of the form Z ν J ν (••), remain bounded at large Z.…”

Section: Solutionsmentioning

confidence: 99%

“…Although there are issues with Wheeler-DeWitt theory, it is very often used as an approximation to a theory of quantum gravity, and it is therefore useful to see what predictions it makes in this respect [11][12][13]. Such studies have been performed, for example, in the context of black holes [14][15][16][17], wormholes [18][19][20], and cosmology [21][22][23] (also see references therein). With this in mind we perform the analysis here.…”

Section: Introductionmentioning

confidence: 99%

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Topology and volume effects in quantum gravity: Wheeler–DeWitt theory

Brännlund¹,

DeBenedictis²,

Lauman³

2014

Class. Quantum Grav.

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We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological state, dictating the topology of the two-surfaces of the space-time, and a geometric state, which controls the geometry and is comprised of solutions to the Wheeler-DeWitt constraints. Within this symmetry reduced theory an eigenvalue equation is derived for the two-volume of spacetime, which for spherical topology is fixed to a value of 4π. However, for the other topologies it is found that the spectrum can be discrete and hence the universe, if in one of these other topological states, may only possess certain possible values for the two-volume, whereas classically all values are allowed. We analyze this result in the context of pure gravity (black holes).

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Section: Solutionsmentioning

confidence: 99%