Wave functions for the Schwarzschild black hole interior

Cartin, Daniel; Khanna, Gaurav

doi:10.1103/physrevd.73.104009

Cited by 34 publications

(46 citation statements)

References 23 publications

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“…The numerical results are based on using the triad component p c as an internal clock, however, our results suggest that p c bounces and hence would not play the role of a good clock. Thus to reconcile our results with those of [21,22], the numerical evolutions would probably require different initial conditions to incorporate both the expanding and contracting parts of the wave-packets at the initial instance in "time". This issue is solved in the isotropic case by including a scalar field that plays the role of a global internal clock.…”

Section: Discussionmentioning

confidence: 75%

“…In the works cited, numerical instabilities of the difference equation are found which bring into question whether any effective picture is valid near the singularity. In [21] it is argued that no proper semi-classical states exist unless the Immirzi parameter γ is less the the accepted value in the LQG literature raising a further question. In this article, our aim has been to probe the improved, non-constant δ quantization and thus we do not see a direct contradiction.…”

Section: Discussionmentioning

confidence: 99%

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Loop quantum dynamics of the Schwarzschild interior

2007

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We examine the Schwarzschild interior of a black hole, incorporating quantum gravitational modifications due to loop quantum gravity. We consider an improved loop quantization using techniques that have proven successful in loop quantum cosmology. The central Schwarzschild singularity is resolved and the implications for the fate of an in-falling test particle in the interior region is discussed. The singularity is replaced by a Nariai type Universe. We discuss the resulting conformal diagram, providing a clear geometrical interpretation of the quantum effects.

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Section: Discussionmentioning

confidence: 75%

Section: Discussionmentioning

confidence: 99%

Loop quantum dynamics of the Schwarzschild interior

2007

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“…In such models, limitations similar to that of a cosmological constant have been observed as possible instabilities of solutions in classical regions or the lack of a sufficient number of semiclassical states [27,28,29]. For the partial difference equations of anisotropic models in loop quantum cosmology, stability issues can be much more severe than in isotropic models and thus lead to further consistency tests which might help to restrict possible quantization freedom (see, e.g., [30]). In this paper we therefore introduce the general setting of anisotropic models taking into account lattice refinements of Hamiltonian constraint operators, focusing mainly on the anisotropic model which corresponds to the Schwarzschild interior.…”

Section: Introductionmentioning

confidence: 99%

Lattice refining loop quantum cosmology, anisotropic models, and stability

Cartin²,

2007

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A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is being refined during dynamical changes of the volume. In general, this leads to a new feature of dynamical difference equations which may not have constant step-size, posing new mathematical problems. It is discussed how such models can be evaluated and what lattice refinements imply for semiclassical behavior. Two detailed examples illustrate that stability conditions can put strong constraints on suitable refinement models, even in the absence of a fundamental Hamiltonian which defines changes of the underlying lattice. Thus, a large class of consistency tests of loop quantum gravity becomes available. In this context, it will also be seen that quantum corrections due to inverse powers of metric components in a constraint are much larger than they appeared recently in more special treatments of isotropic, free scalar models where they were artificially suppressed.

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“…At odd integer multiples of µ 2 = 2δ 2 , we obtain a recurrence relation which requires s 2δ1,2(2n+1)δ2 = s −2δ1,2(2n+1)δ2 for all integer n. There are thus reflection symmetry conditions which directly follow from the dynamical law even in the presence of parity-violating terms. (This symmetry has been observed first in the vacuum case [46].) However, evolution away from µ 1 = ±1 depends on whether µ 1 is positive or negative if parity is not preserved.…”

Section: Cosmological Implicationsmentioning

confidence: 94%

Fermions in loop quantum cosmology and the role of parity

Bojowald

Das

2008

Class. Quantum Grav.

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Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it is not possible to avoid strong quantum regimes by positing a large matter content. Moreover, possible parity violating effects are important especially in loop quantum cosmology whose basic object is a difference equation for the wave function of the universe defined on a discrete space of triads. The two orientations of a triad are interchanged by a parity transformation, which leaves the difference equation invariant for ordinary matter. Here, we revisit and extend loop quantum cosmology by introducing fermions and the gravitational torsion they imply, which renders the parity issue non-trivial. A treatable locally rotationally symmetric Bianchi model is introduced which clearly shows the role of parity. General wave functions cannot be parity-even or odd, and parity violating effects in matter influence the microscopic big bang transition which replaces the classical singularity in loop quantum cosmology.

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Wave functions for the Schwarzschild black hole interior

Cited by 34 publications

References 23 publications

Loop quantum dynamics of the Schwarzschild interior

Loop quantum dynamics of the Schwarzschild interior

Lattice refining loop quantum cosmology, anisotropic models, and stability

Fermions in loop quantum cosmology and the role of parity

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