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Claus Kiefer

Publications and source records attributed to Claus Kiefer.

At least 73 records · Page 4Linked to original sources
arXiv2009

Indefinite oscillators and black-hole evaporation

We discuss the dynamics of two harmonic oscillators of which one has a negative kinetic term. This model mimics the Hamiltonian in quantum geometrodynamics, which possesses an indefinite kinetic term. We solve for the time evolution in both the uncoupled and coupled case. We use this setting as a toy model for studying some possible aspects of the final stage of black-hole evaporation. We assume that one oscillator mimics the black hole, while the other mimics Hawking radiation. In the uncoupled case, the negative term leads to a squeezing of the quantum state, while in the coupled case, which includes back reaction, we get a strong entangled state between the mimicked black hole and the radiation. We discuss the meaning of this state. We end by analyzing the limits of this model and its relation to more fundamental approaches.

gr-qc↗
arXiv2009

Classical and quantum LTB model for the non-marginal case

We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the non-marginal case (defined by the fact that the shells of the dust cloud start with a non-vanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.

gr-qc↗
arXiv2009

Does time exist in quantum gravity?

Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.

gr-qc↗
arXiv2009

On the quantum fate of singularities in a dark-energy dominated universe

Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue whether some of these singularities, the big freeze and the big demarrage, can be avoided in quantum cosmology. We use the framework of quantum geometrodynamics. We restrict our attention to a class of models whose matter content can be described by a generalized Chaplygin gas and be represented by a scalar field with an appropriate potential. Employing the DeWitt criterium that the wave function be zero at the classical singularity, we show that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found. These solutions thus avoid the classical singularity. We discuss the reasons for the remaining ambiguity in fixing the solution.

gr-qc↗
arXiv2009

Why do cosmological perturbations look classical to us?

According to the inflationary scenario of cosmology, all structure in the Universe can be traced back to primordial fluctuations during an accelerated (inflationary) phase of the very early Universe. A conceptual problem arises due to the fact that the primordial fluctuations are quantum, while the standard scenario of structure formation deals with classical fluctuations. In this essay we present a concise summary of the physics describing the quantum-to-classical transition. We first discuss the observational indistinguishability between classical and quantum correlation functions in the closed system approach (pragmatic view). We then present the open system approach with environment-induced decoherence. We finally discuss the question of the fluctuations' entropy for which, in principle, the concrete mechanism leading to decoherence possesses observational relevance.

astro-ph↗
arXiv2008

Quantum geometrodynamics: whence, whither?

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.

gr-qc↗
arXiv2008

Measurement Analysis and Quantum Gravity

We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.

gr-qc↗
arXiv2008

Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity

In a recent publication we developed a canonical quantization program describing the gravitational collapse of a spherical dust cloud in 2+1 dimensions with a negative cosmological constant $-Λ\equiv -l^{-2}<0$. In this paper we address the quantization of the Banados--Teitelboim--Zanelli (BTZ) black hole. We show that the mass function describing the black hole is made of two pieces, a constant non-vanishing boundary contribution and a discrete spectrum of the form $μ_n = \frac{\hbar}{l}(n+ \frac 12)$. The discrete spectrum is obtained by applying the Wheeler--DeWitt equation with a particular choice of factor ordering and interpreted as giving the energy levels of the collapsed matter shells that form the black hole. Treating a black hole microstate as a particular distribution of shells among the levels, we determine the canonical entropy of the BTZ black hole. Comparison with the Bekenstein--Hawking entropy shows that the boundary energy is related to the central charge of the Virasoro algebra that generates the asymptotic symmetry group of the three-dimensional anti-de Sitter space AdS$_3$. This gives a connection between the Wheeler--DeWitt approach and the conformal field theory approach.

gr-qc↗
arXiv2007

Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

We develop the canonical theory of gravitational collapse in 2+1 dimensions with a negative cosmological constant and obtain exact solutions of the Wheeler--DeWitt equation regularized on a lattice. We employ these solutions to derive the Hawking radiation from black holes formed in all models of dust collapse. We obtain an (approximate) Planck spectrum near the horizon characterized by the Hawking temperature $T_{\mathrm H}=\hbar\sqrt{GΛM}/2π$, where $M$ is the mass of a black hole that is presumed to form at the center of the collapsing matter cloud and $-Λ$ is the cosmological constant. Our solutions to the Wheeler-DeWitt equation are exact, so we are able to reliably compute the greybody factors that result from going beyond the near horizon region.

gr-qc↗
arXiv2007

Quantum cosmology with big-brake singularity

We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical version of the model in some detail, our main interest lies in its quantization. We formulate the Wheeler-DeWitt equation and derive solutions describing wave packets. We show that all such solutions vanish in the region of the classical singularity, a behaviour which we interpret as singularity avoidance. We then discuss the same situation in loop quantum cosmology. While this leads to a different factor ordering, the singularity is there avoided, too.

gr-qc↗
arXiv2007

Gibbs' paradox and black-hole entropy

In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm of the particle number. We discuss here how analogous situations arise in the statistical foundation of black-hole entropy. Depending on the underlying approach to quantum gravity, the fundamental objects to be counted have to be assumed indistinguishable or not in order to arrive at the Bekenstein--Hawking entropy. We also show that the logarithmic corrections to this entropy, including their signs, can be understood along the lines of standard statistical mechanics. We illustrate the general concepts within the area quantization model of Bekenstein and Mukhanov.

gr-qc↗
arXiv2006

Quantum phantom cosmology

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.

hep-th↗
arXiv2005

Quantum Gravity: General Introduction and Recent Developments

I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics, loop quantum gravity). I then address quantum gravitational aspects of string theory. This is followed by a discussion of black holes and quantum cosmology. I end with some remarks on the observational status of quantum gravity.

gr-qc↗
arXiv2005

Semiclassical approximation to supersymmetric quantum gravity

We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem Σ$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bosonic case, are discussed.

gr-qc↗
arXiv2005

Quantum Cosmology and the Arrow of Time

Although most fundamental laws are invariant under time reversal, experience exhibits the presence of irreversible phenomena -- the arrows of time. Their origin lies in cosmology, and I argue that only quantum cosmology can provide the appropriate formal framework. After briefly reviewing the formalism, I discuss how a simple and natural boundary condition can lead to the observed arrows of time. This yields at the same time interesting consequences for black holes.

gr-qc↗
arXiv2004

On the interaction of mesoscopic quantum systems with gravity

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non-relativistic expansions of the Klein-Gordon and Dirac equations in the post-Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.

gr-qc↗
arXiv2004

Hawking temperature from quasi-normal modes

A perturbed black hole has characteristic frequencies (quasi-normal modes). Here I apply a quantum measurement analysis of the quasi-normal mode frequency in the limit of high damping. It turns out that a measurement of this mode necessarily adds noise to it. For a Schwarzschild black hole, this corresponds exactly to the Hawking temperature. The situation for other black holes is briefly discussed.

gr-qc↗