Session L8: Quantum Aspects of Gravitation

A local Hamiltonian for spherically symmetric gravity coupled to a scalar field

Using Ashtekar's new variables we present a gauge fixing that achieves the longstanding goal of making gravity coupled to a scalar field in spherical symmetry endowed with a local Hamiltonian. It opens the possibility of direct quantization for a system that can accommodate black hole evaporation. The gauge fixing can be applied to other systems as well.   

Accumulation of Quantum Fluctuation Effects in a Time Dependent Spacetime

Certain observables in quantum gravity can be expressed as a double integral in time of a Riemann tensor correlation function. These observables include measures of angular blurring and spectral line broadening due to quantum fluctuations. On a flat background, these effects do not grow with increasing distance between a source and a detector, due to cancellation of anticorrelated fluctuations. We discuss the possibility that a time dependent background, such as a cosmological model with small oscillations in the scale factor, can upset these cancellations and lead to effects which grow with distance. This possibility will be illustrated with a simple analog model involving a charged particle oscillating near a mirror. In the quantum gravity context, noncancellation of fluctuations might lead to observable effects.   

Rigorous construction of Hartle-Hawking type states from a Wick rotation

For a large class of black hole spacetimes with a static exterior region we consider a massive scalar quantum field propagating in this spacetime and we give a rigorous mathematical construction of states that extend thermal states in the exterior region, following a strategy proposed by Hartle and Hawking (1976). In particular, we perform a Wick rotation in the exterior region and compactify the imaginary time coordinate to obtain thermal states at any temperature. We show that the initial data of these states can be extended across the bifurcation surface, which yields a state on the entire spacetime. At temperatures other than the Hawking temperature these states are known not to be ``regular'' (i.e. Hadamard). Our explicit construction allows us to point out several subtleties in the construction, concerning the choice of Euclidean Green's function, analytic continuation of the Green's function and the heat kernel and the expected regularity of the state at the Hawking temperature.   

Coherent States and Quantum Geometry Phenomenology

The combinatorics of quantum geometry can raise the effective scale of the spatial geometry granularity predicted loop quantum gravity. However the sharply peaked properties of states built from SU(2) coherent states challenge the idea that such a combinatorial lever arm might lift the scale of spatial discreteness to an observationally accessible scale. For instance, the Livine-Speziale semi-coherent states exhibit no such lever arm. In this talk I discuss how an operational point of view suggests a different class of coherent states that are not built from states with microscopic classical geometry. These states are introduced, compared to previous coherent states, and the status of the combinatoric lever arm is discussed.   

Volume dynamics and quantum gravity

Polyhedral grains of space can be given a dynamical structure. In recent work it was shown that Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space results in a spectrum in excellent agreement with loop gravity. Here we present preliminary investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable which has important consequences for loop gravity: If the classical volume generates a chaotic flow then the corresponding quantum spectrum will generically be non-degenerate and the volume eigenvalue continues to act as a good label for spin network states. On the other hand, if the volume flow is classically integrable then the degeneracy of the corresponding quantum spectrum will have to be lifted by another observable. We report on progress distinguishing these two cases. Either of these outcomes will impact the direction of future research into volume operators in quantum gravity.   

Breakdown of the Weak Equivalence between Passive Gravitational Mass and Energy of a Composite Quantum Body

It is shown that passive gravitational mass operator of a composite quantum body in the post-Newtonian approximation of the General Relativity does not commute with energy operator. For the simplest composite quantum body - a hydrogen atom - a breakdown of the weak equivalence between passive gravitational mass and energy at a microscopic level can be experimentally detected by studying unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field. On the other hand, the weak equivalence between the expectation value of passive gravitational mass and energy is shown to survive at a macroscopic level for stationary quantum states. For mixed quantum states, a breakdown of the above mentioned equivalence at macroscopic level leads to time dependent oscillations of the expectation values of passive gravitational mass.   

Quantum singularities in static and conformally static spacetimes

The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by several examples: a Friedmann-Robertson-Walker space-time with cosmic string, Roberts space-time, Fornav space-time, and the HMN metric. Future areas of research are discussed.   

Temperature of the Vacuum Accelerated by External Fields

Using the result of M\"uller et al. [1], we show that in a constant electric field $E$, the electron fluctuations $\langle \bar\psi\psi\rangle$ display a thermal Bose spectrum with temperature $T=eE/m\pi=a/\pi$. This result contrasts with the Fermi spectrum and Hawking-Unruh temperature $T_{HU}=a/2\pi$ expected from viewing the vacuum fluctuations of the electrons as accelerated [2,3]. We consider the temperature in the electric field as a function of magnetic moment $g$. We find that the temperature in the electric field arises from the Dirac spinor nature of the electron with $g=2$ and, setting arbitrarily $g=1$, we recover the Hawking-Unruh $T_{HU}=a/2\pi$ with a Fermi spectrum. \\[4pt] [1] B. Muller, W. Greiner, and J. Rafelski, Phys. Lett. A63, 181 (1977).\\[0pt] [2] L.C.B. Crispino, A. Higuchi, George E.A. Matsas, Rev. Mod. Phys. 80, 787 (2008).\\[0pt] [3] W.-Y. Pauchy Hwang and S. P. Kim, Phys.Rev. D80, 065004 (2009).