Session J16: Quantum Aspects of Gravitation I

Hawking radiation in loop quantum gravity

We use the recently found exact solution representing a spherically symmetric quantum space-time to perform a quantum field theory in quantum space time analysis of a scalar field. The main influence of the presence of the quantum geometry is to yield a theory that effectively lives on a lattice due to the discreteness of space-time in loop quantum gravity. This in particular has consequences for the structure of the quantum vacua. Essentially all singular behaviors are removed by the discreteness. The resulting formula for the Hawking radiation suffers only small corrections, at least for macroscopic black holes and their natural frequencies and coincides with a formula that had been heuristically derived in the past.   

Non-singular AdS-dS transitions in a landscape scenario

In the multiverse scanario allowing eternal inflation, it is an important problem to understand transitions between different vacua, of which the ones from anti-deSitter to de-Sitter is forbidden in the classical theory. In this talk, we consider toy landscape potentials: a double well and a triple well potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics of loop quantum cosmology for the k$=-$1 FRW model. We show that due to the non-perturbative quantum gravity effects as understood in loop quantum cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In the future evolution, an anti-deSitter bubble universe does not encounter a big crunch singularity but undergoes a big bounce occurring at a scale determined by the underlying quantum geometry. These non-singular transitions provide a mechanism through which a probe or a ``watcher,'' used to define a local measure, can safely evolve through the bounce and geodesics can be smoothly extended from anti-deSitter to de-Sitter vacua.   

Effective dynamics of Kantowski-Sachs spacetime in loop quantum cosmology

We study singularity resolution in Kantowski-Sachs spacetime in the effective loop quantum cosmology setting for various matter models such as dust, radiation, cosmic strings, cosmological constant and scalar fields. We find the inverse triad correction and bounds on energy density, shear scalar and expansion scalar. The evolution of universe after bounce is studied and found that a Nariai-like spacetime is obtained for different choices of matter. We analyze the stability of these quantum Nariai-like spacetimes with respect to homogeneous perturbations and find that unlike classical Nariai spacetimes, these are stable.   

Two-point function for a BEC analogue black hole when a mass term is present

The two-point function for phonons is computed using quantum field theory in curved space techniques for a Bose-Einstein condenstate that serves as an analogue black hole. This is done in the case that the BEC is moving at a constant speed in a particular direction and excitations of the mode functions occur in the transverse direction as well as the direction of motion. The calculation reduces to an effective 1+1 dimensional calculation and the transverse excitations add a mass term to the mode equation for the phonons. The mass term significantly changes the character of the low frequency modes in the region well outside of the sonic horizon. The effects of this on the two point correlation function are investigated.   

Inequivalence Between Active Gravitational Mass and Energy for a Composite Quantum Body

We derive active gravitational mass operator for the simplest composite quantum body -- a hydrogen atom [1]. We show that, despite the fact that it does not commute with energy operator, taken in the absence of gravitational field, the equivalence between the expectation values of active gravitational mass and energy survives for stationary quantum states. Inequivalence between active gravitational mass and energy reveals itself as time-dependent oscillations of the expectation values of active gravitational mass for non-stationary quantum states. \\[4pt] [1] A.G. Lebed, Advances in High Energy Physics, accepted (2014).   

Quantum-Mechanical Correction to the Speed of Light in a Gravitational Potential

We consider a model in which the gravitational potential energy of massive particles is included in the Hamiltonian of the Dirac equation. This results in a predicted correction to the speed of light that is proportional to the fine structure constant [1]. The correction to the speed of light obtained in this way depends on the gravitational potential and not the gravitational field, which is not gauge invariant and presumably nonphysical. Nevertheless, the predicted results are in reasonable agreement with experimental observations from Supernova 1987a, where the first neutrinos arrived 7.7 hours before the first photons.\\[4pt] [1] J.D. Franson, arXiv:1111.6986.