Plenary Session 3

General Relativity - in particular if applied to the central mass problem – contains a singularity: The Schwarzschild singularity, which leads to the prediction of black holes.

Our new concept is: No theory should contain singularities. This will also be applied to quantum electrodynamics: In General Relativity it leads us to Pseudo-Complex General Relativity. Black holes disappear and a new “Weltbild” for the cosmos emerges.

After 40 years of active research the question of the fate of information that falls into a black hole is still open [1]. In this talk I will discuss recent results [2] that allow us to compute the entanglement entropy production in black hole evaporation. In particular I present a study of the information release in a model that takes into account the loop quantum gravity resolution of the black hole singularity [3]. The analysis of this phenomenon provides new insights into the entanglement structure of space-time during and after the complete evaporation of the black hole.

References

[1] S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) ~10, 2460.

[2] E. Bianchi and M. Smerlak, Entanglement entropy and negative-energy fluxes in two-dimensional spacetimes, (2014), arXiv:1404.0602

[3] C. Rovelli and F. Vidotto, Planck stars, (2014), arXiv:1401.6562

We exploit the recently found exact solution of the quantum constraints of loop quantum gravity in vacuum with spherical symmetry to analyze a quantum field theory living on the quantum space time. The main effect of the quantum background is to lead to field equations that are discrete for the quantum field theory. The Hartle-Hawking, Unruh and Boulware vacua are all recovered with small modifications, but the discrete structure eliminates all infinities asssociated with physical quantities computed on the vacuum. We also briefly address the issue of Lorentz invariance and the emergence of limitations on the matter content of the theory.

References

[1] R. Gambini, J. Pullin, arXiv: 1312:3595, to appear in CQG.

We briefly comment upon the parallel between graphene and high energy fermions and explore the possibility of using the former as a test bed for the latter rather like Reynold's numbers in a wind tunnel. We also point out that there are parallels to Quantum Gravity approaches, which indeed provide a novel explanation for such effects as the FQAE.

The physical meaning of the diffeomorphisms in the general relativistic theories will be discussed, the issues of time evolution in terms of the Dirac observables and physical Hamiltonian will be addressed. New proposals for geometric deparametrization will be presented. The quantum part of the lecture will concern the canonical LQG. New, improved formulations of the quantum Hamiltonian will be proposed. New applications for LQG will be offered. Original results that will be presented in this lecture were obtained in collaboration with: Dapor, Duch, Kaminski, Swiezewski, Alesci, Assanioussi, Dziendzikowski and Sahlmann.

This talk is based on [1,2,3]. Until less than 10 years ago, post-Newtonian (pN) analysis was the only possible systematic method for obtaining gravitational waveforms corresponding to binary inspiral. However, these were cut-off before the merger, until the recent availability of direct results from numerical relativity computations, which could include the complete merger and ring-down phase of the orbital evolution. Unfortunately these calculations are not yet of sufficient precision to strenuously test pN methods intrinsically. By contrast, the gravitational self-force approach has become capable of advancing to extremely high precision, and of thereby testing most of the various techniques used in pN calculations. Although restricted to the extreme-mass-ratio limit, self-force calculations are now able to verify both the methods and results of pN work, and even of extending it. In fact, as will be demonstrated, they now have high enough precision to be able to determine new coefficients analytically.

References

[1] Abhay G Shah, John L Friedman and Bernard F Whiting, Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation, 7pp, published in Phys.Rev. D 89 064042 (March 18, 2014), arXiv:1312.1952 [gr-qc]

[2] Luc Blanchet, Guillaume Faye and Bernard F. Whiting, Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries, 12 pp, published in Phys.Rev. D 89 064026 (March 11, 2014), arXiv:1312.2975 [gr-qc]

[3] Luc Blanchet, Guillaume Faye and Bernard F. Whiting, High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries, 33 pp, submitted to Phys.Rev. D (May 20, 2014), arXiv:1405.5151 [gr-qc].