Particle Creation by Gravitationally Collapsing Dust Shells

Abstract: In this work some aspects of quantum field theory in the gravitational collapse of dust shells are studied. As a model for possible backreaction effects in the background space-time of an evaporating collapsing shell a derivation of the 2D renormalized energy-momentum tensor is presented by using the Davies-Fulling-Unruh (DFU) formula for a conformal massless scalar field with an exterior generalized Vaidya metric. The flux of particles created - the so called pre-Hawking radiation- at future null infinity is obtained for shells following time-like as well as null trajectories in the presence and absence of backreaction. Finally, by using the four dimensional Einstein's equations it is shown that the condition for a compact horizonless object emanating a time-dependent Hawking-like flux $\dot{M}(u)\sim -1/M(u)^2$ is that the collapsing shell remains pressureless at the expense of moving at an un-physical superluminal speed. The only physically admissible solution is therefore to have a vanishing pre-Hawking flux at late-times which makes the formation of an apparent horizon an unavoidable conclusion.

Close

Singularity Avoidance of the Quantum LTB Model for Gravitational Collapse

Abstract: In classical General Relativity, singularities signal a breakdown of the theory. One line of inquiry that can be followed to investigate whether quantum gravitational effects could resolve this peculiar behavior is to quantize classical models for gravitational collapse, for example the Lemaître--Tolman--Bondi (LTB) model for spherically symmetric, self-gravitating dust.

Using a symmetry reduced treatment of the marginally bound LTB model based on Quantum Geometrodynamics, we show that close to the classical singularity the dynamics of the system follow a particular effective Hamiltonian. The general form of this Hamiltonian can be recovered in an alternate approach to quantizing the marginally bound LTB, where the dust cloud's general behavior is characterized by its outermost shell.

In this approach, which we develop here, an action for this outermost shell is derived starting from the Einstein--Hilbert action, and the resulting Hamiltonian quantized. Because the dust naturally provides a preferred notion of time, one can construct a Hilbert space as in ordinary quantum mechanics, and impose unitary evolution on its states. We then show that those states avoid the classical singularity. Furthermore, for a wave packet initially approximating the classical trajectory the collapse to a singularity is replaced by a bounce, effectively a transition from black to white hole. Finally we discuss some implications of this bouncing behavior by constructing a quantum corrected spacetime describing dust collapse based on this wave packet: the nature of the horizon, the lifetime of the temporary ‘grey’ hole, and the effective pressure facilitating the bounce.

Close

On the various aspects of relativistic inhomogeneous cosmology

Abstract: Modern cosmology has observational access to two very distinct epochs in the history of the Universe: the very-high-redshift surface of last scattering and the low-redshift large-scale structure. One of the aims of relativistic cosmology is to bridge these two epochs with an accurate description of gravitationally induced dynamics that causally lead from one epoch to the other. In my talk I will present some of the constituents of this major endeavour, including:

- methods of modelling gravitational instability evolution and calculating its statistical outcome: the mass function on galaxy cluster scales. These are based on the scalar averaging formalism, with the Zel'dovich approximation serving as a closure condition and the silent universe models (Einstein equations with no rotation and no energy transfer).

- arguments against the Green and Wald formalism which appeared to invalidate the coupling of expansion to structure formation

Some of the presented results will be put in the context of the current and future astronomical sky surveys.

Close

Abstract: Anti-de Sitter space (AdS) is a maximally symmetric Loretzian metric characterized by a negative scalar curvature. It has been shown that a String theory in assymptotic flat AdS bears correspondence to a Quantum field theory invariant under conformal transformations living on the boundary of the this space such that a strongly coupled CFT implies for the string dual a Classical AdS gravity theory. But to model systems like heavy ion collisions which involve studying transient, non-equilibrium solution system, a non stationary study of the dynamics on AdS side is necessary. Perturbations on Minkowski have been studied to show that it is stable at linear and non linear level as waves dissipate by dispersion. Recent claim has been that the AdS space on the other hand is unstable at the non linear level (Dafermos, Anderson 2006). These generic small and finite perturbations of AdS become large and give rise to formation of small Black Holes. The conjecture then follows that Black holes are not an exception but the only expected outcome of a perturbed AdS space. An overview and current status of this conjecture will be presented.

In part II, a brief introduction to Inflation and the attractive reasons that motivate its study is presented. Inflation, a rapid expansion of the early universe, is well accepted in contemporary cosmology. This phase may be driven be several fields, whose potential is not well known, and often includes some random component. The discussion will begin with the Old Inflation model leading on to the Slow Roll Inflation hypothesis and the subsequent landscape of models that came with it. We discuss how constraints from Planck Data ie, the Universe as we know it today help in narrowing down the possible realization of inflation from a landscape of models available. We conclude with the outlook of the future BICEP2, LIGO and PLANCK experiments.

Further reading:
[1] P. Bizon, arXiv:1312.5544
[2] G. Martinon, arXiv:1708.05600
[3] J. Martin, arXiv:1807.11075
[4] S. Tsujikawa et al, arXiv:astro-ph/0507632

Close

Abstract: What are observables in Hamiltonian GR with electromagnetism? Do they change? Hamiltonian observables often have been defined as having 0 Poisson bracket with each first-class constraint. A reforming literature has redefined gauge transformations using not separate first-class constraints, but a tuned sum thereof, the gauge generator G. G in GR changes the 4-metric by a 4-d Lie derivative.

The classical definition of the Lie derivative is like comparing 1am CET and 1am CEST, so demanding a 0 Poisson bracket trivially yields the absence of change. A more plausible definition of observables would use G in all cases and allow a 4-d Lie derivative (not 0) for the bracket in GR; then tensor fields like the 4-metric are observables.

One can further test this definition using massive photons with and without artificial gauge freedom (Stueckelberg and Proca) and massive gravitons with and without clock fields. Unlike earlier definitions, the new definition yields equivalent observables for these equivalent theories.

But if internal and external gauge symmetries are both present, do the 0 and Lie derivative conditions mesh? Observables should be electromagnetically invariant and spatio-temporally covariant. Thus the electromagnetic field F and space-time metric g are observables. Hamiltonian observables are local fields, vary spatio-temporally, and agree with the Lagrangian.

Close

Abstract: We consider the wave equation, $\Box_g \psi=0$, in fixed flat Friedmann–Lemaître–Robertson–Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface $\{t=0\}$. The initial data sets are characterized by the condition that the Neumann data should dominate, in an appropriate $L^2$–sense, up to two spatial derivatives of the Dirichlet data. For these initial configurations, the $L^2(\mathbb{T}^3)$ norms of the solutions blow up towards the Big Bang hypersurfaces of FLRW and Kasner with inverse polynomial and logarithmic rates respectively. Our method is based on deriving suitably weighted energy estimates in physical space. No symmetries of solutions are assumed.

Close

Abstract: Asymptotic Safety constitutes a mechanism for obtaining a quantum theory of gravity within the framework of quantum field theory. The key ingredient in this scenario is a non-trivial renormalization group fixed point for the gravitational interactions which ensures the consistency and predictive power of the construction. This talk concisely summarizes the current status of the program before discussing properties of the gravitational flows emerging from spacetimes carrying a foliation structure. We also comment on relations to Monte Carlo simulations carried out within the Causal Dynamical Triangulation program and the scale-dependence of Lorentz-symmetry violating interactions at low energy.

Close

A mechanism for quantum correlations in emergent quantum mechanics

Abstract: In this talk, a particular approach to emergent quantum mechanics will be described. In this context, a new way to look to quantum entanglement is discussed. We will highlight differences with the standard description of entanglement in quantum theory.

Close

Gauge fixing and the semiclassical interpretation of quantum cosmology

Abstract: We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that time emerges only when the gravitational field is (semi)classical. We show that the usual results of the semiclassical interpretation can be obtained by gauge fixing, both at the classical and quantum levels. By ‘gauge fixing’ we mean a particular choice of the time coordinate, which determines the arbitrary Lagrange multiplier that appears in Hamilton’s equations. In the quantum theory, we adopt a tentative definition of the (Klein–Gordon) inner product, which is positive definite for solutions of the quantum constraint equation found via an iterative procedure that corresponds to a weak coupling expansion in powers of the inverse Planck mass. We conclude that the wave function should be interpreted as a state vector for both gravitational and matter degrees of freedom, the dynamics of which is unitary with respect to the chosen inner product and time variable.

Close

Functional renormalization group equation for Lorentzian spacetimes

Abstract: In the covariant approach to quantum gravity, a perturbative treatment of the Fierz–Pauli Lagrangian for the massless spin-2 graviton results in a theory which is power-counting non-renormalizable i.e. new divergences are expected to arise at each order of perturbation theory. Explicit calculations verified that cancellation of the divergent terms occur to one-loop in the absence of matter rendering the theory one-loop renormalizable, but at two-loops the existence of a divergent pole, called the Garoff–Sagnotti term, proves two-loop perturbative non-renormalizability. Asymptotic safety, provides a method to determine a well-defined theory of gravity, both in the IR and UV, using methods developed in Quantum Field Theory, following an initial non-perturbative treatment in the implementation of the background field. In this scenario, the flow of the coupling constants (Newton's constant and Cosmological constant) in the UV is studied via the Functional Renormalization Group Equation (FRGE). The existence of a non-Gaussian fixed point in their flow provides the UV completion of the theory implying a well-defined theory at all energy scales. In this talk, we will develop the tools essential for the construction of the FRGE for Lorentzian spacetimes. Then, we shall establish the asymptotic behavior obtained and compare it with the results found using a Euclidean signature. Finally, a covariant way of considering only foliated spacetimes will be introduced.

Close

Black hole evaporation: Entropy analysis and GUP corrections

Abstract: We have studied the entropy budget per particle emitted in blackbody radiation and determined explicit coarse-grainning models for classical and quantum entropies. As the process is unitary, the entropy is exactly compensated by the “hidden information” in the correlations that we choose not to consider within the specific selected coarse-graining. Our goal is to extend these ideas to a black hole evaporation process. In order to carry out this calculation we adopted a variant of the “average subsystem” approach, but consider a multipartite pure system that includes the influence of the rest of the universe. In addition, the entropy budget should be corrected at the last stages of evaporation, due to quantum gravity effects. We have been shown recently how these effects (expressed in terms of the generalized uncertainty principle) modify the Hawking flux when we approach the Planck size.

Close