Singularities of general relativity and their quantum fate

Abstracts, Slides & Videos

Andrzej Krasiński, Singularities you might not be familiar with (i.e. strange kinds of Big Bang) (download pdf, YouTube)

In the talk I will present examples of interesting consequences (which are inprinciple observable) of nonsimultaneous Big Bang and shell crossingsingularities in Lemaitre - Tolman (LT) and Szekeres cosmological models.Specifically, after briefly introducing these models, I will discuss thefollowing topics: (1) How observations of type Ia supernovae can be accountedfor using an LT model without introducing "dark energy"; (2) How gamma-raybursts can be explained as blueshifted relic radiation in an LT model withnonsimultaneous Big Bang. (3) Evidence that strong blueshifts can exist inquasi-spherical Szekeres models; (4) How a shell crossing in an LT model wouldreveal its presence to an observer.

Andrzej Królak, Detection of gravitational waves from binary black hole mergers (download pptx. YouTube)

Claes Uggla, The structure of generic singularities and the underlying reasons for that structure (download pptx, YouTube)

I will argue that Lorentzian causal structure, general covariance, and scale invariance are first principles that play a key role for the nature of generic spacelike singularities in GR. To contextualize and bring a new perspective to the role of these first principles for some of the chaotic aspects of generic spacelike singularities, I will consider spatially homogeneous Bianchi type VIII and IX models in Horava-Lifshitz gravity, thus breaking and replacing relativistic first principles with anisotropic scalings of Lifshitz type. It turns out that GR in this context corresponds to a bifurcation where chaos becomes generic. For models that are different than the critical GR case, Cantor sets turn out to play a key role. In addition I will give examples that illustrate connections between spacelike singularities and weak null singularities, and I will also discuss permanent and recurring spikes.

Claus Kiefer, Fate of singularities in quantum gravity (download pdf, YouTube)

Singularities occur frequently in classical general relativity. In my talk, I shall address the question whether and how these singularities can be avoided in quantum gravity. Since a final theory of quantum gravity is not yet known, this question must be addressed within a concrete approach and for simple models. I shall report about the situation in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. The models are of two types: cosmological models with classical singularities such as big rip or big brake and models of dust shells that classically collapse to a black hole. I shall show that these singularities can be avoided in quantum geometrodynamics and shall discuss the underlying mechanism.

David Garfinkle, Numerical simulations of classical and quantum spikes (download ppt, YouTube)

Edgar Shaghoulian, Timelike BKL singularities and chaos in AdS/CFT (YouTube)

We will primarily focus on the relevance of timelike BKL singularities in the context of AdS/CFT, highlighting various implications for the dual field theory. We will also sketch arguments that the approach to a timelike BKL singularity can be modeled by a chaotic billiard ball problem on hyperbolic space, and that this generic chaotic behavior is probably lost in higher than 3+1 dimensions.

Edward Wilson-Ewing, Bouncing cosmologies from quantum gravity condensates (download pdf)

We study the effective cosmological dynamics, emerging as the hydrodynamics of simple condensate states, of a group field theory model for quantum gravity coupled to a massless scalar field and reduced to its isotropic sector. The quantum equations of motion for these group field theory condensate states are given in relational terms with respect to the scalar field, from which effective dynamics for spatially flat, homogeneous and isotropic space-times can be extracted. The result is a generalization of the Friedmann equations, including quantum gravity modifications, in a specific regime of the theory. The classical Friedmann equations of general relativity are recovered in a suitable semi-classical limit for some range of parameters of the microscopic dynamics. An important result is that the quantum geometries associated with these group field theory condensate states are non-singular: a bounce generically occurs in the Planck regime. For some choices of condensate states, these modified Friedmann equations are very similar to those of loop quantum cosmology.

Ewa Czuchry, Singularity avoidance in the Mixmaster

Mixmaster universe is an anisotropic cosmological model comprising the Friedmann model a special case. Towards the big-bang singularity the isotropy of space is dynamically unstable, thus the quantization of the isotropic models alone appears to be insufficient to describe the earliest Universe. In my talk I will present the quantum version of the Mixmaster universe obtained by implementing affine coherent state quantization combined with a Born-Oppenheimer-like adiabatic approximation, widely utilized in quantum molecular physics. The resolution of the classical singularity occurs by means of a repulsive potential generated by the quantization procedure. The quantized anisotropic degrees of freedom behave as radiation energy density. The Friedmann-like lowest energy eigenstates of the system seem, in opposite of classical case, to be dynamically stable against small anisotropy perturbations.

Jakub Gizbert-Studnicki, Phase structure of Causal Dynamical Triangulations model in 4D (download pdf, YouTube)

I will discuss a quantum gravity model defined by Causal Dynamical Triangulations. Identification of the phase structure and order of the phase transitions is a first step in the quest for a continuum limit of CDT where, following the asymptotic safety conjecture, singularities are wiped out and the resulting theory of quantum gravity becomes nonperturbatively renormalizable. I will present the recently updated CDT phase diagram and discuss geometric properties of the new „bifurcation" phase. I will also briefly describe the impact of topology on CDT phase structure.

Jakub Mielczarek, Nonlinear field spaces - a remedy for singularities

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space can have a nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of the talk is to discuss extension of this concept to the domain of field theories, the so-called Nonlinear Field Space Theory (NFST). After presenting the motivation and general aspects of the approach we will focus on analysis of the prototype (quantum) NFST of a scalar field. The case of compact field space is especially interesting, which is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born-Infeld theory. As we show, the field space compactness introduces an upper bound on the matter energy density. This result will be discussed in the context of homogeneous and isotropic cosmological singularity.

Jerzy Kijowski, "Generalizations'' of General Relativity Theory are equivalent to its standard version (download ppt, YouTube)

It was proved 30 years ago that the so called "f(R)-theory", i.e. theory of gravity derived from a non-linear Lagrangian L=f(R(g)), where R(g) denotes scalar curvature of the metric g, is equivalent to the standard Einstein theory for a new metric interacting with an additional matter field. It was proved 25 years ago that the same is true if we allow dependence of the Lagrangian upon the entire Ricci tensor, and not only upon its trace R. It was proved few years ago that the same is true for a Lagrangian which depends in an arbitrary way upon the entire curvature tensor, and not only Ricci. In my talk I am going to show that the same is true also for Lagrangians of "higher differential order", i.e. depending upon (covariant) derivatives of the curvature tensor up to a fixed order "n". We conclude that attempts to describe "dark matter" or "dark energy" in terms of an exotic theory of gravity do not give more than just adding new (maybe exotic) matter fields to the existing theory of gravity.

John Klauder, Enhanced Quantization: Solving the Insoluble (download pdfYouTube)

Canonical quantization relies on promoting classical "Cartesian phase-space coordinates " to quantum operators, although this may lead to insoluble problems (e.g., $\phi^4_n$, with spacetime dimension $n>4$). Instead, an alternative classical/quantum connection, which admits arbitrary classical canonical coordinate transformations and explains "Cartesian coordinates", can also yield the usual results for many systems as well as acceptable results for insoluble problems. This alternative procedure---called Enhanced Quantization---also provides a clarification of "trivial" or "nonrenormalizable" models, and solving some insoluble examples will show the power of the new approach. Finally, a quantum treatment of the classical model of gravitational spikes by Ashtekar, Henderson, and Sloan is presented.

Jose Senovilla, Trapped submanifolds and singularity theorems (download pdf, YouTube)

Singularity theorems are incompleteness results in Lorentzian geometry, not specific to General Relativity. Therefore, they can be applied to general theories of gravity and also in arbitrary dimensions. The classical theorems require, in 4 dimensions, the existence of either a point, a surface or a hypersurface whose future is fated to have a compact boundary. This carries over to general spacetime dimension ("surface" being replaced by a co-dimension two submanifold). The question arises: why these 3 particular types and not other possible submanifolds with different dimension? This question is most relevant in higher dimensions, where there are plenty of possibilities left over. In this talk I will prove that the singularity theorems remain valid by leaving the dimension of the doomed submanifold free, deeply clarifying as a by-product the meaning of other assumptions in the theorems ---such as the convergence/energy conditions. This has far-reaching consequences, and opens the door to many unexpected novel applications. As a particular illustrative example, I will consider the important case of compact extra-dimensions.

Ken-ichi Nakao, On rapidly rotating geometry (download pdf, YouTube)

It is well known fact that the singularity in the over-spinning Kerr spacetime is naked. It may be usually concluded that the cosmic censorship prohibits the over-spinning Kerr geometry in our universe. However, it is not clear whether the cosmic censorship is available in our universe. Furthermore, even if the cosmic censorship is available, the geometry similar to the over-spinning Kerr one around the naked singularity might appear in our universe. In this talk, the efficiency of extracting the energy from the vicinity of the Kerr naked singularity and its astrophysical significance will be mentioned. Furthermore, it will be shown that there is no lower bound on the “size” of an over-spinning spherical thin shell whose outside is transiently described by the over-spinning Kerr geometry, even if reasonable energy conditions hold. The possibility of the formation of such a transient configuration in our universe will also be discussed.

Manuel Krämer, Singularity resolution in Wheeler-DeWitt quantum cosmology (download pdf, YouTube)

Quantum cosmology with the Wheeler-DeWitt equation provides a mathematically rather simple testbed to study the possibility of singularity avoidance in quantum gravity. Based on Claus Kiefer's talk, I will present the canonical quantization of several cosmological models that exhibit classical singularities in more detail. This includes singularities, where quantities like energy density or pressure diverge at a certain point in time (Big Rip, Big Brake), as well as a milder type of singularity, where only higher derivatives of the Hubble parameter diverge. I will discuss in which of these cases singularities are avoided in the quantized model and will describe which criteria for singularity avoidance were used.

Marek Abramowicz, Detection of gravitational waves: consequences for quantum gravity

The LIGO measurements of the gravitational wave front, corresponding to the "ringdown", seriously challenge some quantum alternatives to black holes, among them gravastars, firewalls and naked Horava's singularities. The same is true when one considers the gravitational wave "afterglow", i.e. a weak burst of electromagnetic radiation detected(?) by other instruments (gamma-ray satellite Fermi) – they also already give constraints on these hypothetical quantum objects. Thus, for the first time, some quantum gravity (strong-field) ideas may be experimentally tested.

Martin Bojowald, Space-time structure and singularity resolution (download pdf, YouTube)

Proposals for singularity resolution are usually first formulated in homogeneous minisuperspace models, but the corresponding restrictions make it impossible to see the full space-time structure and the fate of covariance. One class of modified theories, which includes loop quantum cosmology, may resolve singularities but has resulted in covariant models with non-standard space-time structures. In particular, quantum effects at high density imply signature change to 4-dimensional Euclidean space whenever curvature is bounded in these models. This talk reviews general results and implications.

Mihalis Dafermos, Weak null singularities in the interior of dynamic vacuum black holes

I will discuss a forthcoming theorem on the structure of black hole interiors for dynamical vacuum spacetimes (without any symmetry) and what this means for the question of the nature of generic singularities in general relativity and the celebrated strong cosmic censorship of Penrose. This is joint work with Jonathan Luk (Cambridge).

Pankaj Joshi, Gravitational collapse, black holes and naked singularities (download pptx, YouTube)

The final fate of massive collapsing stars has been a fundamental topic in black hole physics and gravitation theory for past many decades. The general theory of relativity predicts necessary occurrence of a space-time singularity in such a scenario when the matter cloud collapses under its own gravity on exhausting its internal nuclear fuel. Such a singularity, which is a super-ultra dense region, may or may not be covered within a horizon of gravity. It is in fact the formation and behavior of the apparent horizon that decides whether the space-time singularity is enveloped in a black hole, or it may be visible to far away observers in the Universe. The formation of event and apparent horizons in gravitational collapse is very much a subject of active current investigations. We point out that the apparent horizon and trapped surfaces formation is determined in terms of initial data for collapse and the allowed evolutions by Einstein equations, emphasizing the computational aspects and techniques involved, numerical and analytical. The black hole and naked singularities in collapse involve key open issues such as genericity and stability related to these outcomes, and other aspects in terms of their applications in relativistic astrophysics. We discuss some of these recent developments, including implications for quantum gravity, and possible observational perspectives.

Parampreet Singh, Status of Singularity Resolution in Loop Quantum Cosmology (download pdf, YouTube)

In the last decade, rigorous quantization of various symmetry reduced models has been successfully performed in Loop Quantum Cosmology. Numerical simulations with a variety of states in different models have confirmed that the big bang singularity can be successfully resolved, and is replaced by a bounce. A combination of analytical, phenomenological and numerical methods has uncovered a picture of the Planck epoch with a rich physics. This includes indications for resolution of all strong curvature singularities in different spacetimes, non-singular inflationary models, and Kasner transitions in quantum Bianchi-I spacetime. In this talk, I will review some of these developments and summarize the current state of the art in this field.

Patrick Peter, Bouncing quantum cosmological solutions in the dBB approach (download pdf, YouTube)

The trajectory-based approach is especially meaningful in quantum cosmology as it provides a clear picture of the Universe evolution. Concentrating on special Bianchi I and FLRW minisuperspaces for which the Hilbert space of solutions can be explicitly constructed, there exists a variety of non singular bouncing solutions that are naturalny predicted whose perturbations can be analysed consistently in a unified framework.

Serge Parnovsky, Naked singularities: classification, general solution, quantum effects, etc (download ppt, YouTube)

This is a brief review of my old studies of timelike naked singularities (NS) in General Relativity. It includes the topics: general oscillating timelike singularity and its matching with oscillating BKL solution near spacelike singularity; classification of NSs: point-like, linear and paradox-like NSs; non-gravitational fields near NS; gravitational fields of rotating bodies and quantum effects during formation and near NSs.

Simone Zonetti, Resolving gravitational singularities with affine coherent states (download pdf, YouTube)

In this talk I will present some results on the resolution of black hole and cosmological singularities: by looking at simple models such as 1+1 dimensional dilaton gravity and FLRW cosmology, and using affine coherent states, it is possible to build semi-classical models, comparing classical and quantum solutions. Singularities are systematically removed, and thermodynamical properties of (affine) black holes can be investigated.

Tomasz Bulik, Astrophysics of binary black holes detected by LIGO (download odp)

Vladimir Belinski, The generic inhomogeneous Big-Bang with isotropic expansion, (download pdf, YouTube)

It is shown that near cosmological singularity the shear viscosity can suppress anisotropy of expansion and generic solution (without any presupposed symmetry) following initially the Friedmann isotropic dynamics exists.