Atlantic General Relativity 2014

Transcription

1 Venue Atlantic General Relativity 2014 Department of Mathematics & Statistics University of New Brunswick, Fredericton May 6 7, 2014 registration and all talks will be in Tilley Hall room 404 (top floor of Tilley Hall) lunches and coffee breaks will be provided if you need a campus parking permit, please see Sanjeev Seahra after you arrive on Tuesday Internet if your home institution is part of the eduroam network, you should be able to log in to UNB s eduroam portal using your home institution s credentials we also have a number of temporary guest accounts available Tuesday dinner we are planning on having a conference dinner at 7 pm on Tuesday, May 6 at The King Street Ale House (546 King Street, directions on back pages) the plan will be for everyone to cover their own bill if you want to come along and haven t already let us know, please tell Sanjeev Seahra before noon on Tuesday, May 6

2 Tuesday, May 6, :30 08:50 Registration 08:50 09:00 Opening remarks 09:00 10:00 Bianca Dittrich (Perimeter Institute) Quantum space time engineering 10:00 10:30 Coffee 10:30 11:00 Jonathan Ziprick (University of New Brunswick) Initial data for cosmology in Loop Gravity 11:00 11:30 Steffen Gielen (Perimeter Institute) Space as a quantum gravity condensate 11:30 12:00 Ivan Booth () Closest Safe Approach to an Accreting Black Hole 12:00 13:00 Lunch 13:00 13:30 Hari Kunduri () The first law of soliton mechanics 13:30 14:00 Daniel C. Guariento (Universidade de Sao Paulo and Perimeter Institute) Cosmological black holes: causal structure and field sources 14:00 14:30 Sharmila Dhevi () Thermodynamics of charged AdS black holes 14:30 15:00 Coffee 15:00 15:30 David W. Tian () Lessons from f(r, R 2 c, R 2 m, L m ) gravity: smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling 15:30 16:00 Syed Moeez Hassan (University of New Brunswick) Inflation from a massive polymer field 16:00 16:30 Shohreh Rahmati (University of New Brunswick) Effects of non-standard kinetic terms on parametric resonance 19:00-21:00 Conference Dinner The King Street Ale House

3 Wednesday, May 7, :00 10:00 Bianca Dittrich (Perimeter Institute) New representations for loop quantum gravity 10:00 10:30 Coffee 10:30 11:00 Dario Brooks (Dalhousie University) Invariant classification of four-dimensional neutral signature metrics 11:00 11:30 Nathan Musoke (Dalhousie University) Holonomy of 4-dimensional neutral signature metrics 11:30 12:00 Andrew Day (University of Western Ontario) Wormholes and curvature flows 12:00 13:00 Lunch 13:00 13:30 Mehdi Saravani (Perimeter Institute) Dynamical emergence of universal horizons during the formation of black holes 13:30 14:00 Uzair Hussain () Covariant and gauge invariant master equations for perturbations of AdS4-Schwarzschild black holes 14:00 14:30 Aghil Alaee Khangha () Existence of small deformations of extreme black hole initial data 14:30 15:00 Coffee 15:00 15:30 Julian Barbour (University of Oxford) Shape Dynamics: motivation and concepts 15:30 16:00 Jack Gegenberg (University of New Brunswick) Quantum structure of a black hole horizon

4 Abstracts Shape Dynamics: motivation and concepts Julian Barbour University of Oxford Shape Dynamics (SD) arose from the desire to implement a relational dynamical theory of a closed universe along lines anticipated by Leibniz and Mach. In creating General Relativity (GR), Einstein had this aim but attacked the problem indirectly and left the status of Mach s Principle in a very confused state. I will indicate how a direct approach leads, rather remarkably, to a theory that locally is indistinguishable from GR but introduces a notion of simultaneity and suggests alternative ways to attack fundamental problems in gravitational theory. The key concepts and methods of SD will be presented in simple terms. Closest Safe Approach to an Accreting Black Hole Ivan Booth In this talk I will examine the causal and geometric horizons of dynamical black holes in (Lemaitre- Tolman-Bondi) collapsing dust spacetimes. Marginally trapped tubes in these spacetimes may be spacelike, timelike or null and may also be sourced from or disappear into shell-crossing singularities which we resolve with (timelike) shockwaves. The timelike separation function between the causal and geometric horizons is a rather complicated function; in particular it generally does not depend monotonically on the concentration of the pulse of accreting matter. Finally, I consider the application of this work for future space explorers seeking to make a closest (non-terminal) approach to a black hole horizon. This work was done in collaboration with Benjamin Tippett (UBC-Okanagan). Invariant classification of four-dimensional neutral signature metrics Dario Brooks Dalhousie University We investigate the mathematical properties of four-dimensional neutral signature Ricci flat Walker and Kundt spaces for which all of the polynomial scalar curvature invariants vanish. The main part of the talk will be focused on the equivalence problem in geometry applied to these VSI metrics. The main results of the project are discussed in detail with emphasis given on the explanation of the equivalence method due to Cartan and Karlhede. We conclude the discussion showing that the equivalence algorithm provides all necessary information to determine the equivalence of these pseudo-riemannian manifolds. Wormholes and curvature flows Andrew Day University of Western Ontario We investigate the application of Ricci flow and mean curvature flow on generalized non-compact spherically symmetric 3-dimensional manifolds. We then apply the flow equations explicitly to the case of wormhole geometries and also discover an equivalence between the intrinsic and extrinsic geometric flows.

5 Thermodynamics of charged AdS black holes Sharmila Dhevi I will review some results on the critical behavior of charged and rotating AdS black holes in arbitrary (spacetime) dimensions. Born-Infeld(BI) black holes have also been taken into account via the Born- Infeld action. The critical behavior is studied in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. In any dimension greater than or equal to three, for charged(including BI) and rotating black holes, the critical exponents coincide with those of the Van der Waals system. However, charged and rotating black holes in three dimensions do not exhibit any critical phenomena. New representations for loop quantum gravity Bianca Dittrich Perimeter Institute Loop Quantum Gravity is based on the Ashtekar-Lewandowski representation. This representation is based on a vacuum describing a totally degenerate spatial geometry. Excitations from this vacuum lead to regions with non-vanishing spatial vacuum. This description makes the construction of states describing extended geometries difficult. The expectation is that this would require a condensation of many excitations into a new vacuum. In this talk I will introduce a new representation for loop quantum gravity which realized this idea. The new vacuum describes geometries with zero curvature and excitations are now parametrized by curvature. I will also explain that this construction can be generalized to other vacua, if these are described by topological quantum field theories. This will allow to expand loop quantum gravity around different vacua and thus facilitate the construction of physical states, describing extended geometries. Quantum space time engineering Bianca Dittrich Perimeter Institute Given (a set of) fundamental models of quantum space time, for instance spin foam models, we aim to understand the large scale physics encoded in these fundamental models. Renormalization and coarse graining address this issue and help to understand how large scale physics depends on parameters in the fundamental models. I will review recent work on coarse graining and renormalization of spin foam and analogue models, revealing possible large scale phases, depending on parameters of the microscopic models. I will explain how these phases are connected to topological field theories and possible vacua for the theory of quantum gravity, e.g. loop quantum gravity.

6 Quantum structure of a black hole horizon Jack Gegenberg University of New Brunswick We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive 1/X 2 potential. The variable X that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region. Space as a quantum gravity condensate Steffen Gielen Perimeter Institute We discuss the proposal that space itself could be described as a condensate of elementary geometric building blocks, and its concrete implementation in the group field theory (GFT) formalism for quantum gravity. In this scenario, the condensation of many quantum gravity degrees of freedom into the same microscopic state represents a spatially homogeneous metric geometry. We show how, using this idea of condensation, an effective cosmological dynamics can be computed directly from the microscopic dynamics of a proposed group field theory action (which itself arises from a second quantisation picture for spin foam models/loop quantum gravity), illustrating this rather general procedure with examples that point at the possible cosmological phenomenology of our approach. Cosmological black holes: causal structure and field sources Daniel C. Guariento Universidade de Sao Paulo and Perimeter Institute Exact solutions of General Relativity that describe a black hole in an expanding universe look deceptively simple, yet they display interesting peculiarities such as a rich causal structure and a puzzling behavior of the source matter, be it from a fluid interpretation or from the field theory point of view. We will review one of the simplest of such solutions, the so-called generalized McVittie metric, which describes a dynamic black hole with a time-dependent mass in an expanding universe. Inflation from a massive polymer field Syed Moeez Hassan University of New Brunswick We study the inflation produced by a massive scalar field that has been quantized using Polymer Quantization. The background is a flat Friedmann-Robertson-Walker (FRW) spacetime. We look at the dynamics of the system and compare with the results of a classical massive scalar field.

7 Covariant and gauge invariant master equations for perturbations of AdS4-Schwarzschild black holes Uzair Hussain In [arxiv:gr-qc/ ] Poisson et. al. (2005) introduced a practical formalism for perturbations of spherically symmetric spacetimes in 4D. They apply this formalism to the Schwarzschild spacetime and write covariant master equations, including perturbative sources. In this talk I will outline how the same formalism can be used to write covariant master equations for an AdS4-Schwarzschild Black Hole. Existence of small deformations of extreme black hole initial data Aghil Alaee Khangha Cauchy initial data for solutions of Eisntein s equations consist of a Riemannian manifold M with metric h and extrinsic curvature K. Valid data (h,k) must satisfy constraint equations which form an elliptic system on M. In this talk I consider the following problem: given initial data corresponding to a vacuum extremal 5d black hole solution of Einstein s equations, can one find small deformations of this data with the same asymptotic behaviour and symmetries?. We prove the existence of a one parameter maximal family of solutions. This family of data is second order differentiable with respect to an appropriate norm and it has the same angular momentum and area of the event horizon of an extreme Myers-Perry black hole. Moreover, the geometry of this family is close (in a suitable sense) to the extreme Myers-Perry initial data set. The first law of soliton mechanics Hari Kunduri I will discuss the derivation of a mass formula and a mass variation law for asymptotically flat, stationary spacetimes in a general five dimensional theory of gravity coupled to an arbitrary set of Maxwell fields and uncharged scalar fields. If the spacetime is globally regular (i.e. the spacetime is a gravitational soliton), these mass formulas reduce to a sum of magnetic flux terms defined on its non-trivial 2-cycles (bubbles). If there is a black hole, we obtain a mass variation law more general than previously obtained, which also has contributions from the bubbles exterior to the black hole. This can be interpreted as the first law of black hole mechanics in a background soliton containing bubbles. Holonomy of 4-dimensional neutral signature metrics Nathan Musoke Dalhousie University The holonomy of a manifold is a measure of the extent to which parallel transport around a closed loop fails to preserve the vector transported. Some properties of holonomy from the literature will be presented and applied to the classification of 4-dimensional neutral signature metrics, specifically degenerate cases in the classification by scalar curvature invariants. Some explicit examples of four-dimensional neutral signature Walker (but not necessarily degenerate Kundt) spaces for which all of the polynomial scalar curvature invariants vanish are examined.

8 Effects of non-standard kinetic terms on parametric resonance Shohreh Rahmati University of New Brunswick I discuss the phenomenon of preheating in the early universe when the matter field action involves non-standard kinetic terms motivated by polymer quantization, Dirac-Born-Infled inflation, and other models. Dynamical emergence of universal horizons during the formation of black holes Mehdi Saravani Perimeter Institute Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of such a fluid. In particular, we focus on the incompressible limit of the fluid (or Constant Mean Curvature foliation) in the space-time of a spherically collapsing shell within an asymptotically cosmological space-time. In this case, ignoring the fluid back reaction, we can analytically show that an observer inside 3/4 of the Schwarzschild radius cannot send a signal outside, after a stage in collapse, even using signals that propagate infinitely fast in the preferred frame. This confirms the dynamical emergence of universal horizons that have been previously found in static solutions. We argue that this universal horizon should be considered as the future boundary of the classical space-time. Based on arxiv: Lessons from f(r, R 2 c, R 2 m, L m ) gravity: smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling David W. Tian This paper studies a generic fourth-order theory of gravity with Lagrangian density f(r, Rc, 2 Rm, 2 L m ). By considering explicit R 2 dependence and imposing the coherence condition f R 2 = f R 2 m = f R 2 c /4, the field equations of f(r, R 2, Rc, 2 Rm, 2 L m ) gravity can be smoothly reduced to that of f(r, G, L m ) generalized Gauss-Bonnet gravity. We use Noether s conservation law to study the f(r 1, R 2..., R n, L m ) model with nonminimal coupling between L m and Riemannian invariants R i, and conjecture that the gradient of nonminimal gravitational coupling strength µ f Lm is the only source for energy-momentum non-conservation. This conjecture is applied to the f(r, Rc, 2 Rm, 2 L m ) model, and the equations of continuity and non-geodesic motion of different matter contents are investigated. Finally, the field equation for Lagrangians including the traceless-ricci square and traceless-riemann (Weyl) square invariants is derived, the f(r, Rc, 2 Rm, 2 L m ) model is compared with the f(r, Rc, 2 Rm, 2 T ) + 2κL m model, and consequences of nonminimal coupling for black hole and wormhole physics are considered. The arxiv article number is: [gr-qc].

9 Initial data for cosmology in Loop Gravity Jonathan Ziprick University of New Brunswick In the first-order formalism of General Relativity, the intrinsic geometry of a spatial hypersurface Σ is given by a two-form E and the extrinsic geometry by a connection one-form A. If the hypersurface Σ has constant intrinsic and extrinsic curvature, then it represents initial data for de Sitter cosmology. In this talk, we introduce a remarkable choice of fields (A, E) describing such initial data for which the curvature of the connection vanishes F (A) = 0. This flat connection allows for a symplectomorphism between the general relativity phase space in terms of (A, E) and the phase space for loop gravity, setting the stage for a study of cosmological dynamics in terms of the loop gravity variables.

10 4/24/2014 Google Maps Walk 2.1 km, 25 min Directions from Tilley Hall to King Street Ale House Tilley Hall Fredericton, NB E3B, Canada Use caution - may involve errors or sections not suited for walking 1. Head northeast 67 m 2. Turn left toward Bailey Dr 100 m 3. Turn right onto Bailey Dr 27 m 4. Turn left toward Dineen Dr 39 m 5. Turn right toward Dineen Dr 30 m 6. Turn left toward Dineen Dr 100 m 7. Turn right onto Dineen Dr 10 m 1/2

11 4/24/2014 Google Maps 8. Turn left onto University Ave 1.0 km 9. Slight left onto Rue Waterloo/NB-102 N 160 m 10. Slight left onto King St Destination will be on the left 600 m King Street Ale House 546 King St, Fredericton, NB E3B 1E6, Canada These directions are for planning purposes only. You may find that construction projects, traffic, weather, or other events may cause conditions to differ from the map results, and you should plan your route accordingly. You must obey all signs or notices regarding your route. Map data 2014 Google 2/2