Loop Quantum Gravity and Planck Stars

Transcription

1 Loop Quantum Gravity and Planck Stars carlo rovelli Planck stars collaborators: Francesca Vidotto: Aurélien Barrau: Hal Haggard: Compact black hole core Phenomenological analysis for astrophysical observations Black to white hole quantum tunnelling j l v n Ε III Δ II t=0 r=0 I

2 Things have changed in quantum gravity: 1. Tentative theories do exist (finite, Lorentz invariant, GR limit, 4d ) 2. Quantum gravity measurements are not anymore unthinkable

3 Loop Quantum Gravity What is Loop Gravity (LQG)? See also talk by Jerzy Lewandowski, just after this

4 What is Loop Quantum Gravity (LQG)? is a canonical quantisation of GR! is spin networks! is spinfoams! LQG What is Loop Gravity (LQG)? is polymer quantisation is Ashtekar Lewandowski measure is twisted geometries! is quantum theory of the geometry of spacetime is group field theory! is Thiemann s Hamiltonian constraint!

5 Covariant loop quantum gravity. Full definition. n 0 Kinematics State space Operators: H = L 2 [SU(2) L /SU(2) N ] where 3 (hl ) h l l n spin network (nodes, links) Dynamics Transition amplitudes Vertex amplitude W C (h l )=N C Z A(h vf )= Z Y dh vf SU(2) f Y X dge 0 SL(2,C) f j (h f ) Y v A(h vf ) (2j + 1) D j mn(h vf )D (j+1) j jmjn (g e g 1 e 0 ) h f = Y v h vf With a cosmological constant λ > 0: " Amplitude: SL(2,C) SL(2,C)_q network evaluation. v e f C q = e i ~G Units: " 8 ~G =1 spinfoam (vertices, edges, faces)

6 Electricity + quantum = quanta of light, photons Gravity + quantum = quanta of space

7 Quantum theory: If we confine a particle in a small region, its energy grows General Relativity: If the energy grows, it falls into its own black hole There is a minimal scale The Planck scale R> r ~G c 3 = L Planck cm

8 Geometrical quantities (area, volume, ), A a,v have discrete spectrum A a = l 2 P p ja (j a + 1) Minimal volume But because of Heisenberg principle, geometry is quantum fuzzy at small scale See also talks Mehdi Assanioussi, and ungiven talk by Simone Speziale

9 The mathematics that describes these fuzzy discrete geometries is called: spin network theory (Penrose 70) j l v n Spin network states,j l,v n i Basic states of Loop Quantum Gravity

10 Evolution and spacetime: spinfoams Spin network: Spinfoam

11 Covariant loop quantum gravity. Full definition. n 0 Kinematics State space Operators: H = L 2 [SU(2) L /SU(2) N ] where 3 (hl ) h l l n spin network (nodes, links) Dynamics Transition amplitudes Vertex amplitude W C (h l )=N C Z A(h vf )= Z Y dh vf SU(2) f Y X dge 0 SL(2,C) f j (h f ) Y v A(h vf ) (2j + 1) D j mn(h vf )D (j+1) j jmjn (g e g 1 e 0 ) h f = Y v h vf With a cosmological constant λ > 0: " Amplitude: SL(2,C) SL(2,C)_q network evaluation. v e f q = e i ~G Units: " 8 ~G =1 C See Etera Livine review talk See also talks by Antonia Zipfel, Wolfgang Wieland spinfoam (vertices, edges, faces)

12 Newton: Particles Space Time Faraday-Maxwell: Particles Fields Space Time Special relativity: Particles Fields Spacetime Quantum mechanics: Quantum-Fields Spacetime General relativity: Particles Covariant Fields Quantum gravity: Covariant Quantum fields Matter, time and space: all emerge from a quantum field See talk by Francesca Vidotto

13 Quantum fields The quanta of a field are particles (Discreteness of the spectrum of the energy of each mode)

14 Quantum gravity Quantum granularity of spacetime (Discreteness of the spectrum of geometrical operators)

15 Key features 1. Boundary states represent geometries where geometry operators have discrete spectra (LQG 1990 ) " 2. The classical limit is related (via Regge discretisation) to classical GR (with cosmological constant) (Barrett et al, Conrady-Freidel, Bianchi-Perini-Magliaro, Engle, Muxin Han..., )" 3. The amplitudes with positive cosmological constant are UV and IR finite (Muxin Han, Fairbairn-Meusburger, 2011, Muxin Han 2013) Main open Issues 1. Effects of radiative corrections? (High spin bubbles (Riello), Many vertices, renormalization, GFT )" See talks by Sera Ariwahyoedi, Benjamin Bahr, Daneile Oriti 2. How to test the theory? (Cosmology, Astrophysics, )

16 IV. What happened at the big bang?

17 IV. What happened at the big bang? ȧ 2 a 2 = 8 G 3 LQG ȧ 2 a 2 = 8 G 3 1 Pl Effective repulsive force See Julian Grain review talk See talks by Ed Wilson-Ewing, Jaume Haro, Linda Linsefors, Emanuele Alesci, Andrea Dapor

18 Big Bang Big Bounce

19 The big bounce of the Universe

20 Loop Quantum Cosmology Loop Quantum Gravity power spectrum (ratio to standard power spectrum). In blue are the current data points. Agullo, Ashtekar, Nelson, PRL 2013

21 V. Where does matter falling into a black hole go? See Jorge Pullin talk: BH s states LQG Alejandro Perez: entropy and entanglement in LQG Eugenio Bianchi talk: time evolution of BH s entropy

22 Main physical lesson from loop quantum cosmology:" " When the matter reaches the Planck density, a strong repulsive force of quantum gravitation origin develops." " Can we use this to understand what happens in the interior of a black hole? Black holes Planck Stars

23 t r = r in r =2m r

24 t E burst = hc/(2r f ) 3.9 GeV r = r in r =2m r Francesca Vidotto, CR, arxiv: ;

25 E burst = hc/(2r f ) 3.9 GeV ] -1 [GeV dn de energy spectrum of photons egamma Entries Mean RMS ~10 MeV From ~200 light years Short gamma-ray burts Isotropic E [GeV] One event per day Detectable? Aurélien Barrau, CR:

26 E down Δ E up Ε III Δ II t=0 r=0 I Black hole white hole quantum tunnelling H. Haggard, CR: arxiv:

27 n 0 l Tentative quantum theories of gravity exist n Main prediction: a limit in divisibility of space We have equations for tentatively studying the big bang Black holes may tunnel into white holes r=0 Ε III I Δ II t=0