Experimental search for Planck Stars

Transcription

1 Experimental search for Planck Stars Francesca Vidotto with A.Barrau, H. Haggard, C. Rovelli SISSA, Trieste - September 3rd, 2014 Experimental Search for Quantum Gravity

2 Singularity resolution No need to violate SEC Loop Quantum Gravity is a theory about spacetime quanta: canonical SU(2) group variables Minimal area gap Hamiltonian constraint Holonomy corrections (v,") He = a a) sin( 3 8 G 2 a3 + Hmatt 5* * *104 v *104 a 8 G = 1 2 a * * * * " -0.2 c t P covariant SU(2) group variables Minimal area gap Simplicity constraint Maximal acceleration { ~ + L ~ =0 K 0 Boost generator Rotation generator z P = 1/a motion of an accelerated observer in spacetime evolution of spacetime seen by an observer W (, j) = hj, j Y ei Kz Y j, ji Rovelli,Vidotto

3 What have we learnt from Loop Quantum Cosmology? 0 quantum classical expanding solution Big Bounce Quantum Tunneling superposition φ -0.6 Effective repulsive force Planck density -0.8 Size Planck length -1 V b m m P `3P cm *10 4 2*10 4 3*10 4 4*10 4 5*10 4 V v v contracting solution Ashtekar,Pawlowski, Singh, Vandersloot see talks by Grain and Martin-Benito

4 Where does matter falling into a Black Hole go? Planck Stars Quantum Tunneling superposition Effective repulsive force Planck density Size Planck length r b m m P `P See works by Barrau, De Lorenzo, Haggard, Pacillo, Rovelli, Speziale, Vidotto See also related works by Bianchi, Smerlak, Perez, Gosh, Frodden, Gambini, Pullin Rovelli, Vidotto see talk by Rovelli

5 Effective theory Vidotto, Rovelli t Eddington-Finkelstein coordinates ds 2 = r 2 d 2 +2dv dr F (r)du 2 horizon F (r) =(1 =1 2mr 2 2m/r) r m Hayward Koch, Saueressig r = 0 r = rin r = 2m r

6 Effective theory Vidotto, Rovelli t Eddington-Finkelstein coordinates ds 2 = r 2 d 2 +2dv dr F (r)du 2 horizon F (r) =1 2mr 2 r m Hayward Koch, Saueressig r = 0 r = rin r = 2m r

7 Effective theory Vidotto, Rovelli t Eddington-Finkelstein coordinates trapped horizon ds 2 = r 2 d 2 +2dv dr F (r)du 2 F (r) =1 2mr 2 r m Hayward Koch, Saueressig r = 0 r = rin r = 2m r

8 Different cases: 1. Hawking evaporation only 2. Bounce 3. Black to White Bounce m f < 1 p 2 m i t b m 3 m f 1 p 2 m i t b m 3 t b m 2 m f m i

9 1. Hawking evaporation only Vidotto, Rovelli t m f < 1 p 2 m i t b m 3 no information paradox: no firewalls r = 0 r = rin r = 2m r

10 2. Bounce Vidotto, Rovelli t m f 1 p 2 m i t b m 3 no information paradox: no firewalls Sin = Slost t = 0 r = 0 r = rin r = 2m r

11 Mass-loss Rate Halzen et al. Nature 353 dm dt = f(m) m 2 mass decreases temperature increases new particles produced Integrated over Hubble time: m i = 3 th f(m) 1 m f /m i 1/3 f(m): the branching ratio depends on the internal dof Page time: m f /m i = 1 p 2 The only parameter is the initial mass of the BH m i g m f g r f cm E burst = hc 2r f 3.9GeV The bigger the BH, the lower is the emitted burst

12 Experimental search for Planck Stars 1. Which signal? 2. From where? 3. Of which origin? 4. Have we already seen it? Barrau, Rovelli

13 1. Which signal? Barrau, Rovelli The energy of most of the emitted photons is not Eburst - uu channel: mean energy spectrum of secondary photons N egamma Entries Mean RMS MonteCarlo PYTHIA code inputs: ecm=3.9 GeV events= Ē 0.03 E burst 10 MeV E(GeV)

14 , s quarks (t and b are too heavy), gluons and ns is shown on Fig. 3. The little peak on the right How many photons? sponds to directly emitted photons that are clearly ominant. By also taking into account the emission Total particle emitted, each species according to # internal dof utrinos and leptons of all three families (leading to ally no gamma-rays and therefore being here a pure ng energy), we obtain <N burst > e question of the maximum distance at which a sinurst can be detected naturally arises. If one 5 requires asure N mes photons in a detector of surface S, this 4 10 ply given by R det = r S<Nburst > ] -1 [GeV dn de. (3.1) 4 N 10 2 mes e set, e.g., N mes 10 photons in a 1 m 2 detector, leads to R 205 light-years. The maximum distance at which such an event 10-1 earest star. This is a tiny galactic patch 10-2 around us. egamma Otherwise stated, single event detection of exploding Planck stars is e detected is just a few tens times the distance to sponds to Planck stars that have masses between m f and m( t) at the beginning of the observation time, within the volume R<R det. In this case, m( This number n( given by dm i /dm = m 2 (3f(m)t + m 3 ) 2/3. t) issimply: m( t) = m 3 f +3f(m) t 1 3. (3.4) n( t) = t) is (estimated for a unit volume) Z m( t) m f dn dm dm, (3.5) Entries where dn/dm is the di erential mass spectrum of Mean Planck stars today, still per unit volume. Importantly, RMS the shape of this mass spectrum in the interesting region is mostly independent of the initial shape. This is exactly true only in the limit m 3f(m)t H and constitutes a rough approximation here. To get orders of magnitude, we however assume this to be correct. direct emission In this case, due to the dynamics of the evaporation, dn/dm / m 2. This can be straightforwardly seen by writing dn/dm = dn/dm i dm i /dm, where dn/dm i is the initial mass spectrum and E [GeV]

15 2. From where? Barrau, Rovelli R det = r S<Nburst > 4 N mes. Maximal distance: if S=1m 2 Nmes=10 ==> Rdet~200 light years local Distribution: isotropic

16 4. Of which origin? Barrau, Rovelli black holes formed at the beginning of the universe (recombination time ~ 13.4 billion years ago) Primordial Black Holes for mi ~ g we have N det < 4 DM 3m f PBH S<Nburst > 4 N mes Assume a wide spectrum for PBH: dn = m 1 dm i h N( t) = 1+3w 1+w i, m R f mmax m f dn dm dm PBH N max det sr, ctrum. As t P (k) / k n formation at radiation dominated era h i dn dm m 5 9 Today s spectrum: 2 (m m )+m 2 m 2 (m m) R m( t) dn dm dm up to one Expected detection in t event per day

17 5. Have we already seen it? Barrau, Rovelli Very Short GRB: short time scale local bubble origin harder spectrum Diffuse Emission: ] -1 [GeV dn de 5 10 egamma energy spectrum of photons Entries Mean RMS integrated emission over huge distance the smaller BH, the higher the burst harder spectrum red shift dominates E [GeV]

18 Experimental search for Planck Stars 1. Which signal? Ē 0.03 E burst MeV 2. From where? Local and Isotropic 3. How often? One event per day 4. Of which origin? Primordial Black Holes 5. Have we already seen it? Maybe: VSGRB

19 3. Black to White Bounce Haggard, Rovelli t m f m i t b m 2 The bigger the BH, the lower is the emitted burst (but bigger flux) r = 0 r = rin r = 2m r

20 3. Black to White Bounce Haggard, Rovelli t m f m i t b m 2 The bigger the BH, the lower is the emitted burst (but bigger flux) r = 0 r = rin r = 2m r

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22 Black to White Bounce Phenomenology Hájíček, Kiefer Haggard, Rovelli Quantum pressure quantum tunneling quantum region Planck density object radius >> Planck length quantum effects appear at r b m m P r 7 6 2m 1 3 `P t = 0 trapped horizon asymptotic proper time m2 `P r = 0 emission at E burst 10MeV r=const space-like in the trapped region

23 Experimental search for Planck Stars v Which signal? E burst 10MeV 2. From where? Isotropic (close or distant) 3. How often? TBC, but enough 4. Of which origin? Primordial Black Holes 5. Have we already seen it? Maybe: Fast X-ray Burst

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25 Summary Effective repulsive force BH are bounce in slow motion Size Planck length Quantum Gravity Phenomenology 1. Which signal? E burst 3.9 GeV 2. From where? Local and Isotropic 3. How often? One event per day 4. Of which origin? Primordial Black Holes 5. Have we already seen it? VSGRB

26 Summary Quantum Tunneling Effective repulsive force Metric for Black-to-White process BH are bounce in slow motion Size Planck length Quantum Gravity Phenomenology 1. Which signal? E burst 3.9 GeV E burst 10MeV 2. From where? Local and Isotropic 3. How often?? One event per day 4. Of which origin? Primordial Black Holes 5. Have we already seen it? VSGRB Fast x-ray Burst