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Francesca Vidotto, Planck Stars Planck Stars the final fate of quantum no-singula black hoes and its phenoenoogical cosequences Francesca Vidotto UPV/EHU - Bilbao SINGULARITIES OF GENERAL RELATIVITY AND THEIR QUANTUM FATE Warsaw - May 23rd, 2018 Planck Stars the final fate of quantum no-singula black hoes and its phenoenoogical cosequences Francesca Vidotto UPV/EHU - Bilbao SINGULARITIES OF GENERAL RELATIVITY AND THEIR QUANTUM FATE Warsaw - May 23rd, 2018 QUANTAQUANTA OF OFSPACE SPACETIME It is a theory about quanta of spacetime Each quantum is Lorentz invariant The states are boundary states at fixed time SL(2, C) SU(2) ! i The physical phase space is spanned by SU(2) group variables L⌅ = L ,i=1, 2, 3 l { l} gravitational field operator (tetrad) SU(2) generators i i Geometry is quantized: AΣ = LlLl. l Σ ⇥ ∈ 2 2 i j k VR = Vn,Vn = ijkLlL Ll” . 9 | l | n R ∈ Discrete spectra: minimal non-zero eigenvalue Spinfoam & Singularities Francesca Vidotto QUANTIZATION OF THE CLASSICAL ACTION 1 GR action S[e, !]= e e F ⇤[!]+ e e F [!] (Holst term) ^ ^ γ ^ ^ Z Z BF theory S[e, ω]= B[e] F [ω] ^ Z 1 Canonical variables ⇥,B=(e e)⇤ + (e e) ^ γ ^ a i On the boundary n = e n nie =0 SL(2, C) SU(2) i i a ! ni =(1, 0, 0, 0) B (K = nB, L = nB⇤) ! Simplicity constraint K<latexit sha1_base64="0y/FFa7mathXZtw2BIirz4YmJ9k=">AAAB8XicdZDLSgMxFIYz9VbrrerSTbAIrkqmldYulIIbQRcV7AXboWTSTBuaZIYkI5Shb+HGhSJufRt3vo2ZtoKK/hD4+M855JzfjzjTBqEPJ7O0vLK6ll3PbWxube/kd/daOowVoU0S8lB1fKwpZ5I2DTOcdiJFsfA5bfvji7TevqdKs1DemklEPYGHkgWMYGOtu6uz3hALgeF1P19ARVQulVEFWkCVEqrNoFyq1qBrIVUBLNTo5997g5DEgkpDONa666LIeAlWhhFOp7lerGmEyRgPadeixIJqL5ltPIVH1hnAIFT2SQNn7veJBAutJ8K3nQKbkf5dS82/at3YBKdewmQUGyrJ/KMg5tCEMD0fDpiixPCJBUwUs7tCMsIKE2NDytkQvi6F/0OrVHRR0b05KdTPF3FkwQE4BMfABVVQB5egAZqAAAkewBN4drTz6Lw4r/PWjLOY2Qc/5Lx9At+VkGE=</latexit> = γL Spinfoam & Singularities Francesca Vidotto QUANTIZATION OF THE CLASSICAL ACTION 1 GR action S[e, !]= e e F ⇤[!]+ e e F [!] (Holst term) ^ ^ γ ^ ^ Z Z BF theory S[e, ω]= B[e] F [ω] ^ Z 1 Canonical variables ⇥,B=(e e)⇤ + (e e) ^ γ ^ a i On the boundary n = e n nie =0 SL(2, C) SU(2) i i a ! ni =(1, 0, 0, 0) B (K = nB, L = nB⇤) ! <latexit sha1_base64="ndQ2aEbhq4qkZGdxGHkiP5YSQmg=">AAAB7XicdVDLSgMxFM34rPVVdekmWARXQ6ZVp26k4MZlBfuAdiiZNNPGZpIhyQhl6D+4caGIW//HnX9jpq2gogcuHM65l3vvCRPOtEHow1laXlldWy9sFDe3tnd2S3v7LS1TRWiTSC5VJ8SaciZo0zDDaSdRFMchp+1wfJX77XuqNJPi1kwSGsR4KFjECDZWavVG2GTTfqmM3Nq5V/U9iFyEKtWL2oz4Nf8MepbkKIMFGv3Se28gSRpTYQjHWnc9lJggw8owwum02Es1TTAZ4yHtWipwTHWQza6dwmOrDGAklS1h4Ez9PpHhWOtJHNrOGJuR/u3l4l9eNzVRLciYSFJDBZkvilIOjYT563DAFCWGTyzBRDF7KyQjrDAxNqCiDeHrU/g/aVVcD7nezWm5frmIowAOwRE4AR7wQR1cgwZoAgLuwAN4As+OdB6dF+d13rrkLGYOwA84b58+Bo+O</latexit> <latexit sha1_base64="ndQ2aEbhq4qkZGdxGHkiP5YSQmg=">AAAB7XicdVDLSgMxFM34rPVVdekmWARXQ6ZVp26k4MZlBfuAdiiZNNPGZpIhyQhl6D+4caGIW//HnX9jpq2gogcuHM65l3vvCRPOtEHow1laXlldWy9sFDe3tnd2S3v7LS1TRWiTSC5VJ8SaciZo0zDDaSdRFMchp+1wfJX77XuqNJPi1kwSGsR4KFjECDZWavVG2GTTfqmM3Nq5V/U9iFyEKtWL2oz4Nf8MepbkKIMFGv3Se28gSRpTYQjHWnc9lJggw8owwum02Es1TTAZ4yHtWipwTHWQza6dwmOrDGAklS1h4Ez9PpHhWOtJHNrOGJuR/u3l4l9eNzVRLciYSFJDBZkvilIOjYT563DAFCWGTyzBRDF7KyQjrDAxNqCiDeHrU/g/aVVcD7nezWm5frmIowAOwRE4AR7wQR1cgwZoAgLuwAN4As+OdB6dF+d13rrkLGYOwA84b58+Bo+O</latexit> Simplicity constraint K<latexit sha1_base64="0y/FFa7mathXZtw2BIirz4YmJ9k=">AAAB8XicdZDLSgMxFIYz9VbrrerSTbAIrkqmldYulIIbQRcV7AXboWTSTBuaZIYkI5Shb+HGhSJufRt3vo2ZtoKK/hD4+M855JzfjzjTBqEPJ7O0vLK6ll3PbWxube/kd/daOowVoU0S8lB1fKwpZ5I2DTOcdiJFsfA5bfvji7TevqdKs1DemklEPYGHkgWMYGOtu6uz3hALgeF1P19ARVQulVEFWkCVEqrNoFyq1qBrIVUBLNTo5997g5DEgkpDONa666LIeAlWhhFOp7lerGmEyRgPadeixIJqL5ltPIVH1hnAIFT2SQNn7veJBAutJ8K3nQKbkf5dS82/at3YBKdewmQUGyrJ/KMg5tCEMD0fDpiixPCJBUwUs7tCMsIKE2NDytkQvi6F/0OrVHRR0b05KdTPF3FkwQE4BMfABVVQB5egAZqAAAkewBN4drTz6Lw4r/PWjLOY2Qc/5Lx9At+VkGE=</latexit> ˆ = γˆL Boost generator Rotation generator Rovelli,Vidotto 1307.3228 Maximal acceleration: no curvature singularities! (spacetime can be geodesically incomplete for some artificially patched manifolds Geroch ‘68) Spinfoam & Singularities Francesca Vidotto Quantum Black Holes QuantumBlack BH EXPLOSION “ Vidotto, Rovelli 1401.6562 Rovelli Vidotto, Planck Star” quantum quantum region Francesca Vidotto Francesca B l a c k - t o - W h i t e tunnelling Quantum Black Holes QuantumBlack BH EXPLOSION “ Vidotto, Rovelli 1401.6562 Rovelli Vidotto, Planck Star” quantum quantum region Francesca Vidotto Francesca B l a c k - t o - W h i t e tunnelling Scenario 1 Quantum Black Holes Francesca Vidotto T. BANKS AND M. O'LOUGHLIN 47 AND M. O'LOUGHLIN 47 u (r, n }=e T. BANKS(2.4) tion, but here the dilaton dynamics gives rise to an infinite set of spherically symmetric solutions of the In terms of these fields the Lagrangian is source free field equations in a finite region. We have (2.4) tion, but here the dilaton dynamics gives rise to an u n }=e 2 AND M. O'LOUGHLIN 47 (r, — — T. BANKS tried to restrict the solution by assuming a cosmological S= &—g [ —u R+2u (Ba) 4(Bu) 2u e infinite set of spherically symmetric solutions of the form for the metric ds = — (dr dQ ) in- Infterms of these fields the Lagrangian is source free field equations indH+a(r)a finite region.+rWe have side the shell, but this is inconsistent with the field equa- u +Quen }=e (2.5) (2.4) triedtion,to butrestricthere thethe solutiondilaton dynamicsassuminggivesa cosmologicalrise to an (r, — — ].) — by S= &—g [ u R+2u (Ba) 4(Bu) 2u e tions. Similarly, an attempt to solutionskeep the thethree- forminfinitefor theset metricof sphericallyds = —symmetricdH+a(r) (dr +r dQof ) in- f 41 The equations Inoftermsmotionof thesefor fieldsthis theLagrangianLagrangian areis given in dimensionally conformallyfield Oatin formfinite of the metric,We have with – source free equations a region. side the shell, but this is inconsistent with the field equa- interact with (2.5) on the coarse Appendix A. Of course,+Queto find interior solutions with conformaltried to factorrestrict tiedthe solutionto the bydilaton,assumingis inconsistent.a cosmological We — — —38 — the three- S= & g [ u R+2uthe exterior(Ba) 4(Bu)extremal2u e tions. Similarly, an attempt to keep zero magnetic field to match onto T. BANKS ANDhaveM.notO'LOUGHLINbeen able to come= — with a natural 47ansatz. we The equations off motion for this Lagrangian are given in dimensionallyform for the conformallymetric ds OatdH+a(r)upform of(drthe+rmetric,dQ ) in-with dilaton solution, we set =0 in the above equation. smooth solutions exist. Appendix A. Of Qcourse, to find interior solutions with(2.5)Nonetheless,conformalside the shell,factorwebuttiedbelievethistois theinconsistentthatdilaton, withis inconsistent.the field equa-We series for the +Quefields o and (t, expanding The power Theretions.are manySimilarly,smoothan attemptsolutionsto ofkeepthe thevacuumthree- field ] is that the increase zero magnetic fieldu (r, nto}=ematch onto the exterior extremal (2.4)havetion,not butbeenhereablethe todilatoncome dynamicsup with givesa naturalrise to ansatz.an 2 from the shell towards the interior,motion foris this Lagrangian are given in to a manifold with the of a but also The equations of restricted topology 26 dilaton solution, we set Q =0 in the above equation. equationsNonetheless,dimensionallyinfinite set weofconformallysphericallybelieve thatOatsymmetricformsmoothofsolutionsthesolutionsmetric,of thewithexist. In termsA. ofOfthesecourse,fields tothe findLagrangianinterior issolutions withhemi-three-spherefield cross time.in aOurfinite matchingWe conditionshave The powerAppendixseries for the fields o and (t, expanding Thereconformalsourceare freemanyfactor smoothtiedequationsto thesolutionsdilaton, ofisregion.inconsistent.the vacuum Wefield zero magnetic field2 to match onto the —exterior —extremalfix onlyhavetriedthenotto restrictbeenvaluesabletheofsolutiontothecomemetricbyupassumingwithfunctionsa anaturalcosmologicalandansatz.dilaton from the shell towardsS= &the—g interior,[ —u R+2uis (Ba) 4(Bu) 2u e equations restricted to a manifold with the topology of a ~ ].) — u (r, n) =R (~)dilaton1—solution,f we[1+set Q(r)n=0 in+thef2(r)nabove equation. alongNonetheless,formthe timelikefor the wemetricworldbelieveds line= thatdH+a(r)of smooththe collapsing(drsolutions+r dQshell,)exist.in- leav- R (~) f, hemi-three-sphere cross time. Our matching conditions fields and expanding41 side the shell, but this is inconsistent with the field equa- The power series for2+Quethe o (t, (2.ing5) theirThere normalare many derivativessmooth solutionsundetermined.of the vacuumThusfieldthere – functions and dilaton fix only the values of the metric interact with tions. Similarly, an attempt to keep the three- on the coarse from the shell towards the interior, is ~ seems to be plentyrestrictedof torooma manifoldfor patchingwith the intopologya nonsingularof a u =R 1— (2.6) inalongequationsthe timelike world line of the collapsing shell, leav- (r, n) (~)The equations +f3(r)nof motion[1+ for(r)n+this+Lagrangianf2(r)n], are given38 Oat form of the metric, with R (~) f, vacuumhemi-three-spheredimensionallysolution. conformallycross time. Our matching conditions Appendix A. Of course, to find interior solutions with ing conformaltheir normalfactor derivativestied to the dilaton,undetermined.is inconsistent.ThusWethere we n = 2 Tofixobtainonly thesomevaluesfeelingof theformetricthe motionfunctionsofandthe dilatoncollapsing o (r, ) [ln(R (r) zero}+d,magnetic(r)n +fieldd2(~)nto match onto the exterior extremal seemshaveto notbe plentybeen ableof toroomcomefor patchingwith a naturalin a nonsingularansatz. + ~ (2.6) the arbitraryup assumption that u n) =R (~) 1— +f3(r)n (r)n ], shell alongwe3 havethe timelikemade
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