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Vidotto-Guadalupe-18.Pdf Quantum Insights o Primordial Black Holes as Dak Mate Francesca Vidotto UPV/EHU - Bilbao 2ND WORLD SUMMIT ON EXPLORING THE DARK SIDE OF THE UNIVERSE Guadalupe Island - June 29th, 2018 THE DARK SIDE OF GRAVITY Caution: not a complete list! DARK ENERGY Cosmological Constant (or more complicated GR modification) Gravitational Backreaction see Buchert’s talk Quantum Gravity: Spacetime Discreteness Perez, Sudarsky, Bjorken 1804.07162 … DARK MATTER Mond, Mimetic Gravity and other classical modification of GR Bimetric Gravity see Henry-Couannier’s talk N-body Equivalence Principle Alexander, Smolin 1804.09573 Quantum Gravity: Minimal Acceleration Smolin 1704.00780 Emergent Gravity Verlinde 1611.02269 … Primordial Black Holes see also Garcia-Bellido’s talk Quantum Gravity Phenomenology Francesca Vidotto PRIMORDIAL BLACK HOLES PBHs are the least exotic beast in the dark universe zoo of theories PBHs are a viable DARK MATTER candidate * careful with old constraints in the literature! PBHs are interesting even if they are not all DARK MATTER * PBHs can be used to test QUANTUM GRAVITY Quantum Gravity Phenomenology Francesca Vidotto IN THIS TALK: QUANTUM GRAVITY 1. QG makes PBH remnants stable * Quantum Gravity: minimal aerea 2. QG cures GR singularities * NO central BH singularity, NO cosmological singularity: instead a bounce 3. QG allows for Black-to-White tunnelling * Decay happens faster than the Hawking evaporation: new phenomenology 3 different scenarios discussed in this talk Quantum Gravity Phenomenology 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 u n }=e (2.4)AND tion,M. O'LOUGHLINbut here the dilaton dynamics gives rise to47 an (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 +Que(r,—n }=e— — — (2.5) (2.4) triedtion,to butrestricthere thethe solutiondilaton bydynamicsassuminggivesa cosmologicalrise to an S= & g [ u R+2u (Ba) 4(Bu) 2u e tions.infiniteSimilarly,set an attemptsymmetricto solutionskeep theof thethree- f form for the metricof sphericallyds = —dH+a(r) (dr +r dQ ) in- The equations Inoftermsmotionof thesefor fieldsthis theLagrangianLagrangian areis given in dimensionallysource free conformallyfield equations Oatin aformfinite ofregion.the metric,We have with (2.5) side the shell, but this is inconsistent with the field equa- Appendix A. Of course,+Queto find interior solutions with conformaltried to factorrestrict tiedthe solutionto the bydilaton,assumingis inconsistent.a cosmological We &— —u —4(Bu) —2u e tions. Similarly, an attempt to keep the three- zero magnetic fieldS=to matchg [ ontoR+2uthe exterior(Ba) extremalT. BANKS ANDhaveM.notO'LOUGHLINbeen able to come= — with a natural 47ansatz. 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. that smooth solutions exist. Appendix A. Of Qcourse,+Queto find interior solutions with(2.5)Nonetheless,conformalside the shell,factorwebuttiedbelievethistois theinconsistentdilaton, withis inconsistent.the field equa-We The power series for the fields o and (t, expanding Theretions.are manySimilarly,smoothan attemptsolutionsto ofkeepthe thevacuumthree- field zero magnetic fieldu (r, nto}=ematch onto the exterior extremal (2.4)havetion,not butbeenhereablethe todilatoncome dynamicsup with givesa naturalrise to ansatz.an from the shell Thetowardsequationsthe ofinterior,motion foris this Lagrangian are given in restricted to a manifold with the topology of a 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 dilaton solution, we set =0 in the above ~equation. form timelikefor the metricworldds line= —dH+a(r)of the collapsing(dr +r dQshell,) in- leav- u (r, n) =R (~) 1— f [1+f,Q(r)n +f2(r)n alonghemi-three-sphereNonetheless,the we crossbelievetime.that Oursmoothmatchingsolutionsconditionsexist. The Rpower(~) series for the fields o and (t, expanding(2.ing5) theirside thenormalshell, butderivativesthis is inconsistentundetermined.withthethevacuumfieldThusequa-fieldthere 2+Que fixThereonly arethe manyvalues smoothof the solutionsmetric functionsof and dilaton is tions. Similarly, an attempt to keep the three- from the shell towards the interior, ~ seemsequationsto be plentyrestrictedof torooma manifoldfor patchingwith the intopologya nonsingularofleav-a u (r, n) =R (~)The 1—equations +f3(r)nof motion[1+ for(r)n+this+Lagrangianf2(r)n], (2.are6)given inalong the timelike world lineOatofformthe collapsingof the metric,shell,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 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 worldfairlyline of the collapsing shell, leav- (r, dilaton solution, we set [1+=0 in the above+f2(r)nequation. vacuum solution. smooth solutions exist. ec- Q we believe that (8) f, Nonetheless, (7) (6) R (2.7) (5) ↵ +d3(~)n + ], (~) =0 The power series for the fields o and (t, expanding ing their normal derivatives theundetermined.motionthe vacuumtheThuscollapsingfieldthere o (r, n ) = [ln(R (r) (r)n +d2(~)n ToThereobtainare somemany feelingsmooth forsolutions of of white }+d, .The is seems to be aplenty of room for patching in a nonsingular ⌧ from thetheshell towards termsthe interior,are determined shellequationswe haverestrictedmade theto fairlya manifoldarbitrarywith theassumptiontopology ofthata (2.13) 3 where the coefficients of leading (2. +f3(r)n + ], 6) fi(r)— the line vacuum solution. 2 by continuity of+d3(~)nand cr +across],the shell. The metric is(2.7) hemi-three-sphere cross time. Our matching conditions P ⌦ 2 the motion the collapsing m n = fixTo obtainthesomevaluesfeelingtheformetric functionsof and dilaton d of maximum —ho (r, ) [ln(R n)(r) }+d,and(r)nthe+d2(~)ncoefficients have only a 2 =diag[ (r, 4 g& where the coefficientsn), g(r, of],the leading terms are determined~ (2.13) 2 u n) =R (~) 1— (r)n +f2(r)n This shellalongfi(r)—wethehaveustimelikeamade worldthe fairlyfirst-orderline arbitraryof the collapsingordinaryassumptionshell,differentialthatleav- ⌧ (r, [1+ gives single region. the expansion, f, < R = 0 which gives continuity of and cr across(~)the shell. The metric is(2.7) m +d3(~)n + + by P ], ing their normal derivatives undetermined. Thus there . obtained behaves 2 The solution so A for R l equation (r). 4 2 2 finite — ⌧ ⌧ h n) and the coefficients have in . The Ricci tensor g& =diag[ (r, n), g(r, ], (2.8) seems to be plentya of room for patching a nonsingular ⌧ r', l h(r, n)=1+h&(r)n+h2(r)nwhere the coefficients+h3(r)nof the leading++f3(r)nterms +are determined], (2.like6) R(r)=Q+e as ~~oo. We can then (2.use13) this Thisvacuumgivesfi(r)—solution.us a single first-order ordinary differential dx the expansion, = ⌧ solution to check that the other coefficient functions, to 2 cr the shell. The metric is . of and across 8 by continuity s = P (2.9) equation obtainfor Rsome(r).feelingTheforsolutionthe motionso ofobtainedthe collapsingbehaves ⌧ + l +g3(r)n To + 48 n 2 g(r, n)=1+g, (r)n+g2(r)no ) (r)n d2(~)n ) (r, [ln(R (r) }+d, + leading order, are well behaved for all finite values of ~. r 2 2 — (space-like) surfaces foli- have 6 =diag[ h +h3(r)nn) and the coefficients(2.8) r', 2 h(r, n)=1+h&(r)n+h2(r)n(r, n), g(r, ], + like as We can thenthatuse this − have made the fairly~~oo.arbitrary assumption m g& shellR(r)=Q+ewe l ⌧ ⌧ We can continue this procedure perturbatively, to verify ⌧ l The equationsthe thatexpansion,we have+d3(~)nto describe+ ], this system now (2.7) This gives us a single first-order ordinary differential 9 solution to check that the other coefficient functions, to m ). + 2 o.+g3(r)n + (2.9) that the coefficients in the expansion in powers of n are is easily
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