11

Black holes and extra dimensionsBlack holes and extra dimensionsDejanDejan StojkovicStojkovic

Case Western Reserve UniversityCase Western Reserve University

University of OxfordUniversity of OxfordFeb 28, 2006Feb 28, 2006

22

MotivationMotivationBlack holes:Black holes: most interesting and intriguing solutions of most interesting and intriguing solutions of Einstein's equationsEinstein's equations

Extra dimensionsExtra dimensions seem to be necessary in an ultimateseem to be necessary in an ultimatetheory of high energy physicstheory of high energy physics

BraneBrane world modelsworld models →→ large extra dimensionslarge extra dimensions

Higher dimensional black holes as classical solutionsHigher dimensional black holes as classical solutions

Black holes in accelerators!Black holes in accelerators!

33

OutlineOutlineBlack holes Black holes –– basicsbasics

Extra dimensions Extra dimensions –– basicsbasics

Higher dim. black holes in Higher dim. black holes in branebrane world modelsworld modelsi) black holes in accelerators i) black holes in accelerators -- LHCLHCii) black holes by cosmic rays ii) black holes by cosmic rays -- Auger ObservatoryAuger Observatory

Problem: ultraProblem: ultra--fast proton decayfast proton decay

Realistic models with stable proton: Realistic models with stable proton: Black holes will NOT be observed at the Auger ObservatoryBlack holes will NOT be observed at the Auger Observatory

44

Black HolesBlack Holes

LaplaceLaplace in 18th century, Newtonian mechanics:in 18th century, Newtonian mechanics:

Eg = GmMr= 1

2mc2 → rg = 2GM/c

2

• Particle rotating around a massive object

•• LaplaceLaplace called them called them ““Dark StarsDark Stars””

55

• Einstein, 1915, General RelativityEinstein, 1915, General Relativity

•• Schwarzschild metric, 1916Schwarzschild metric, 1916::

ddss22 == −−¡¡11 −− 22GGMM

cc22rr

¢¢ccddtt22 ++

¡¡11 −− 22GGMM

cc22rr

¢¢−−11ddrr22 ++ rr22ddΩΩ

→rr == rrhhoorriizzoonn == 22GGMM//cc22

aatt rr == rrhhoorriizzoonn tt aanndd rr eexxcchhaannggee tthheeiirr rroolleess

aatt rr == 00 mmeettrriicc hhaass ttrruuee ssiinngguullaarriittyy

mmeettrriicc hhaass ccoooorrddiinnaattee ssiinngguullaarriittyy

66

Different types of black holesDifferent types of black holes

•• Black holes formed in collapse of stellar matter Black holes formed in collapse of stellar matter

•• endpoint of stellar evolution, mergers and accretionendpoint of stellar evolution, mergers and accretion

•• mass range: a fewmass range: a few MMSSuunn -- 110099MMSSuunn

•• Primordial black holesPrimordial black holes

•• early universe, large fluctuations in energy densityearly universe, large fluctuations in energy density

•• mass range:mass range: MMPP ll -- MMSSuunn

•• Black holes formed in the LabBlack holes formed in the Lab

•• need accelerator as big as the whole universeneed accelerator as big as the whole universe

•• mass range: a fewmass range: a few MMPP ll ∼∼ 11001199GGeeVV

77

Extra DimensionsExtra Dimensions

•• Our world is manifestly (3+1)Our world is manifestly (3+1)--dimensional on large scalesdimensional on large scales

•• KaluzaKaluza (1921) and Klein (1926) introduced the fifth dimension(1921) and Klein (1926) introduced the fifth dimensionto unify gravity with electromagnetismto unify gravity with electromagnetism

•• 5th dimension rolled on a very small circle5th dimension rolled on a very small circle

•• Size of extra dimension isSize of extra dimension is LLPP ll ∼∼ 1100−−3333ccmm

KaluzaKaluza KleinKlein

88

Higher dimensional objects?Higher dimensional objects?

•• To unify all the interactions we need more than one extra dimenTo unify all the interactions we need more than one extra dimensionsion

KK approach KK approach →→ at least 11 dimensionsat least 11 dimensionsString theory String theory →→ 10 or 11 dimensions10 or 11 dimensions

•• We can have interesting higher dimensional objects We can have interesting higher dimensional objects e.g. higher dimensional black holes, topological defects (strie.g. higher dimensional black holes, topological defects (strings, ngs, branesbranes etc)etc)

•• At distances of quantum gravity effecAt distances of quantum gravity effects become very importantts become very important

•• Problem:Problem: quantum gravity has not been formulated yet quantum gravity has not been formulated yet →→

Can not describe them properly!Can not describe them properly!

LLPP ll ∼∼ 1100−−3333ccmm

99

BraneBrane worlds and large extra dimensionsworlds and large extra dimensions

•• BraneBrane world models have attracted a lot of attention world models have attracted a lot of attention

•• Introduced as a solution to the hierarchy problemIntroduced as a solution to the hierarchy problem

•• They imply existence of large extra dimensionsThey imply existence of large extra dimensions

•• They offer rich higher dimensional phenomenologyThey offer rich higher dimensional phenomenology

•• We can study higher dimensional black holes!We can study higher dimensional black holes!

1010

The hierarchy problemThe hierarchy problem

•• Planck energy scale:Planck energy scale:

•• "Grand Desert" between the scales"Grand Desert" between the scales

•• →→ weak gravityweak gravity

•• Gravity is by far the weakest interaction in natureGravity is by far the weakest interaction in nature

•• For protons, gravity is times weaker than electromagFor protons, gravity is times weaker than electromagnetismnetism

MMPP ll ∼∼ 11001199GGeeVV ÀÀ MMEEWW ∼∼ 220000GGeeVV

FFEEMM == qq11qq22rr22 FFGG == GG

mm11mm22

rr22

GGNNeewwttoonn == 11//MM22PP ll

11003366

1111

The need for physics beyond the SMThe need for physics beyond the SM

•• Validity of SM is probably limited to energies up to 1 Validity of SM is probably limited to energies up to 1 TeVTeV

•• RadiativeRadiative corrections to the Higgs mass:corrections to the Higgs mass:

•• If SM is valid all the way to , i.e. If SM is valid all the way to , i.e. , then, thena rather finea rather fine--tuned cancellation must take place (about 1 part in )tuned cancellation must take place (about 1 part in )

•• If physics beyond the SM is to solve the hierarchy problem, If physics beyond the SM is to solve the hierarchy problem, it has to come not far above the it has to come not far above the TeVTeV scalescale

•• SupersymmetrySupersymmetry

•• Strong (Strong (TeVTeV scale) quantum gravityscale) quantum gravity

∆∆mm22hh '' ΛΛ22

33((22MM22WW++MM22

ZZ++mm22hh−−44mm22

tt ))((3322ππ22vv22))

11001177MMPP ll ΛΛ ∼∼ MMPP ll

1212

Strong gravity Strong gravity ------ ADD modelADD model

ArkaniArkani--HamedHamed, , DimopoulosDimopoulos and and DvaliDvali, Phys. , Phys. LettLett. B 429, 263 (1998). B 429, 263 (1998)

Antoniadis, Antoniadis, ArkaniArkani--HamedHamed, , DimopoulosDimopoulos and and DvaliDvali, Phys. , Phys. LettLett. B 436,257 (1998). B 436,257 (1998)

•• Our universe consists of:Our universe consists of:

•• 3+d space like dimensions (bulk) 3+d space like dimensions (bulk)

•• d dimensions d dimensions compactifiedcompactified to radius Rto radius R

•• Only gravitons are allowed to propagate in all dimensionsOnly gravitons are allowed to propagate in all dimensions

•• SM particles are bound to 3SM particles are bound to 3--dim dim submanifoldsubmanifold ((branebrane))

1313

In this framework:In this framework:

•• Gravity is as strong as the other interactionsGravity is as strong as the other interactions

•• But gravitational force is diluted due to the presence of extraBut gravitational force is diluted due to the presence of extra dimensionsdimensions

•• Weak gravity is only an illusion for an observer located on theWeak gravity is only an illusion for an observer located on the branebrane

1414``Large" extra dimensions``Large" extra dimensions

Flat compact extra dimensionsFlat compact extra dimensions

FFuunnddaammeennttaall ssccaallee MM∗∗ ∼∼ 11TTeeVV

CCoommppaaccttiifificcaattiioonn rraaddiiuuss:: RR ∼∼ 1100 3322dd ·· 1100−−1199mm

dd == 11 ==>> RR ∼∼ 11001133mm ((eexxcclluuddeedd))

dd == 66 ==>> RR ∼∼ 1100−−1111mmmm

VV ccee:: VVeexxttrraa == RRddoolluummee ooff eexxttrraa ssppaa

dd == 33 ==>> RR ∼∼ 1100−−55mmmm

RR ÀÀ TT eeVV −−11

GG44 ≡≡ 11MM22PP ll==

GG44++dd

VVeexxttrraa

dd == 22 ==>> RR ∼∼ 11mmmm ((∼∼ ccuurrrreenntt llaabb lliimmiitt))

1515

. .

Black Holes in acceleratorsBlack Holes in accelerators

Particle accelerator (e.g. Large Particle accelerator (e.g. Large HadronHadron ColliderCollider):):√√ˆssCollision of two particles with COM energyCollision of two particles with COM energy

If an impact parameter If an impact parameter bb is smaller than for a givenis smaller than for a given√√ˆss

BBllaacckk hhoollee wwiitthh aa mmaassss MM ==√√ˆss ffoorrmmss

bb << 44GG√√ˆss

22RRHH

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Large Large HadronHadron ColliderCollider →→ CERN (2007)CERN (2007)

LLHHCC::√√ˆss == 1144TTeeVV

Geometrical cross section for black hole production:Geometrical cross section for black hole production:

σσ((MM )) ≈≈ ππRR22HH

Numerical estimates:Numerical estimates:

110077 bbllaacckk hhoolleess ppeerr yyeeaarr iiff MM∗∗ == 11TTeeVV

LHC LHC -- black hole factory!black hole factory!

1717

Hawking radiationHawking radiation

•• Hawking (1973): black holes radiate Hawking (1973): black holes radiate

•• Virtual particleVirtual particle--antiparticle pairs are being created all the time in vacuumantiparticle pairs are being created all the time in vacuum

•• Usually they disappear almost instantaneouslyUsually they disappear almost instantaneously

•• If a virtual pair is created near the event horizonIf a virtual pair is created near the event horizon

-- one of the particles could escape and become realone of the particles could escape and become real

•• the black hole thereby loses its gravitational energy (mass)the black hole thereby loses its gravitational energy (mass)

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•• Black hole Hawking radiation is thermal!Black hole Hawking radiation is thermal!

•• Black hole decays into all degrees of freedom availableBlack hole decays into all degrees of freedom availableat a given temperature democraticallyat a given temperature democratically

•• Black hole Hawking radiation temperature:Black hole Hawking radiation temperature:

•• Number of particles emitted proportional to black hole entropy:Number of particles emitted proportional to black hole entropy:

•• If and then If and then black hole emits of order 30 quantablack hole emits of order 30 quanta

•• BH event quite different from any other SM event!BH event quite different from any other SM event!

TTHH == 11//RRHH

SS ∼∼ RR22HH

MM22∗∗

MM∗∗ == 11TTeeVV NN ++ 11 == 1100MM == 55TTeeVV

1919

Where do black holes mostly radiate? Where do black holes mostly radiate? BraneBrane or bulk?or bulk?

R. R. EmparanEmparan, G. Horowitz, R. Myers, , G. Horowitz, R. Myers, Phys. Rev. Phys. Rev. LettLett.. 85 499 (2000)85 499 (2000)

““Black holes radiate mostly on the Black holes radiate mostly on the branebrane””

→→ point radiator, spoint radiator, s--mode dominant mode dominant →→ radiates equally in all directions radiates equally in all directions

# of deg. of freedom much larger on the # of deg. of freedom much larger on the branebrane ? (60 SM particles ? (60 SM particles vsvs 1 graviton)1 graviton)

??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

# of deg. of freedom of gravitons in the N+1# of deg. of freedom of gravitons in the N+1--dimensional spacedimensional space--time istime is, so for , so for

V. V. FrolovFrolov, D. , D. StojkovicStojkovic, , Phys. Rev. Phys. Rev. LettLett.. 89:151302 (2002) 89:151302 (2002)

•• LHC: nonLHC: non--zero impact parameter zero impact parameter →→ rotating black holesrotating black holes

•• RRotating black holes otating black holes →→ superradiancesuperradiance →→ graviton emission dominant graviton emission dominant Black holes radiate mostly OFF the Black holes radiate mostly OFF the branebrane !!

λλTT >> RRSS

NN == ((NN ++ 11))((NN −− 22))//22 NN ++ 11 == 1100 wwee hhaavvee NN == 3355!!

2020

Recoil EffectRecoil Effect

V. V. FrolovFrolov, D. , D. StojkovicStojkovic, , Phys. Rev. Phys. Rev. LettLett.. 89:151302 (2002) 89:151302 (2002)

•• Any particle emitted in the bulk can cause a recoil of the blackAny particle emitted in the bulk can cause a recoil of the black holeholefrom the from the branebrane

•• Recoil due to Hawking radiation can be very significant for smRecoil due to Hawking radiation can be very significant for small black holes all black holes (energy of emitted particles comparable to the mass of t(energy of emitted particles comparable to the mass of the black hole)he black hole)

•• Consequences: Consequences:

i) black hole radiation would be suddenly terminated i) black hole radiation would be suddenly terminated

ii) observer located on the ii) observer located on the branebrane would register apparentwould register apparentenergy nonenergy non--conservationconservation

2121

Friction between the black hole and the Friction between the black hole and the branebrane

V. V. FrolovFrolov, D. , D. FursaevFursaev, D. , D. StojkovicStojkovic, , CQGCQG, 21:3483 (2004), 21:3483 (2004)D. D. StojkovicStojkovic,, Phys. Rev. Phys. Rev. LettLett. 94: 011603 (2005). 94: 011603 (2005)

Rate of loss of the angular momentum Rate of loss of the angular momentum

→→ final stationary equilibrium configuratiofinal stationary equilibrium configurationnα = π/2 J = 0

J = π σ a rH cos2 α

2222

Black Holes from Cosmic RaysBlack Holes from Cosmic Rays

J. J. FengFeng, A. , A. ShapereShapere, , Phys. Rev. Phys. Rev. LettLett.. 88:021303 (2002)88:021303 (2002)

•• Cosmic rays are Nature's free Cosmic rays are Nature's free collidercollider

•• Observed events produce COM energy of 100 Observed events produce COM energy of 100 TeVTeV

•• If (quantum gravity energy scale), then If (quantum gravity energy scale), then

—— small black holes can be produced in the atmosphere small black holes can be produced in the atmosphere ——

•• Proposed mechanism:Proposed mechanism:

-- neutrinoneutrino--nucleon scattering deep in the atmosphere nucleon scattering deep in the atmosphere

MM∗∗ ∼∼TTeeVV

2323

Cosmic raysCosmic rays

•• What are cosmic rays? What are cosmic rays?

•• Energetic particles ( )Energetic particles ( )

•• Originate from space (solar, galactic, extragalactic origin)Originate from space (solar, galactic, extragalactic origin)

•• Primary cosmic rays: Hadrons, leptons, photons ??Primary cosmic rays: Hadrons, leptons, photons ??•• Or more exotic Or more exotic ““particlesparticles”” –– monopoles, heavy relics from Big Bang??monopoles, heavy relics from Big Bang??

•• Steep flux ( )Steep flux ( )

110088 eeVV -- 11002200 eeVV

∼∼ 11//EE22..77

2424

Pierre Auger ObservatoryPierre Auger Observatory

Pierre AugerPierre Auger

•• The largest cosmic ray observatoryThe largest cosmic ray observatory

•• Located in Argentina (Located in Argentina (PampaPampa AmarillasAmarillas))

2525

Pierre Auger ObservatoryPierre Auger Observatory

••1600 Water 1600 Water CerenkovCerenkov ground arrays +ground arrays +

•• 4 air fluorescence telescopes4 air fluorescence telescopes

•• spread over 3000spread over 3000

•• Best setup for cosmic ray studiesBest setup for cosmic ray studies

kkmm22

2626

Cosmic neutrinosCosmic neutrinos

•• Cosmic protons scatter off the cosmic microwave background Cosmic protons scatter off the cosmic microwave background to create ultrato create ultra--high energy neutrinoshigh energy neutrinos

•• These neutrinos enter Earth's atmosphere These neutrinos enter Earth's atmosphere

•• They have very weak SM interactions They have very weak SM interactions

•• Dominant interaction:Dominant interaction: ννNN →→ BBHH ++ XX

pp ++ γγCCMMBB →→ nn ++ ππ++ →→ nn ++ μμ++ ++ νν

2727

Crucial points: Crucial points:

•• Neither strong nor electromagnetic interactions can degrade theNeither strong nor electromagnetic interactions can degrade the neutrinoneutrinoenergy before it interacts quantumenergy before it interacts quantum--gravitationallygravitationally

•• Neutrino interaction length is far longer than the thickness Neutrino interaction length is far longer than the thickness of the Earth's atmosphereof the Earth's atmosphere

•• Neutrinos can produce black holes uniformly at all atmospheric Neutrinos can produce black holes uniformly at all atmospheric depthsdepths

•• Protons and photons interact high in atmosphere and cause vertiProtons and photons interact high in atmosphere and cause vertical showerscal showers

Neutrinos Neutrinos →→ Protons Protons →→

•• The most promising signal for neutrinos: The most promising signal for neutrinos: -- quasiquasi--horizontal showers initiated by neutrinos deep in the atmospherhorizontal showers initiated by neutrinos deep in the atmosphere e -- far above the standard model ratefar above the standard model rate

2828

•• The total black hole production cross section in neutrinoThe total black hole production cross section in neutrino--nucleon scattering is:nucleon scattering is:

•• The sum runs over all The sum runs over all partonspartons in the nucleonin the nucleon

•• are the are the partonparton distribution functionsdistribution functions

•• is momentum transferis momentum transfer

•• The cross section for black hole production is found to be severThe cross section for black hole production is found to be several orders of al orders of magnitude higher than the SM cross section formagnitude higher than the SM cross section for

ss == 22mmNNEEνν ,, EECCMM ==√√ˆss

ffii

˜QQ

ννNN →→ LLXX ,, iiff MM∗∗ ≈≈ 11 −− 1100TTeeVV..

ˆσσ == ππRR22ss

σσ((ννNN →→ BBHH)) ==PP

ii

RRddxx ˆσσii((xxss))ffii((xx,, ˜QQ))

2929

•• Numerical Numerical esimatesesimates::

-- Auger can detect black holes in 3 years Auger can detect black holes in 3 years (i.e. BEFORE the LHC data become available)(i.e. BEFORE the LHC data become available)

•• This could be the first window into extra dimensionsThis could be the first window into extra dimensions

•• USA Today version:USA Today version:

"Dozens of tiny black holes may be forming right over our heads."Dozens of tiny black holes may be forming right over our heads... .. A new observatory might start spotting signs of the tiny terrorA new observatory might start spotting signs of the tiny terrors, s, say physicists say physicists FengFeng and and ShapereShapere. They're harmless and pose no . They're harmless and pose no threat to humans."threat to humans."

∼∼ 110000

3030

"Science may be described as the art of systematic over"Science may be described as the art of systematic over--simplificationsimplification..““

Karl Popper, The Observer, August 1Karl Popper, The Observer, August 1982982

3131

Model BuildingModel Building

•• Some things have their natural habitat in the "grand desertSome things have their natural habitat in the "grand desert““that is destroyed by a low scale gravitythat is destroyed by a low scale gravity

•• Like proton stability, neutrino masses...Like proton stability, neutrino masses...

•• Low scale quantum gravity implies very fast proton decay!Low scale quantum gravity implies very fast proton decay!

3232

Black hole mediated proton decayBlack hole mediated proton decay

•• Small scales: spaceSmall scales: space--time fluctuations largetime fluctuations large

•• Hawking: these fluctuations are virtual black holesHawking: these fluctuations are virtual black holes

IIff MMPP ll ∼∼ 11001199GGeeVV,, tthheenn ττpprroottoonn ∼∼ 11004455 yyrrss

IIff MMPP ll ∼∼ 110033GGeeVV,, tthheenn ττpprroottoonn ∼∼ 1100−−1111 sseecc !!!!!!

ττpprroottoonn ∼∼ mm−−11pprroottoonn³³

MMPPll

mmpprroottoonn

´44

3333

Gauging the baryon numberGauging the baryon number

•• One way out is to gauge the baryon numberOne way out is to gauge the baryon number→→ promote a into a gauge symmetrypromote a into a gauge symmetry

•• Problems: Problems:

•• BaryogenesisBaryogenesis-- Before: "We exist Before: "We exist →→ proton must be stableproton must be stable““-- After: "We exist After: "We exist →→ proton must be unstableproton must be unstable““

•• To avoid a new long range interaction, must be To avoid a new long range interaction, must be broken down to some discrete gauge symmetrybroken down to some discrete gauge symmetry

•• Arranging for anomaly cancellation Arranging for anomaly cancellation

•• Gauge couplings unificationGauge couplings unification

•• So far, gauging the baryon number has not proved very attractivSo far, gauging the baryon number has not proved very attractive!e!

UU ((11))BB

UU ((11))BB

3434

An alternative An alternative -- Split FermionsSplit Fermions

N. N. ArkaniArkani--HamedHamed, M. Schmaltz, , M. Schmaltz, Phys. Rev. D 61Phys. Rev. D 61:033005 (2000) :033005 (2000) 300+ citations300+ citations

•• In order to suppress a direct QQQL coupling In order to suppress a direct QQQL coupling we must separate quarks form leptonswe must separate quarks form leptons

•• Quarks and leptons are localized at different points on a thickQuarks and leptons are localized at different points on a thick branebrane•• Or alternatively, on different Or alternatively, on different branesbranes

•• The model yields exponentially small coupling (wave function oThe model yields exponentially small coupling (wave function overlap) verlap) between quarks and leptonsbetween quarks and leptons

•• In the language of virtual black holes: In the language of virtual black holes:

•• Virtual black holes responsible for proton decay must be very lVirtual black holes responsible for proton decay must be very large arge →→ have small probability to be createdhave small probability to be created

3535

•• The propagator between fermions which are separated in extra dimThe propagator between fermions which are separated in extra dimensionsensions(in the high energy and high momentum transfer limit) is(in the high energy and high momentum transfer limit) is

d: separation between the quarks and leptonsd: separation between the quarks and leptonsσσ: the width of the : the width of the fermionfermion wave functionwave function

•• The propagator has the usual 4The propagator has the usual 4--dim form except that the coupling dim form except that the coupling is suppressed by the exponentially small wave function overlais suppressed by the exponentially small wave function overlapp

•• Suppression factor of , Suppression factor of , (which can be achieved for a rather modest hierarchy of (which can be achieved for a rather modest hierarchy of ))

completely saves the proton!completely saves the proton!

ee−−dd22//σσ22 ∼∼ 1100−−2266

dd ∼∼ 1100 σσ

PPeexxttrraa ≈≈ PP44 ee−−dd22//σσ22

3636

Consequences: the price we to have payConsequences: the price we to have pay

D. D. StojkovicStojkovic, G. , G. StarkmanStarkman, D. De, D. De--Chang, Chang, Phys. Rev. Phys. Rev. LettLett 96, 041303 (2006)96, 041303 (2006)

•• Spatial separation between the quark and lepton wave functionsSpatial separation between the quark and lepton wave functionssuccessfully suppresses proton decaysuccessfully suppresses proton decay

•• However, this implies strong consequences for cosmic ray However, this implies strong consequences for cosmic ray neutrino scattering off the atmosphereneutrino scattering off the atmosphere

•• The correct black hole production cross section in collisions The correct black hole production cross section in collisions of of neutrinos with each quark in a nucleon is notneutrinos with each quark in a nucleon is not

•• The correct cross section is multiplied by the large suppressionThe correct cross section is multiplied by the large suppression factor offactor of

ˆσσ == ππRR22HH

1100−−5522

3737

•• Proton contains other Proton contains other partonspartons besides quarks: besides quarks: e.g. gluons, other gauge bosons etc.e.g. gluons, other gauge bosons etc.

•• However:However:

•• Once you separate leptons from quarks, higher order processes Once you separate leptons from quarks, higher order processes are also highly suppressedare also highly suppressed

•• by exponential wave function suppression factorsby exponential wave function suppression factors•• by power law volume suppression factorsby power law volume suppression factors……

3838

Large suppression factors enter the total production cross sectLarge suppression factors enter the total production cross section ion

and render the corresponding probability for the black hole prodand render the corresponding probability for the black hole production uction by cosmic neutrinos by cosmic neutrinos completely uninteresting completely uninteresting for the Auger Observatory!for the Auger Observatory!

σσ((ννNN →→ BBHH))

3939

•• Black holes might still be produced in NN or Black holes might still be produced in NN or γγN scatterings N scatterings

•• Problems: Problems:

•• The Earth's atmosphere is not transparent to nucleons or photoThe Earth's atmosphere is not transparent to nucleons or photons ns as it is to neutrinosas it is to neutrinos

•• SM interactions much stronger SM interactions much stronger

•• One can not expect quasiOne can not expect quasi--horizontal showers deep in the atmospherehorizontal showers deep in the atmosphere

No distinct experimental signature of BH production!No distinct experimental signature of BH production!

4040

••What about leptonWhat about lepton--lepton (e.g. ) scattering?lepton (e.g. ) scattering?

•• is 2000 times smaller than theis 2000 times smaller than the

•• The threshold neutrino energy for The threshold neutrino energy for leptonicleptonic blackblack--hole production hole production is 2000 times higheris 2000 times higher

•• The cosmic neutrinos flux goes down steeply with energy ( The cosmic neutrinos flux goes down steeply with energy ( ))

•• The expected suppression isThe expected suppression is

•• Completely uninteresting for the Auger ObservatoryCompletely uninteresting for the Auger Observatory

∼ 1/E2.7

νe−

me mN

≈ 108

4141

ConclusionsConclusions

•• Fine tuning in the SM implies either new physics or strong gravFine tuning in the SM implies either new physics or strong gravity at ity at TeVTeV scalescale

•• If gravity is strong, we can expect nonIf gravity is strong, we can expect non--perturbativeperturbative quantum gravity effectsquantum gravity effectsat soon available energies in accelerators at soon available energies in accelerators

•• Like mini black hole productionLike mini black hole production

HOWEVER:HOWEVER:

•• The weakest link in The weakest link in TeVTeV scale gravity models scale gravity models →→ fast proton decayfast proton decay

•• Realistic models with stable proton: Realistic models with stable proton: Some of the channels for black hole production are strongly suSome of the channels for black hole production are strongly suppressedppressed

4242

Respectfully Quoted: A Dictionary of Quotations. 1989.Respectfully Quoted: A Dictionary of Quotations. 1989.

Dialog between Lord Michael Faraday (1791 Dialog between Lord Michael Faraday (1791 -- 1867) and the Chancellor of the Exchequer1867) and the Chancellor of the Exchequer

QUOTATION:QUOTATION:

•• Mr. Gladstone, then Chancellor of the Exchequer, had interruptMr. Gladstone, then Chancellor of the Exchequer, had interrupted Lord Faraday in a ed Lord Faraday in a description of his work on electricity to put the impatient idescription of his work on electricity to put the impatient inquiry:nquiry:

““Very well Lord Faraday, but after all, what is the use of it?Very well Lord Faraday, but after all, what is the use of it?““

Like a flash of lightning came the response:Like a flash of lightning came the response:

““Well sir, there is every probability that you will soon be able Well sir, there is every probability that you will soon be able to tax it!"to tax it!"