Ginzburg Conference on Physics May 28 - June 2, 2012 in Moscow

<strong>Ginzburg</strong> <strong>Conference</strong> on PhysicsMay 28 - June 2, 2012 in Moscow

1995: #21. “Black holes” of total 24 problems

Black hole concept,its evolution,modern status of BHs,and open problems

A black hole is a compact massive object, thegravitational field of which is so strong thatnothing (even the light) can escape from it.The boundary of the black hole, called theevent horizon, is a surface at which theescape velocity is equal to the velocity of light.12mv2GMmRRg2GMc2

Black hole gravity is strong:2 2GMc2c2Rg1The Einstein’s theory of generalrelativity is required for its description

Albert Einstein(1879--1955)Spacetime is curved. Spacetime curvature isproduced by the mass. Particles and light raysare geodesics.

GRAVITY1 8MATTERR g R T 2 c4 MATTERGGEOMETRYCAUSALITY

Karl Schwarzschild(1873--1916)In 1916 Karl Schwarzschild, an astronomer,obtained a solution of vacuum Einstein equation,describing a spherically symmetrical static blackhole. He died soon after this.

Black Holes vs Dark Starts“Nature” ofSchw. Singularity:Synge ‘50,Finkelstein ‘58,Fronsdal ‘59,Szekeres ‘60,Kruskal ‘60,Novikov ’63,64

Roy Kerr(1934 --)The most general stationary solution of vacuumEinstein equations describing an isolated blackhole was found in 1963 by Roy Kerr. It isaxisymmetric and uniquely specified by 2parameters: mass M and angular momentum J.

JohnArchibaldWheeler(1911--2008)The name "black hole" was invented in December 1967 byJohn Archibald Wheeler. Before Wheeler, these objects wereoften referred to as "black stars“ or "frozen stars".

Final state of stellar evolution:(1) White dwarf (Chandrasekhar ('31) limit 1.44 M )(2) Neutron star (pulsars, mass limit 3 M )(Landau '32, Baade&Zwicky '34,Oppenheimer&Volkoff '39)(3) Black hole (for M 10M r 30km)g(Oppenheimer&Snyder '39)

In 60’-70’th of the past century manyremarkable results and exact theoremson the BH properties were proved.

Properties of 4D Black HolesPrice ‘72 et all“Black holes have no hair”: Mass, electriccharge and angular momentum are the only 3parameters which specify a stationary BH inEinstein-Maxwell theory (Wheeler, 1971)

Event horizon (BH boundary) is almost everywherenull surface (Penrose, ‘68)Black hole surface topology is (Hawking, ‘72 )Its surface area never decreases (Hawking,’71,72)Soon after their formation black holes becomestationary (the `balding phase’ T r / c ) .Stationary black holes are either static(Schwarzschild) or axially symmetric (Kerr).S2g

Uniqueness theorem: Stationary isolated BHsare uniquely specified by their mass and angularmomentum and are described by the Kerr metric(Israel ’67, Carter ‘71,73, Robinson ‘75)Geodesic equations of motion in Kerr ST arecompletely integrable (Carter ‘68)The Kerr metric besides the evident STsymmetries has also hidden symmetry (Killingand Killing-Yano tensors) (Penrose&Walker ‘70,Penrose&Floyd ‘73)

Massless field equations allow the separation ofvariables (Press ‘72, Press&Teukolsky ’72,73)Black holes are classically stable.

Final state of matter evolutionExotic objects of stellar massToo small and dark to be observed

R.I.P.Black Holes as Graves of Matter

40 YEARS LATER …

At: http://www.google.caBLACK HOLE 116,000,000NEUTRON STAR 4,800,000BH’s `Genealogical tree’

BH theoremsHigher Dim. BHsExact solutionsComplete integrabilityPrimordial BHGrav.Rad. BHSuperM BHGRBBH binariesStellar BHBH models in CMBH interiorInformation lossBH and QG(strings, loops)BH Stat.Phys.BH Quantum Mech.BH thermodynamics

Motivations :(1) Extra-dimensions and string theory(2) Brane-world models(3) Black holes as probes of extra dimensions(4) Micro BHs production in colliders?(4) Generic and non-generic properties of BHs

Higher dimensional gravity is stronger at small scales andweaker at large scales than the 4D one:F G M M / r( D) ( D2)1 2If extra dimensions are compact with size L, then at the distancelarger than L one has standard 4D gravity withG G / L( D) ( D4).ForL0.1 m minteractions.higher dim. gravity may be as strong asother

New fundamental (quantum gravity) scale m ~ m ( L / l )r ~ l ( L / l ) . m is the lowest mass of a classical BH.k/( k2)* Pl Pl*17For k 2 and L 0.1mm,m* ~ 1TeV and r*~ 10 cm.*PlPlk/( k2)Properties of HD black holes witharedetermined by D-dim Einstein equations, so thattesting their properties in our 4D experimentsone probes extra dimensions (e.g. micro BHat colliders?) . At the moment there is no anyindications on micro BH creation at LHC.rgL

"To think that LHC particle collisions at highenergies can lead to dangerous black holes isrubbish. Such rumors were spread by unqualifiedpeople seeking sensation or publicity.“Academician Vitaly <strong>Ginzburg</strong>, Nobel Laureate inPhysics, Lebedev Institute, Moscow, andRussian Academy of SciencesIn: The safety of the LHC, CERN document,http://public.web.cern.ch/public/en/lhc/safetyen.html,(2003)

If in D-dimensional ST there exist D- 2Abeliansymmetry group, the vacuum Einstein equationsreduce to a nonlinear sigma model, which is acompletely integrable system.In 5D: black holes with 3 parameters(mass and 2 angular momenta).Black rings (Emparan&Reall '08), etc...

5D vac. stationary black holes

(1) No Uniquness Theorem: For givenand J more than one BH solution(2) Stability of HD BHs ?M

Complete integrability of geodesic equations andcomplete separation of variables in HJ and KG eqs.Complete integrability in 5D rotating black holes(V.F.&Stojkovich ‘03)The most general higher dimensional black holesolution (Chen, Lu, Pope ‘07) : (A)dS-Kerr-NUT

All Kerr-NUT-AdS metrics possess a generatorof symmetries (Principle KY tensor, V.F.&Kubiznak ‘07).A solution of Einstein equations which admits aPKYT is Kerr-NUT-AdS metric (Krtous,V.F.&Kubiznak ’08, Houri,Oota, Yasui ‘09)PKYT generates enough symmetries to makegeodesic equations completely integrable(Page,Krtous,Kubiznak,VF ’07)Complete separation of variables.

Existence of the innermost stable circular orbits(ISCOs) differs GR from Newtonian mechanics2GmM LU ;2r 2mr2LU 0 r ;GmMIn Newtonian theory theradius of a circular orbitcan be arbitrary small(No stable bounded orbits in HD gravity !)Anthropic principle excludes D>4 with Ledim

Schwarzschild BH:r 3r 6MISCOEISCOg/ m8 / 9BH efficiency: 5.72%Extremal Kerr BrISCOEISCO M/ m 1/ 32H (J/M =1):BH efficiency: 42.36%

Gravitational perturbations of a black holebehave like an oscillator with dampingg exp( it), i, 1 2 1 2M f ( J / M ), M F( J / M ).An excited black relaxes to its `ground'stationary state by emitting gravitational waves.They `bring' us information about M and J.

Bekenstein 72-73, Hawking74-75dMAS , A 4 r2M2,g4 lT8T dS2Plc3GkMM1

StephenHawking(1942 --)In 1974 British physicist Stephen Hawkingproved that black holes are quantum unstable.

The vacuum near a black hole is unstable.The gravitational field is so strong that itproduces particles. As a result the black holeemits as a heated black body with temperature:kTc3106MK8GM M

cPlanck units: 105g,PlGcGG10 , 10 secc33 cm 433 Pl 5Life-time of a black hole:tBH3 3 M M 17 10 secPl 1015 g Pl Hawking effect is important for mini-black-holes only

Equivalenceprinciple inquantum domainUnruh effectand AnomalousDoppler effect

Black holes have very high efficiencyof rest-mass-to-energy transformationBlack holes are now used as anatural engine model whenever it isrequired to explain large energyproduction in a small compact spaceregion

Total number of stars in our Galaxy is11about 10 . Estimated number of blackholes in it is about 108 910. The numberof neutron stars is up to 10 times larger .

More than 20 stellar mass BHsobservedAll of them are X-ray sourcesin binariesAll except 4 are in our Galaxy

Persistent BHs ( Syg X 1, LMC X 1, LMC X 3)Transient BHs

Newtonian mechanics is used to determinethe mass of the BH candidates.GR is required to obtain confirmationsMatter, falling onto BH, forms an accretion disk.ISCO radius determines its inner edge, as well astemperature and luminosity of the disk and shortestperiod of fluctuations of its radiationMeasuring of BH spinIron X-ray line broadeningMicroquasars

Gamma-ray bursts (GRB) are the brightest objects in the Universe.They are observed once or twice a day, as highly energeticexplosions. They are registered as a lower energy gamma-raybursts, which last typically a few seconds. The distribution of GRBsover the sky is homogeneous. The sources of most GRBs arebillions of light years away from the Earth. The energy releasedduring a burst is about 10^51 erg within a few seconds.It is believed that the central engine of the(long) gamma-ray bursts is a black hole formedby a collapse of a massive rapidly rotating star.

BH as a classical object: M 105gPrimordial BHs: M M 210g33Stellar mass BHs: M 3M 100M6 10Supermassive BHs: M 10 10M

The galactic center harbours a compact object ofvery large mass (named Sagittarius A*), stronglysuspected to be a supermassive black hole.The estimated mass of the central BH is about4 million solar masses within a volume withradius no larger than 6.25 light-hours (45 AU).

Stars in Keplerian orbits around central black holehigh-precision measurement of BH mass: 4106MPeriastron of closest encounter: ~ 2000(star S2 has period about 15.2 yrs)r gGetting even closer: X-ray & IR flares, some withperiodicity ~ 17min hot spot in inner disk, at ~ 10 r g

“It is likely that a BH exists at thecenter of every massive galaxy.“From the Summary of the talk by Stefanie Komossa(MPE Garching) at the Black Holes VI meeting at NovaScotia, Canada, May 2007However the mechanism of SMBM formation andtheir role in the galaxies evolution are not clear.

Tidal disruption of a star at close encounter of BHGMbGmR3b2RMm1/3b

Primordial Black HolesMany different mechanisms of PBH production inthe Early Universe have been discussed:(i) Initial density fluctuations;(ii) Soft equation of state during phase transitions;(iii) Collapse of cosmic strings;(iv) Bubble collisions.No evidence of existence ofPBHs was found

CollapseEvaporation Pure Black Thermal state hole radiation

What are microscopical degrees of freedomresponcible for BH entropy S A4 l2(1) Each (2 lPl) element of BH surface ha2Pl?s 1 bit ofentropy Quantum gravity is required(2) Universality problem:BH is determined by lowenergy physics parameters(3) BH is a ground (vacuum) state of classicalgravitational field gravity should bean emergent phenomenon

String theoryAdF/CFTLoop gravityBH entropyproblemInducedgravity2+1 gravityKerr/CFT

Gravitational radiusr2GM2c3"The spatial volume inside the black hole is rg".Is this right? No, this is completely wrong!g

plays the roleof time inside BHSlice r const hastopologyS2 RSpatial volumer ( t / c) r2 3ggContractinganisotropic universe

“Through A Black Hole Into A New Universe?”V.F., Markov, Mukhanov, Phys.Lett. B216 (1989) 272;“Black Holes As Possible Sources Of Closed andSemiclosed Worlds” ,V. F., Markov, Mukhanov,IC/88/91. May 1988. Phys.Rev. D41 (1990) 383;“How many new worlds are inside a black hole?”Barrabes and V. F. Phys.Rev. D53 (1996) 3215Buonanno, Damour, Veneziano ‘99: “Gravitational instability, leadingto the possible formation of many black holes” … each of whichbecomes the place of “birth of a baby Friedmann universe after aperiod of dilaton-driven inflation”.Smolin, The Life of the Cosmos ‘97: “A collapsing black holecauses the emergence of a new universe on the "other side",whose fundamental constant parameters (speed of light, Plancklength and so forth) may differ slightly from those of the universewhere the black hole collapsed. Each universe therefore gives riseto as many new universes as it has black holes.”

Birth: Matter is generated during the inflation.Its large scale structure in our worldis a result vacuum fluctuations amplificationin the early inflating UniverseLife: Supernova explosions -> heavy elements-> planets and lifeDeath: Black holes are `matter graves’ in ourUniverseReincarnation: Black holes as origin of newuniverses: `Life after death’ ???????????

http://www.amazon.ca/Introduction-Black-Physics-Valeri-Frolov/dp/0199692297