Experimental Evidence of Black Holes 7 0 0 2 n a J AndreasMüller∗ 9 Max–Planck–InstitutfürextraterrestrischePhysik,p.o. box1312,D–85741Garching,Germany E-mail: [email protected] 1 v 8 ClassicalblackholesaresolutionsofthefieldequationsofGeneralRelativity. Manyastronomi- 2 2 calobservationssuggestthatblackholesreallyexistinnature. However,anunambiguousproof 1 fortheirexistenceisstilllacking. Neithereventhorizonnorintrinsiccurvaturesingularityhave 0 7 beenobservedbymeansofastronomicaltechniques. 0 Thispaperintroducestoparticularfeaturesofblackholes. Then,wegiveasynopsisoncurrent / h astronomical techniques to detect black holes. Further methods are outlined that will become p - important in the near future. For the first time, the zoo of black hole detection techniques is o completelypresentedandclassifiedintokinematical,spectro–relativistic,accretive,eruptive,ob- r t s scurative, aberrative, temporal, and gravitational–waveinduced verification methods. Principal a and technical obstacles avoid undoubtfullyproving black hole existence. We critically discuss : v alternativestotheblackhole. However,classicalrotatingKerrblackholesarestillthebesttheo- i X reticalmodeltoexplainastronomicalobservations. r a SchoolonParticlePhysics,GravityandCosmology 21August-2September2006 Dubrovnik,Croatia Speaker. ∗ (cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ ExperimentalEvidenceofBlackHoles AndreasMüller 1. Introduction Black holes (BHs) are the most compact objects known in the Universe. They are the most efficient gravitational lens, a lens that captures even light. Albert Einstein’s General Relativity (GR)isapowerful theory todescribe BHsmathematically. Itisatheory that describes Gravity as curved space–time. In a sense, Gravity is not a force but a geometric feature of a deformable 4D continuum. Accordingtothispicture,BHsareanextremeformofcurvedspace–time containing a curvature singularity thatswallowsmatterandlight. Astonishingly, at the advent of GR in 1916 the first solution of Einstein’s complicated field equation was found in the same year. This (external) Schwarzschild solution [120] describes the simplestBHtypemathematically. However,thenotionblackholewascoinedsignificantlylater,in 1967bytherelativist JohnArchibaldWheeler. It soon became clear that nature may allow for the existence of these mysterious objects. In the classical GR collapse of massive stars nothing can stop gravitational pressure so that a BH forms. This picture was essentially pushed forward by the work of Julius Robert Oppenheimer and Hartland Snyder in1939 [105]. Theresult ofthese developments isthe firstBHmassfamily: stellar–mass BHs. IntheSixtiestheunderstandingofactivegalacticnuclei(AGN)likequasarsandradiogalaxies delivered another piece to the BH puzzle [137, 116, 80, 81]. The extreme quasar luminosities of 1047 erg/s 1014L 1 could be explained by BHs that swallow matter. Accretion turned out to ∼ ⊙ bethemostefficientprocess toproduce radiation inthewholerange ofelectromagnetic emission. However, estimateswiththeEddington relation [38]pointed toBHsinthecenters ofgalaxies that are significantly more massive than the first family. Thissecond massfamily iscalled supermas- sive black holes (SMBHs). Paradoxically, the darkest object in the Universe produces the most powerful source of luminosity. Of course, this mechanism works outside the event horizon that markstheultimateblackness. Nowadays,astrophysicists areconvinced thatstellar–massBHsplay the key role in black hole X–ray binaries (BHXBs) such as microquasars, in gamma–ray bursts (GRBs), and maybe also in ultra–luminous X–ray sources (ULXs)[43, 31]. Recently, it has been shown that thetimescale ofX–rayvariations from stellar and supermassive BHsare infactphysi- callylinkedifonecorrects fortheaccretion rate[88]. Thesamephysicsisatwork. The giant SMBHs are supposed to inhabit almost any center of galaxies causing an active quasars–like phaseinanearlierstateofthegalaxyevolution. Localgalaxiescontain non–activeor dormantSMBHs. Currently, there is an active debate on the cosmological role of BHs. In hierarchical galaxy formationscenariosisitpossibletoexplainluminousquasarsatcosmologicalredshiftz 6[133]. ∼ SMBHsareformedoncosmological timescalesfromseedBHswithseveralhundredsolarmasses. Probably, these seeds originated from the first population of very massive stars. The initial BHs grew by merging and accretion to form the nearby SMBHs. In the same scenarios it is possible to explain the spin–up of BHs in this context of BH growth. The spin distribution is dominated by rapidly spinning BHs–essentially bygasaccretion. Maximally spinning BHsarethe result of thindiskaccretion butsimilarlyforthickdiskaccretion about4/5haveveryhighspins,a 0.8M ∼ [134]. 1L 3.85 1033erg/s ⊙≃ × 2 ExperimentalEvidenceofBlackHoles AndreasMüller Another interesting finding is the so–called luminosity—dependent density evolution. Data from ROSAT,XMM–Newton, and Chandra surveys have been collected together to provide huge sampleswith 1000AGN[62]. Basedonthesedataitcouldbeshownthatthenumberdensityof ∼ high–luminosity AGN(’quasars’) peaksatsignificantly lowercosmological redshift thanforlow– luminosity AGN(’Seyfertgalaxies’). Thisanti–hierarchical growthcanbeexplained theoretically [91]. Currently, astronomers use multi–wavelength surveys to collect a huge amount of observa- tionaldata. Theanalysisrevealsinteresting connections betweengalaxyandcentralSMBH.There seemstobeacosmological linkbetweenthetwothatpointstowardsco–evolution scenarios. A thorough introduction to BH physics and BH phenomenology has been given by Jorge Zanelli and Neven Bilic´ at this school, see [16] and references therein. Another review can be foundin[100]2 This contribution is devoted to experimental techniques in astronomy that are used to detect cosmic BHs. After an introduction into BH features a complete presentation and classification of detection methods is given. We have a closer look at BH spin measurements. Finally, we criticallydiscussthequestionwhatweobserve: Whataretheastronomicalfacts? Whatarepossible alternatives totheclassical BHsolutions? 2. Black holefeatures Inthepresentpaper,thetreatmentisrestrictedtoclassicalBHsi.e.the(external)Schwarzschild solution [120]andtheKerrsolution [68]. Essentially, thisisjustifiedbytworeasons: first,space– timerotationisacrucialingredientforBHastrophysicse.g.intheviewofparadigmsforrelativistic jets launching in AGN [17] and GRBs[92, 93]. There is still no rotating BH alternative available todatethatcouldreplaceaclassicalKerrBH.Second,theregimeofclassicalGRissupposedtobe agood choice insome distance toaBHcandidate. Deviations from GRsolutions due toquantum gravity effects are expected to emerge at length scales that are comparable to the Schwarzschild radius or even smaller. This is currently ’out of astronomical range’. The regime of strong grav- ity has already clear signatures starting at some distance to the horizon and getting stronger as approaching the hole. As suggested by relativistic emission line diagnostics this critical distance amountstoseveraltensgravitational radii[99]. Hence,therestrictiontoclassicalGRBHsolutions issufficient. The natural length scale of GR is the gravitational radius defined by r =GM/c2 with New- g ton’s constant G and vacuum speed oflight c. Forone solar mass, M =M =1.989 1033g, the ⊙ × Schwarzschild radius amounts to R 3km. In theory, it is convenient to use geometrized units S ≃ G=c=1 so that length is measured in units of mass M [97]. We measure BH rotation in terms of the specific angular momentum (Kerr parameter) that holds a=J/M =GM/c [32]. At first glance,theKerrparametercantakeanyvaluebetween Mand+Mbutthecasesa= Mdevelop − ± a naked singularity that is forbidden [108]. Accretion theory favours a limit of a =0.998M max | | [127]. Toprepare todetection techniques for BHs,wefirstarrange the properties ofthese objects in thenexttwosubsections. 2Downloadathttp://www.mpe.mpg.de/˜amueller/downloads/PhD/PhD_AMueller.pdf 3 ExperimentalEvidenceofBlackHoles AndreasMüller 2.1 Blackness TheblacknessofBHsisaresultofstronglycurvedspace–timeforcinglightrays(nullgeodesics) tobendbacktothegravitationalsource. Thisisaconsequenceoftheircompactness. Asuitablepa- rametertomeasurecompactness ofastellarbodywithmassM andradiusr isthedimensionless ∗ ∗ quantity [100] C GM /(c2r ), (2.1) ≡ ∗ ∗ whichisdenotedcompactness parameter hereafter. C varies between zero and unity where a value close to unity signals an extremely compact object. Letuslookatsomeexamples: WhitedwarfsattheChandrasekharlimitmaysatisfyC WD ≃ 0.0004, neutron stars hold C 0.16, quark stars may have C 0.37, Schwarzschild BHs3 NS QS ≃ ≃ holdC =1/2 and extreme Kerr BHssatisfyC =1. Therefore, BHsrotating at their limit4 SBH KBH represent themostcompactobjects intheUniverse. In the framework of classical GR a point mass is described by the (external) Schwarzschild solution. Schwarzschild BHs represent a one–parameter family in GR. The static Schwarzschild space–time isfullydescribed bythemassparameterM. GR tells us that mass causes gravitational redshift effects i.e. the strong pull of gravity shifts radiation emittednearmassestowardstheredspectralrangeandtheintensityisreduced, too. This is mathematically described by ageneral relativistic Doppler factor or g–factor for short hereafter [99]. Theg–factorisameasureforboth,energyshiftofemissionandsuppression orenhancement ofintensityascomparedtotheemitter’srestframe. gisgenerallyafunctionofthevelocityfieldof the emitter (as measured in asuitable observer’s frame e.g. the zero angular momentum observer, ZAMO), the curved space–time (represented by metric coefficients), and constants of motion of thephoton asdiscovered in[26]. Oneimportant metriccoefficient istheredshift orlapsefunction a thatmeasurestheamountofgravitationalredshiftofphotonsandtimedilation. Itholdsforstatic BHs 2M a = 1 , (2.2) S r − r and isknown asSchwarzschild factor. Inagood approximation, anyslowlyrotating massmaybe described bythisfactor. Incontrast, KerrBHsbelongtoatwo–parameter familydescribed bytwophysical quantities, mass M,and specific angular momentum a[11]. InBoyer–Lindquist form [23], aKerrblack hole isgivenbythelineelement5 ds2= a 2dt2+w˜2(df w dt)2+r 2/D dr2+r 2dq 2, (2.3) − − whereexpression (2.2)canbegeneralized tobethelapseforrotatingBHs r √D a = . (2.4) S 3Here,theeventhorizonradiusisassumedtobethe’surface’ofaBH. 4a=MisassumedhereforsimplicitybuttheexactvalueofthemaximumangularmomentumofBHsisstillunder debate.Usually,oneassumesThorne’slimita 0.998M[127],seehowever[8,121]foralternatives. ≃ 5Thesignatureofthemetricis( +++)throughoutthepaper. − 4 ExperimentalEvidenceofBlackHoles AndreasMüller Othermetricfunctions satisfy D = r2 2Mr+a2, (2.5) − r 2 = r2+a2cos2q , (2.6) S 2 = (r2+a2)2 a2D sin2q , (2.7) − w = 2aMr/S 2, (2.8) w˜ = S sinq /r . (2.9) Per definition, any classical BH horizon satifies D =0 and consequently a =a =0. Since S g(cid:181) a , the redshift influences any emission of electromagnetic radiation in the vicinity of a BH. Observed intensity of radiation satisfies Fobs (cid:181) g3 so that spectral flux is strongly reduced as the n emitter approaches to the event horizon. The consequence is the main BH feature: darkness and evenblacknessattheeventhorizon. ForstaticSchwarzschildBHs,a=0,thereisonlyonehorizon that is located at the Schwarzschild radius, R =2M. For rotating Kerr BHs there are in fact two S horizons thathold r =M M2 a2, (2.10) H± ± − p wherer+denotestheouterhorizonandr theinnerhorizon. TheinnerorCauchyhorizoncanonly H H− be intersected once i.e. it is a one–way ticket to the curvature singularity. Following the cosmic censorship conjecture byRogerPenrose theintrinsic ’true’ singularity ishidden bythesehorizons [108]. Weconclude thattheessentialBHindicator isdarknessasaresultfromgravitational redshift. Hence, astronomers seek for ’black spots’ (BS) in the sky especially at positions where BH can- didates are supposed to be e.g. in X–ray binaries (XRBs), gamma–ray burst remnants (GRBRs), possibly in centres of globular clusters and confidently in centres of galaxies. The technical chal- lenge is to resolve these tiny spots. The apparent size q of the next SMBH in the centre of the BH Milky Way can be found on the micro–arcsecond (m as) scale! We provide a useful equation to computethisimmediately fromBHmassM andBHdistanced: q = 2arctan(R /d) BH S 2R /d S ≃ M 1kpc 39.4 m as. (2.11) ≃ ×(cid:18)106M (cid:19)×(cid:18) d (cid:19) ⊙ Thevaluesareadapted toSMBHsthathavetypical massesthatrangefrommilliontobillionsolar masses and typical distances from several kpc to Mpc6. It is sufficient to consider only the first ordertermofthearctanexpansion sinceR /d 1forcosmicBHcandidates. S ≪ 2.2 Rotatingspace–time Kerr BHs reveal a speciality that lacks in case of Schwarzschild BHs: rotation of space– time. The spin of Kerr BHs forces anything to co–rotate: matter, light, close observers, because 61pc=3.26lightyears 3.1 1018cm ≃ × 5 ExperimentalEvidenceofBlackHoles AndreasMüller spaceitselfrotates. Theforcingpropertyiscalledframe–dragging. Theframe–draggingfrequency already introduced as w in Eq. (2.8), parameterizes the rotation of space as viewed from infinity. Approaching the Kerr BH, the ’spin of space’ steeply increases, w (cid:181) r 3. It is important to note − thatSchwarzschild BHsforceanything nottorotate, w =0,afeature thatmaybeentitled asanti– frame–dragging. KerrBHsareendowedwithazonewheretherotation ofspace–time becomes extraordinarily strong. Itcalledtheergoregionthatisoblate. Theouteredgeoftheergoregion, theergosphere, can becomputedaccording tog =0andwefind tt r (J )=M+ M2 a2cos2J . (2.12) erg − p Themetriccoefficientflipssignatthisradius: itisnegativeforr>r andpositiveforr<r . In erg erg theequatorialplane,J =p /2,theergosphereliesattheSchwarzschildradius–independentofBH spin. However,forlowerpoloidal anglestheergosphere approaches theBHhorizon andcoincides withitatthepoles, J =0. Frame–dragging can be nicely interpreted by an analogue to electromagnetism, called grav- itomagnetism [128]. From this view, a Kerr BH interacts by gravitoelectric and gravitomagnetic forces withitssurroundings. Gravitoelectric forcesarejustordinary gravitational forces attracting test bodies. But the interpretation of gravitomagnetic forces is more complicated: One relevant phenomenon associated with gravitomagnetic forces is the Lense–Thirring effect. It simply states that two gyroscopes interact by exchanging gravitomagnetic forces. One realisation of two gyro- scopes is a rotating BH surrounded by a rotating accretion disk. In this case the Kerr BH pushes the rotating accretion disk into the equatorial plane by means ofgravitomagnetic forces [12]. The transitionregioncanbefoundat102to104gravitationalradii. Theaccretiondiskwhobblesaround the BH. Hence, hot disk radiation that is detected in the X–ray range might be variable and show quasi–periodic featuresinthepowerdensity spectrathataredominatedbytheLense–Thirring fre- quency[130]. BH rotation is important: Rapidly rotating space–time plus magnetic fields are the main in- gredients to drive relativistic jets magnetohydrodynamically. Recently, numerical non–radiative general relativistic magnetohydrodynamics (GRMHD)simulations have shown that Kerr BHsro- tatingneartheirlimitareefficientrotatorstospin–upmagneticfieldlinesanddrivePoyntingfluxes [70,77,89]. Schwarzschild BHsarenotsufficient toexplain theobserved relativistic jetsofAGN andGRBs. Finally,Fig.1givesacomparisononBHsandcomparesstatic(left)withrotatingBHs(right). Westressthatthisisjusta’structuralview’showingthemainBHfeatures. Butitisnotaninvariant view because it is based on the radii of a specific coordinate system. A better and invariant view ontoBHsispossible byusingcurvature invariants suchastheKretschmannscalar[64]–however, thisisnotthatintuitive. We summarize this section that blackness and rotating space–time are the two observable properties ofclassical blackholes. 3. Black holedetection methods How can one detect acosmic BH? In principle, one can distinguish direct and indirect meth- 6 ExperimentalEvidenceofBlackHoles AndreasMüller Figure 1: Architecture of static Schwarzschild (left) and rotating Kerr BHs (right). We assume the same mass. OneimmediatelynoticesthatKerrBHsaremorecompactthanSchwarzschildBHs. ods. Direct evidences for cosmic BHs means that an astronomer has to prove the key features of a classical black hole by observations: the event horizon and the curvature singularity. Dueto the cosmic censorship conjecture by Roger Penrose [108] BH intrinsic singularities are hidden by an event horizon. Therefore, a proof of the curvature singularity seems to be impossible. The proof of an event horizon means to show strong evidence for a zero–emission region because at event horizons the general relativistic Doppler factor vanishes exactly, g = 0, due to zero redshift (or lapse)a =0. Ononehand,thisiscertainlydifficultbecauseanyastronomicalbrightnessmeasure- ments involve errorbars sothat onlyag 0–statement could bemadeatbest. Ontheother hand, ≈ Hawking has demonstrated that in a semi–classical quantum gravity description (quantized fields on a GR background metric) black hole event horizons radiate [63]. Based on these arguments, it seemsprincipally impossible toprove direct evidence for cosmic BHsby means ofelectromag- netic radiation. We feel that the only possibility for direct methods consists in clear signatures of gravitational wavesaspointedoutrecently [1,14]. Hence,thediversityofcurrentmethodscouldbesummarizedasindirectmethods. Astronomers measure the amount of mass and the associated volume. From density arguments one may arrive at the plausible conclusion that nothing else can fit but a BH. Of course, astronomers have to test thouroughly ifalternative scenarios mayfitsuchascompact stellar clusters orother typesofcom- pact objects, e.g. neutron stars, boson stars, or fermion balls etc. If not, a good BH candidate is detected. In the following, we present different methods that are in use by astronomers. But we also go beyond practice and show further methods that might be applied in the near future. All these methodsareclassifiedbyasuitablelabel. 3.1 Kinematicalmethods Kinematical methods to detect black holes are widely–used and very successful. The simple idea is that moving objects that feel the deep gravitational potential of the black hole serve as tracers to derive properties of the black hole i.e. mass and spin. Hence, it is an indirect method because the observer does not care about the black hole itself, but about the tracer. In practise 7 ExperimentalEvidenceofBlackHoles AndreasMüller suitabletracersareluminousstars,gasorflaringobjects. Anytestbodythatisluminousenoughto be detected on Earthcan inprinciple serve asdynamical tracer. Typically the tracer surrounds the BH on Keplerian orbits. In that case, the tracking time scale is determined by the Keplerian time scaleatgivenradius. Pioneering work The first BH was detected by the Canadian astronomer Tom Bolton in 1971 [22]. He studied the X–ray binary system Cygnus X–1. Bolton was able to measure the radial velocities of the giant O–star HDE 226868. Therefore, he determined the mass function by a kinematical method. ThecompactcompanionwasfavouredtobeastellarBHbecausealternatives such as awhite dwarf or aneutron star were ruled out. Today, the BHin Cygnus X–1amounts to 10M and HDE226868 has 18M . Theorbital period amounts to 5.6days. Thisisthe first ∼ ⊙ ∼ ⊙ historical BHverification. Single stellar orbits Another example is the compact radio source Sgr A* that is associated with the SMBH in the Galactic Centre (GC). Unfortunately, the view is obscured in the optical wavebandsothatastronomers havetouseradiowaves,near–infrared (NIR)radiation orX–raysto look into the centre of the Milky Way. Thefirstinfrared group started in 1992 tomonitor gas and motions of stars around the GC BH [36, 37]. Essentially, these results are confirmed by another group [54, 55]. Proper motion and radial velocity measurements reveal Keplerian orbits of the S–stars allowing to determine a periastron distance of 16 light hours for the star S2. Fig. 2 shows nicely the Kepler ellipses of this innermost star and other S–stars. From this the distance of the Galactic Centre is updated to be R =7.62 0.32 kpc. From Kepler’s third law a central mass of 0 ± (3.61 0.32) 106 M isdeduced[40,106]. ± × ⊙ This compact and dark mass is very likely a SMBH because any other alternatives such as compact star clusters, boson stars, orfermion balls are ruled out [51, 117]. Stars orbiting SMBHs are thereby suitable tracers to determine BH features. Astronomers plan follow–up projects to approachtheBHinourGalaxyandtoprobeGReffects(seeSec.3.6)However,intheoreticalunits thestarS2isstillfarawayfrom theBHbecause theperiastron distance amounts 1600 R . This S ≈ is rather the asymptotical flat region of space–time, a (r =1600 R ) 0.9997. Strong gravity S S ≃ effects become important at a few tens Schwarzschild radii as proposed by relativistic emission linediagnostics [99]. M–s relation But not only single stars are suited. Ensembles of stars that follow their orbits in groups can also be used e.g. if the resolution is not sufficient enough to detect single stars. This situation is typical for distant galaxies. Slit spectroscopy of galactic nuclei is a valuable tool to analyse stellar velocity dispersion profiles. The study of galaxy samples shows evidence for a strong correlation between mass of the central BH, M, and the stellar velocity dispersion, s , the prominent M–s relation[50]. Plottedaslog–linear relation log(M/M )=a +b log(s /s ), (3.1) 0 ⊙ with a suited reference value chosen to s = 200 km/s this correlation can be fitted to galaxy 0 samples. Recent results fit the slope to b =4.0 0.3 [129]. This value undershoots significantly ± firstfitsofb =5.27 0.4[47]andovershootsanotheroneb =3.75 0.3[50]. Previously,another ± ± relation was found that links BH mass and bulge mass [83]. Both correlations hint for a physical 8 ExperimentalEvidenceofBlackHoles AndreasMüller Figure2:ObservedorbitalshapesofsixS–starsorbitingtheGalacticCentreSMBHasprojectedtothesky. TheimageisbasedonNIRobservationstakenfrom[40]. connectionbetweenstarsfromthegalacticbulgeandthecentralBH.Thereisacontroversialdebate ifSeyfertsandquasarsfollowthesameM–M relation[90]ornot[135]. bulge The M–s relation is also theoretically understood [59, 2]. However, very recent results from M31 (including Milky Way and M32) state that the M–s relation has significant intrinsic scatter – at least at low BH masses [13]. The redshift evolution of the M–s relation was probed by usingquasars[122]. Whereasfaintnormalgalaxiesdropoutofobservability, theseluminousAGN can still be detected at high cosmological redshifts. BH masses are measured from continuum luminosities and width of Hb lines. Narrow [OIII] line widths serve as tracers to determine the velocity dispersions. Out to z 3 the M–s relation is still complied. However, at very high ≃ redshifts, thereareobservational hintsthatthestrongcorrelation, M(cid:181) s 4,breaksdown. Recently, itwassuggested touseacurvedM–s relation[136]. Reverberation mapping Another kinematical verification method of black holes involves the emission of gas. It is called reverberation mapping technique. The broad line regions (BLRs)are supposed to be luminous matter clouds almost consisting of hydrogen that surrounds a galactic core. Due to their fast motion emission lines are significantly broadened by the Doppler effect. Therefore,thelinewidthisameasureforthevelocityoftheBLRs,s . Anotheressentialparameter involved in reverberation mapping isthedistance oftheBLRstothe centre ofthat galaxy, r. This is determined by comparing primary emission from the galactic core (continuum radiation) with secondary emission fromtheBLRs(emission lines)whichisnothing elsethantheresponse ofthe 9 ExperimentalEvidenceofBlackHoles AndreasMüller coreradiation. FromtheVirialtheoremthecentralmassisdeduced tobe M rs 2/G. (3.2) ≈ Today,astronomers areconvincedthatinnearlyanycenterofagalaxythereisaSMBH.Anactive i.e. accreting SMBH thereby causes the enormous AGN luminosity. In the local Universe the SMBHs in galaxies are dormant and inactive e.g. Sgr A* or M31*. But if there are luminous orbiting clouds available such asBLRs(especially forAGNtype–1 i.e.AGNthatallow observers tolookintothecore),thenthereisgoodchancetomeasuretheBHmass. Maser emission The next kinematical method that is based on gas motion involves maser line emission. Water masers can be found in the molecular torus located at the pc scale of a galaxy. Thiscoherent microwaveemission from Keplerian rotating gasorbiting theSMBHcanbeusedto measurethecentralmass. IncaseofNGC4258,theBHmasscouldbedeterminedto3.6 107M × ⊙ within0.13pc[111]andincaseNGC3079astronomers found2 106M enclosed within0.4pc × ⊙ [73]. KinematicalBHspinmeasurements Itischallenging todeterminewhetherornotaBHrotates by using kinematical techniques. In most cases indicators are to far away from the BH. Due to w (cid:181) r 3 behaviour, rotationofspace–timeisextraordinarilystrongonlyatafewgravitational radii − distance totheBH. Quasi–periodicflareemission closetotheGCBHhasbeenobservedinNIRandinX–rays: The NIR flare exhibits a quasi–periodicity of 17 min that is interpreted as relativistically modulated ∼ emission ofcirculating gas. AssumingthattheflareemittermovesatlaststableKeplerian circular orbit(=innermoststablecircularorbit,ISCO)theobservedperiodmatchestoaKerrparameterfor the GC BHtobe a 0.52 0.26 [52]. The powerdensity spectra of the X–ray flares observed at ≃ ± the GC BH revealed distinct peaks yielding periods of 100 s, 219 s, 700 s, 1150 s, and 2250 s. ∼ A comparison with characteristic frequencies associated with accretion disks i.e. Lense–Thirring precession, Keplerian orbital, vertical, and radial epicyclic frequency, match to a BH satisfying M =2.72 106M and a=0.9939M [7]. The nature of the flare emitters – possibly linked to × ⊙ accretion flowororbiting stars–isstillunknown. 3.2 Spectro–relativistic methods In general, the notion spectro–relativistic refers to relativistic effects in observed spectra that can be used to determine BH properties. The condition for this idea to work is of course that the emitterhastobesufficientlyclosetotheBH. FeKlines Letusassumeaverysharplineprofileintherestframeoftheemittere.g.anaccretion disk. Further, this diskrotates around aBHandextends downtothe ISCOi.e.only afewgravita- tional radii away from the event horizon. An astronomical observer in a distant laboratory frame would observe aline profile that isvery different from that in therest frame because the line pho- tonsaresubjecttoanumberofphysical effectsthathappen ontheirwaytotheobserver. First,the DopplereffectproducesaDopplerredshiftatthepartthatisrecedingandaDopplerblueshiftatthe part ofthediskthatisapproaching totheobserver. Theresult isabroadened linemaybewithtwo 10