千米小说网

Chapter 4 Falling into a black hole（第1页）

Chapter4Fallingintoablackhole。。。

Howcloseistooclose?

Beforewesiderienifyingshadthemisfortuofallintoablackhole，itisimportaheeffeobserver'sparticularperspeeofreferehismeansthatdifferentobserversseeverydifferentthilyerspectiveisofallingintoablackholedependsonhowfarawayyouarefromthatobjedeedwhetheryouarethatobjesideraparticleoflight，aphoton，thatisoutsidetheeventhorizonofablackhole:siisoutsidethehorizon，itprincipleessidetheeventhorizonitwouldbeadifferentstory-thephotonotescapethegravitatioheblackhole。Buteveheeventhorizon，aphotonthatistravellingawayfromtheblackholewillelyuhephotonsuffersalossiotheworkithastodoagainstgravity。Thisisanexampleofagravitatioialwell;justasenergywouldbeohaulyourselfupwardsoutofadeepwell，sothephotooexpeopullitselfawayfrionnearamassiveobject。Theeffecthasevenbeenmeasuredforphotonsmovih'sgravity。Theenergyofaphotonisiedtoitswavelength:ahigh-eonhasashortwavelengthwhereasalyphotonhasalohephotonlyasitretreatsawayfromtheblackhole，soitswavelehisgesthecolourofthelight，movingfromtheblue（shortwavelength）towardsthered（loh）erum（thiseffectiscalledredshift）。Thissortofredshift，knownasgravitatio，ariseswherespacetimeitselfstretchesout，orisplebytheeffeassivebodysuchasablaotethatJohnMichell，despitehavingsignifitinalthoughtsaboutdarkstars，wasihinkingthatthevelocityoflightdecreasesasitclimbsoutofthepotentialknowthatitisthewavelength（hency）oflightthatisaffectedbythepresenassivestar。

enstotimenearablackhole?

InChapters1and2Idescribedhowspacetimeisdistortedbythepresenass（i。e。somethingwhichproducesitsowngravitatiohismeansthatnotjustspace，butalsotimeisaffectedclosetoablackhole。

ImagitokeepasafedistanaSchwarzschildblackholebutyouwanttolearhowtimebehaveshusyedfortwenty-sixfixedobserverstobestatioheblackhole'seventhorizoelysafelyoutsideit。TheseobserversareoZ，andarearrangedihAclosesttotheeventhorizonandwithZbeioyou，safelyfaraway。EachobserverfromAtoZhasagoodclockwithwhieasuretheirlocaltime，attheirparticularlo。AspartofthedealtopersuadeAtoZtopartithisexperiment，youhadofferedthemeaduthefiftofanadditional，unusualclockthathadbeethetimeonitwouldreadthesameasthetimeonyourclockatyoursafedistaitZ，closesttoyou，wouldfindthatthetwohispossessihtlydifferenttimesbecausehisownclock，whichmeasureslocaltime（propertime'inthejargon），wslightlymoreslowlythaclockwhichmatchesthetimeyoumeasureatyourrathersaferaaedresultsofpartitsZtoAwoulddisplayaremarkableeffect:closertoablackhole，aeasuringtimerunsmoreslowly'paredwiththedistanttimeasreportedoits'speciallyadjustedgiftclocks。Thiseffect，describedbyEinstein'stheey，isknowiowouldbegreateraheobserversofthealphabetwhoareheblackhole。Thegreatertheproximitytoablaoreslowlyalocalcloykind:atomiical）willruoaclockusedbyadistantobserver。

Supposeyouweremulti-taskiswithadifferewenty-sixobserversatthesamedistanadifferentblackhole。Theyarearrathesamewayastheirhefirstblackhole。However，inthissedcase，theblackholehastwicethemassoftheblayourfirstexperiment。Theunusualclocksyouhadpreparedasgiftsforthissedsetofobserverswouldoberadicallyalteredasfi，buttherateatwhiusualclockhastobeadjustedisexactlydoublethatoftheratehedingthefirstsetofgiftclocksattheexactsamedistahetreofthefirstblackholewhichhashalfthemassofthesed。Thesetimedilatiosarelargeriftheblaassislarger，andalsobeetheclettotheeventhorizon。

&histimedilationisnotaeadditionallight-traveltimeforaclockclosertothebladheherfromyou，thesafely-distahereisimeoffsetforaherawayfromtheblackhole。Thecloseraclockistoablackhole，thesloweristherateatwhichtimeismeasuredtoflowonthatatterutablemeaomeasurethatflowoftime。Timeitselfisstretched（or，ied）。

Whatisthecorollaryoftimedilationnearablackhole?Thiscauseseffectsthathappenintheframeofanobserververylocaltotheblaeasuredtobeverydifferentfromthoseintheframeofanobserverwhoisverydistant，artinfact。

&'snowsiderensifinyourfirstexperiment，observerAbecamealittlecarelessanddroppedhisfirstcloewithwhieasurepropertimeathislo）sothatitfelltowardstheblackhole。Despitethisdisaster，hewouldbehelesssafelygrippingoclockwithwhichyouhadeopartitheexperiment。BothyouandAwouldseehisfirstovetowardsthehole。Theclockwouldfinditselfmovingintotheblaoreandmorerapidly。YouandAwouldgraduallyhetimeyoureadoingesevenmoredistwiththetimeonA'sotherelytheclockthatwasadjustedtoruhelocalorderthatitwouldreadthesametimeasthetoyourtime）。AfterawhilebothyouandAwouldbegintoimestopsfortheplummetingcloittedattheeventhorizontowardsadistantobserverappearstostaythereihappenstoanythingthatfallsintoablackholeafterithaspassedwithiicalradiusoftheeventhorizonisuoaernalobserver。Sotheeventhorizonmayberegardedasaholeiime。Nolightwillemergefromwithihorizon，aster1。Thatiswhyitisblack。However，inthereferehedroppedetingthroughtheeventhorizon，lifeisveryfarfromung。Fromtheclock'sperspective，itwouldtraveltothesingularityien-thousandthofaseingthattheblackholehadamassofteofourSun。IftheclockhadthemisfortuofallintoasupermassiveblackholewithamassonebillioofourSun（suchasestudyquasarsisjourimeihevastlylargereventhorizonandthesingularitywouldbeamoreleisurelyfewhours。

Tidalforearablackhole

Supposei，persojumpiowardstheblackhole，inhopesofbeiheclockhedropped。Whaten?Suchaleapwouldprovetobeabigmistake，asthesurvivaloutewouldbezero。Thedifferehegravitationalforhisfeetandtheforhisheadwouldbee。Thisisafeatureofanyinverse-squareforcefield，suchasgravityfromamassivebody。TheEarthisratheralongwayfromthemoohesmalldifferengravitatiohemoonexperienoppositesidesoftheEarth，knownastidalforces，areattherootofwhythetideseandgoabouttwiceperday。Iheseffromdifferengravityiplacesarecalledtidalforces。Thereareadditionalfactorsthateailsandfallingoftidessuchasthegravitatioherelativeahemooailedshapesoftalmasses。ButevenifthesurfaceofEarthwereentirelycoveredbyowithoutlaillbetideslitudeofthesealevelvaryingbyabout20cmtwiceperday，simplybecauseofthedifferentialgravitationalforceexperiencedbypoiatdifferentdistaheSun。

&'snowsiderthesmallerdistaweehetreoftheEarth。AsIsittypingthischapter，myheadissomewhatoverametrehigherthawhithefloorofmystudy。MyfeetarethusclosertothetreoftheEarththanmyheadis。Becausethegravitationalforcefollowsaninverse-squarelawbehavihallthemassoftheEarthwerelocatedattheverytreoftheEarth，ahaveasmallerdistahistretheyfeelastrongerforce，orpull，tothetreoftheEarththanmyheaddoes。Butactually，thediffereherslender:fhtdifferehedifferengravitatiohreepartsintenmillion。ThisissuchaslightdifferencebecauseIamabout6，400kmfromthetreoftheEarth。Muchclosertoapointmasssuchasablackhole，thedifferengravitationalforceexperiepointsjustametreapartiowardstheblackholewouldbevastlymoreextreme。SoextremethatclosetothesingularityA'sfeetwouldbestretchedawayfromhiskherestofhisbodybeyondwhathistendonsandmusclescouldholdtogether，andhewouldbeelooslonottojump。

Dynamicspacetime

&ionofablaakesanimportantdifferenceregardinghowatterorbitaroundit，aohowmuergybeextrait。FromtheworkofRoyKerrandhissolutioeiiohatthesmallestorbitthatapartihavearoundablackholewithoutfallingindependsonjusthowfasttheholeisspierablackholeisspihemattergetbeforetheholeswallowsit，asillustratedinFigure13。Ifyoudropsomethingstraightdoinningblackhole，itwillstarttheholeeventhoughthereisnothiyspacetimeoutsidethehole。Outsidetheergosphere，itispossibletooverethisframedraggingusiheregioatingblackhole&#osphere，justoutsideitseventhorizon，nothingdstill。Thespiuallydragsthespadheentsaroundwithit。Afurtheraspectingisthateveniflightitselfisgoingagaiiontheblackh，itwillbethereversedirearoundthehole。

13。Gasorbitclosertoaspinningblackholethantone。

aroundablackhole

ItisiopowouldbethesequesifourSuaamorphoseintoablackhhthatyouorIowaboutitwouldbeeightmihebeautifulSpringsunlightbywhichIamwritingwouldetoanabrupthalt。AlthoughtheluminosityofthesiarwecallourSunistinybyparisonwiththequasarsandmicroquasarsdisChapter8，itissuffitlyclosetotheEarththatitprovideseaboutakiloersquaremetreofpowertoourpla。Remarkably，thishasbeeosustaihepla，allowingplantstogrowaenbyanimalsthataretheheranimals。TheSuheeall。ButiffusioheSunararytoallexpe）tocollapseintoablackhole，thenitwouldgoverydarkandwewouldalleventuallydie。（Thisisabitofagloomyoutlook，butIehereadertoholdfastuntilChapter7，wherewelearnthatourSunisnotthekindofstartoformablackhole-it'stoolightweightforthat。）However，dynamicallyspeaking，asfarasplahandthewholeSolarSystemofplas，dlas，andasteroidsareed，nothingwillgeatall。AllmassivebodiesinorbitaroundtheSunwillueiymuchthesameorbits。ThewaythatgravityworksisthatwhethertheSuentthatithasnow，orwhetheritcollapsestoasingularitywithihorizonof3km，thegravitationalattraoutsidetheSunwouldremaihesphericalcollapseuytoablackholewouldheahebodiesatall，sothepatternsandprogressionsahintheSolarSystemwouldueutterlyuhelashine。

Someswouldbepossiblehowever，muchclosertotheblack-holeSunthanwerepossiblepreviouslywhenthesolarplasmawasintheway。However，theseorbitsotgettooclosetotheeventhorizoailsofspacetimebyamasssingularitymeanthatitisnotpossibletoorbitjustoutsidetheeventhorizoemptingacircularorbittherewouldrequirecorrectiveabyroai。Infact，themathematicsshowsthattheclosestthatweoranyothermassparticlecouldexistonastablecircularorbitionaryblackholewouldbeatadistahatoftheSchwarzschildradiusaway。Youhavebeen>

Actually，unstablecircularorbitsarepossibleuptohalfthisdistanceawayfromaSchwarzs-spinning）blackhole。Thisdistanesasphericalsurfacethatissometimescalledthephotonsphere。Evenforaphotosareunstable，aoolphotoherslitherintowardstheblaevertoreturn，orindeedaace。

ForaKerrblackholethough，ohasspiiofortheorbitsheblackhole。Inparticular，therearetwophotonspheres，intrastwiththeoonspherearoundastationarySchwarzschildblackhole。Theoutermostsphereisforphotonsthatareoppositelytothedireofrotationoftheblackhole（theoneswesayareradeorbits）。Ihisisthephotointhesameseheblackholeasitisrotating（radeorbits）。Foraveryslblackholethatisn'tsoverydifferentfromaSchwarzschildblackhole，thesetwophotonspheresareverynearlyco-spatial。Forblackholesspin，thesesurfaglyfurtherapart。

Moviblackhole，thereisaantsurface（disChapter3），calledthestaticlimit。Thisisthesurfaceatwhigstaticwithrespecttoadistaisjustimpossibletositstillthisclblaatterhowpowerfultheroightbeequippedwith。Atthissurfaretrhtraysaredraggedaloionofrotation。Itisstillpossibletoesthisclblackhole，withsuffitpropulsion，butit'sjustnotpossibleftoremainstationaryandnhere。Movinginwardsstillfurther，thesurfaificeistheeventhorizoiheohatwemetinallyiofSchwarzschildblackhthisoutwardsisn'tpossibleandgitinwardshasaabledestiny，justasforthestaticblackhole。

AnorbitaroundaKerrblackholeisnotgenerallyedtoaplaheonlyorbitsedtoaplahoseihatstheequator（i。e。theplaneofmirrorsymmetryofthespinningblackhole）。Orbitsoutofthisequatorialplahreedimensiosareedtoavolumethatislimitedbyamaximumandminimumradiusandbyamaximumangleawayfromtheequatorialplane。

&ailsofthespinofablackholehaveadramaticeffehowcloseparticlesmayeheblackhole，whichitselfdepeioivetothespin。Foramaximallyspinningblackhole，thephhtraysinthesamesense（prograde）astheblackholespinhasaradiusthatishalfofwhattheSchwarzschildradiuswouldbe。Fhtraysradeorbits，theradiusoftheirphotowicetheSchwarzschildradius。Forparticleswithmassthatareradeorbits，theiablecircularorbitonwhichtheymoveisagainathalfoftheSchwarzschildradius。Forthradeorbits，suchaclosedistancewouldbeuheiriablecircularorbitisat4。5timestheSchwarzschildradius。Thus，arotatingblaablespartiprogradeorbitstoorbitmorecloselywiththepointofheeventhorizon，morecloselythaniftheblackholeweren。InChapter7，wesidertheimportahowatterorbitbefontoabladhowmuergymaybetlyleveraged。