Black holes suna bin thermodynamic “laws” — sabon sakamako ya faɗaɗa su zuwa black holes da suke nesa sosai da equilibrium

Black holes suna da “dokoki” masu kama da thermodynamics. Tsarin da ya yi kyau a takarda yana aiki ne kawai idan komai yana cikin equilibrium

Ɗaya daga cikin abubuwan da suka fi ban mamaki a physics shi ne cewa black holes suna nuna halaye kamar abubuwa masu zafi. A farkon shekarun 1970, Bekenstein da Hawking sun lura cewa equations da ke sarrafa black holes suna daidaita, ɓangare zuwa ɓangare, da dokokin thermodynamics: black hole yana da entropy da ya yi proportional da area na horizon ɗinsa, kuma yana da temperature da ya yi proportional da surface gravity. Daga baya Hawking ya nuna cewa temperature ɗin ba kwatanci kawai ba ne—black hole da gaske yana fitar da faint thermal radiation.

Wannan haɗin yana da ginshiƙi a sakamakon da ake kira na farko law of black hole mechanics (Bardeen, Carter da Hawking, 1973). A kalmomi, yana cewa: idan ka matsar da black hole daga steady state guda zuwa wani steady state mai kusa, canjin mass ɗinsa yana daidai da temperature ɗinsa sau canjin entropy, tare da ƙarin term domin spin. Wannan shi ne nau’in black-hole na “heat in equals temperature times change in entropy.”

Amma akwai matsala a kalmar nearby steady state. Dokar 1973 mai tsabta tana kwatanta black holes biyu da suke zaune a equilibrium ba tare da hayaniya ba, bambancinsu kuma infinitesimal ne. Ba ta bayyana wani process na gaske ba—black hole yana haɗiye star, black holes biyu suna merger, ko sabon black hole yana ring down bayan violent birth. Waɗannan su ne yanayin da muke son fahimta sosai, kuma su ne akasin “zama cikin natsuwa.” Dokar mai sauƙi tana yin shiru a daidai lokacin da black hole ya fi ban sha’awa.

Me ya sa gyaran da ya fi bayyana ba ya aiki

Za a iya tunanin mafita tana da sauƙi: kawai a kalli horizon yana ƙaruwa yayin da matter ke faɗa ciki. Matsalar ita ce: wane horizon?

Horizon da yawancin mutane suke tunani—event horizon, ainihin point of no return—yana da wata siffa mai rikitarwa: an ayyana shi da duk future history na universe. Domin sanin inda event horizon yake yanzu, dole ne ka san duk abin da zai taɓa faɗawa black hole har abada. Wannan ba technical detail kaɗai ba ne. Event horizon zai iya fara ƙaruwa a wani yankin sarari da babu matter kuma locally flat ne kafin matter da zai ciyar da black hole ya isa, kawai saboda matter ɗin zai zo daga baya. Area ɗinsa zai iya ƙaruwa inda, a local sense, babu wani abu da ke faruwa.

Wannan yana sa event horizon ya zama mara amfani a matsayin running account na “state” na black hole. Ko a computer simulation, ba za ka iya gano shi daidai ba sai simulation ta ƙare; saboda haka ba za ka iya amfani da shi wajen bibiyar temperature ko entropy daga lokaci zuwa lokaci ba.

Matakin da takardar ta ɗauka: horizon da za a iya ayyana a local level

Sabuwar takardar Abhay Ashtekar, Daniel Paraizo da Jonathan Shu ta gina sakamakonta a kan wata ma’anar horizon dabam — ma’ana ta quasi-local, wadda geometry na yankin da ke kewaye da ita kaɗai ke ayyanawa, ba tare da komawa ga infinite future ba. Waɗannan quasi-local horizons su ne surfaces da numerical relativists suka riga suke amfani da su don gano wurin progenitor black holes, bin merger, da gano wurin remnant a duk tsawon simulation. Thermodynamic laws da aka samar a nan suna aiki ne a sassan quasi-local horizon da suka cika ƙarin conditions na dynamical horizon segment. A kowane irin segment ɗin nan, area yana canzawa ne kai tsaye bisa local energy flux, ba bisa abubuwan da za su faru a distant future ba: yana ƙaruwa idan akwai positive influx; kuma ga evaporating time-like horizon mai negative energy flux, yana raguwa.

Daga nan marubutan suka warware wani ɓangaren da ya fi wahala. A thermodynamics na yau da kullum, system da yake nesa da equilibrium yana da wahalar bayyana da temperature ko pressure guda, domin irin waɗannan quantities suna da ma’ana sosai ne idan system ya daidaita. Black holes suna da wannan matsalar—amma marubutan sun nuna cewa wani fasali na general relativity yana ba da hanya. Black hole a equilibrium—Kerr black hole—ana iya ayyana shi da lambobi biyu kaɗai: girma da spin. Saboda haka marubutan sun gina map da ke ɗaukar kowane state a kan dynamical horizon segment sannan, a kowane cross-section na segment ɗin, ya karanta lambobin equilibrium black hole da state ɗin ya fi kama da shi a wannan lokacin. Ta wannan map, za a iya ba wa black hole mai violent change time-dependent temperature da spin a kan segment ɗin.

Da waɗannan abubuwa — energy da aka ayyana a local wadda ke gudana ta ketare horizon, da instantaneous intensive quantities — sun faɗaɗa first law zuwa black holes da suke nesa da equilibrium gwargwadon hali. Abu mafi muhimmanci shi ne sabon law yana bayyana finite changes da real physical processes suka haifar (matter da gravitational waves suna ketare horizon), ba infinitesimal steps tsakanin frozen states biyu ba. Sun haɗa shi da second law mai dacewa, wanda bayaninsa yanzu ya zama quantitative: canjin horizon area yana da alaƙa kai tsaye da local energy flux — area yana ƙaruwa ƙarƙashin positive influx, ko kuma yana raguwa ga time-like evaporating horizon ƙarƙashin negative flux. Idan aka haɗa first da second laws, suna nuna conclusion guda mai tsabta: ga duk wani phase da dynamical horizon segment yake wakilta, komai tsananinsa, horizon area har yanzu shi ne ma’aunin entropy da ya dace.

Abin da wannan bai tabbatar ba

• Bai warware quantum gravity ba. An tsara core framework ɗin a general relativity; aikace-aikacensa ga black-hole evaporation yana amfani da semiclassical approximation, inda quantum matter fields suke tasiri a kan classical spacetime. Har yanzu yana ɗaukar standard identification na horizon area da entropy a matsayin assumption, maimakon samo wannan entropy daga wani abu mafi fundamental.
• Bai ƙidaya microstates ko bayyana me ke samar da black-hole entropy ba. Yana faɗaɗa bookkeeping na black-hole thermodynamics; ba ya buɗe microscopic degrees of freedom.
• Bai warware black-hole information paradox ba. Wannan matsalar tana cikin quantum theory; takardar ba ta shiga cikinta ba.
• Wannan ba observation ko measurement ba ne. Babu telescope, babu data, babu gravitational-wave signal — mathematics ne. “Temperature” da ake ba dynamical horizon yayin da black hole yake canzawa wani quantity ne da equations suka ayyana daidai, ba abin da za a karanta daga thermometer ba.
• Har yanzu bai bayar da continuous thermodynamic description na dukkan coalescence na black holes biyu ba. Numerical simulations suna tracking quasi-local horizon a dukkan evolution — daga progenitors, ta merger, zuwa remnant — amma a wani ɗan gajeren interval kusa sosai da merger, horizon ɗin ba ya cika conditions da ake buƙata daga dynamical horizon segment. Companion paper ta ce thermodynamic account na wannan interval har yanzu work in progress ne.
• Bai rushe Bekenstein da Hawking ba. Yana faɗaɗa hotonsu zuwa dynamical regime inda equilibrium-only law na asali ba ta da abin cewa.

Yaya ƙarfin shaidar yake?

Mai ƙarfi, idan aka yi la’akari da irin aikin da yake: wani careful, internally consistent work na mathematical physics daga leading group a fannin, wanda aka buga a matsayin Editors’ Suggestion a Physical Review Letters. Wata peer-reviewed companion paper tana ba da dogayen derivations kuma tana tattauna cases da aka taƙaita aka cire daga Letter.

Caveats na gaskiya suna game da nau’in sakamakon, ba ingancinsa ba:

• Yana dogara da conventional assumption cewa horizon area shi ne entropy (area divided by four times Newton’s constant and Planck’s constant). Idan full quantum theory of gravity ta sauya wannan identification, interpretation ɗin zai sauya tare da ita.
• Saboda taƙaitawa da sauƙi, gajeriyar Letter ta gabatar da main derivation ta amfani da axially symmetric, spacelike dynamical horizons. Peer-reviewed companion paper ta yi explicit analysis na time-like dynamical horizons kuma ta gina angular momentum ba tare da rotational Killing field ba. Amma ga evaporating time-like horizons, explicit backreaction treatment kaɗai ne aka iyakance zuwa spherical symmetry.
• “Entropy equals horizon area even out of equilibrium” compelling identification ne da sabbin na farko da na biyu laws suka sa ya zama natural, ba theorem da aka samo daga microscopic statistics ba.

Saboda haka: rigorous extension na tsari mai shekaru hamsin, ba experimental discovery ba kuma ba sabon law of nature da ake jira a gwada ba.

Me ya sa wannan yake da muhimmanci

Dalilai biyu ne: ɗaya practical, ɗaya conceptual.

A aikace, black holes da muke nazari a zahiri yanzu — waɗanda LIGO da Virgo suke jin suna merging — suna shafe muhimman lokutansu nesa da equilibrium. Simulations suna tracking quasi-local horizon daga progenitors, ta merger, zuwa remnant. Quantities da ke wannan takarda suna aiki ne a sassan horizon ɗin da suka qualify as dynamical horizon segments, don haka suna ba da principled way na magana game da entropy da temperature na black hole a mafi yawan matakan merger evolution da lokacin collapse, ba sai bayan komai ya daidaita ba. A ɗan gajeren interval da ke dab da coalescence, quasi-local horizon yana ci gaba da kasancewa tracked amma yana wajen thermodynamic description na yanzu.

A ra’ayi, thermodynamic behavior na black holes yana ɗaya daga cikin 'yan concrete clues da muke da su game da quantum gravity—wurin da gravity, quantum theory da thermodynamics suke haɗuwa a fili. Fayyaɗa daidai ma’anar “entropy” da “temperature” ga black hole da ke sauyawa cikin violent way yana ƙara bayyana target da kowace future quantum theory dole ta cimma. Bai amsa zurfin tambayar menene black-hole entropy a zahiri ba. Ya bayyana tambayar daidai fiye—kuma a wannan ɓangaren physics, wannan babban ɓangare ne na aikin.

Taƙaitaccen bayani

Black holes suna bin laws masu kama da thermodynamics, amma clean “first law” na 1973 ya kwatanta black holes da suke zaune a equilibrium ne kawai, kuma bai iya bayyana actual process ba. Ashtekar, Paraizo da Shu sun faɗaɗa first da second laws zuwa black holes da suke nesa da equilibrium gwargwadon hali — suna feeding, collapsing, ringing down, kuma suna wucewa ta mafi yawan matakan merger — ta amfani da quasi-local horizons, da amfani da thermodynamic laws a dynamical horizon segments nasu, da kuma gina map da ke ba kowane state a kan waɗannan segments instantaneous temperature da spin. Sakamakon shi ne horizon area ya ci gaba da zama ma’aunin entropy da ya dace ga kowane phase da dynamical horizon segment yake wakilta. Ɗan gajeren interval kusa sosai da coalescence bai shiga wannan thermodynamic description ba tukuna, duk da cewa simulations suna ci gaba da tracking quasi-local horizon. Core framework ɗin yana cikin general relativity, tare da semiclassical application ga evaporation; ba quantum gravity ba ne, ba observation ba, ba ƙidayar microstates ba, kuma ba mafita ga information paradox ba.

Binciken ba tare da ƙarin gishiri ba

Abin da takardar ta nuna: Mathematically consistent extension na na farko da na biyu laws na black-hole mechanics zuwa fully dynamical, far-from-equilibrium black holes, wanda aka gina a kan quasi-local horizons da sassan da suka cika conditions na dynamical horizon segments. Yana ayyana finite, process-based na farko law da quantitative na biyu law, kuma yana sa identification na entropy na dynamical black hole da horizon area ya zama natural.

Abin da yake na gaske amma interpretive: Identification “entropy = horizon area” a wajen equilibrium. Sabbin dokokin suna sa ya zama compelling, amma yana gaji standard classical area-entropy assumption maimakon ya derive shi.

Abin da bai nuna ba: Quantum theory of gravity; microscopic origin ko “count” na black-hole entropy; resolution na information paradox; observational ko experimental sakamako; ko temperature da za a iya auna da thermometer.

Manyan iyakoki: Core derivation ɗin yana cikin general relativity, yayin da time-like evaporation application yake amfani da semiclassical approximation; ɗan gajeren interval kusa sosai da binary coalescence ba dynamical horizon segment ne yake wakiltarsa ba, kuma thermodynamic description ɗinsa har yanzu work in progress ne, duk da cewa numerical simulations suna ci gaba da tracking quasi-local horizon; explicit backreaction treatment na evaporating time-like horizons an iyakance shi zuwa spherical symmetry; area-entropy identification assumption ne, ba proof daga statistical mechanics ba.

Yaya yawan amincewa ya kamata mai karatu gaba ɗaya ya yi? Babban amincewa cewa wannan solid, well-regarded theoretical advance ne da gaske ya faɗaɗa black-hole thermodynamics zuwa dynamical regime. Haka kuma babban amincewa cewa ba sabon observation ba ne, ba quantum gravity ba ne, kuma ba resolution na famous information puzzle ba ne. Matsayin da ya dace: mataki na gaske wajen fahimta, wanda aka ɗauka da lissafi ba telescope ba.