January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised International JournalofModernPhysicsD (cid:13)c WorldScientificPublishingCompany 2 1 0 RECENT DEVELOPMENTS IN GRAVITATIONAL COLLAPSE 2 AND SPACETIME SINGULARITIES n a J 7 PankajS.Joshi∗andDanieleMalafarina† 1 TataInstitute of Fundamental Research Homi Bhabha Road, Mumbai 400005 ] India c q - r ReceivedDayMonthYear g RevisedDayMonthYear [ CommunicatedbyManagingEditor 1 v It is now known that when a massive star collapses under the force of its own gravity, 0 the final fate of such a continual gravitational collapse will be either a black hole or a 6 nakedsingularityunderawidevarietyofphysicallyreasonablecircumstanceswithinthe 6 frameworkofgeneraltheoryofrelativity.Theresearchofrecentyearshasprovidedcon- 3 siderableclarityandinsightonstellarcollapse,blackholesandthenatureandstructure . ofspacetimesingularities.Wediscussseveralofthesedevelopmentshere.Therearealso 1 importantfundamentalquestionsthatremainunansweredonthefinalfateofcollapseof 0 amassivemattercloudingravitationtheory,especiallyonnakedsingularitieswhichare 2 hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. 1 These issues have key implications for our understanding on black hole physics today, : v itsastrophysicalapplications,andforcertainbasicquestions incosmologyandpossible i quantumtheoriesofgravity.Weconsidertheseissueshereandsummarizerecentresults X and current progress in these directions. The emerging astrophysical and observational r perspectivesandimplicationsaredicussed,withparticularreferencetothepropertiesof a accretion discs around black holes and naked singularities, which may provide charac- teristicsignaturesandcouldhelpdistinguishtheseobjects. Keywords: Gravitational Collapse;BlackHoles;NakedSingularities Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Stellar collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Final fate of gravitational collapse . . . . . . . . . . . . . . . . . . . . . . 5 3.1 A black hole is born: The Oppenheimer-Snyder-Datt model . . . . . 7 3.2 Predictions of General Relativity . . . . . . . . . . . . . . . . . . . . 9 3.3 What the singularity theorems do not predict . . . . . . . . . . . . . 10 3.4 The cosmic censorship conjecture . . . . . . . . . . . . . . . . . . . . 10 ∗email:[email protected] †[email protected] 1 January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised 2 Pankaj S. Joshi and Daniele Malafarina 4 Recent developments on collapse . . . . . . . . . . . . . . . . . . . . . . . 14 4.1 Collapse studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Collapse formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.1 Regularity and energy conditions . . . . . . . . . . . . . . . . 19 4.2.2 Initial data and matching . . . . . . . . . . . . . . . . . . . . 20 4.2.3 Collapse final states . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.4 Trapped surfaces and outgoing null geodesics . . . . . . . . . 22 4.2.5 An example: Dust collapse. . . . . . . . . . . . . . . . . . . . 23 4.3 Collapse with non-zero pressure . . . . . . . . . . . . . . . . . . . . . 25 4.4 Are naked singularities stable and generic?. . . . . . . . . . . . . . . 26 4.4.1 The genericity and stability of collapse outcomes . . . . . . . 27 4.4.2 Instability of the OSD black hole . . . . . . . . . . . . . . . . 30 4.5 The equation of state. . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.6 Non-spherical collapse . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.7 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5 Structure of naked singularities . . . . . . . . . . . . . . . . . . . . . . . . 45 5.1 Are they always massless or with negative mass? . . . . . . . . . . . 46 5.2 An object or an event? . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.3 Do naked singularities violate causality? . . . . . . . . . . . . . . . . 47 5.4 Local versus global visibility . . . . . . . . . . . . . . . . . . . . . . . 49 5.5 Can energy come out of a naked singularity? . . . . . . . . . . . . . 51 6 Current Status of Cosmic Censorship . . . . . . . . . . . . . . . . . . . . . 55 6.1 Does Cosmic Censorship hold? . . . . . . . . . . . . . . . . . . . . . 55 6.2 Why naked singularities form? . . . . . . . . . . . . . . . . . . . . . 57 6.3 Reformulate Cosmic Censorship? . . . . . . . . . . . . . . . . . . . . 59 7 Astrophysical and observational perspectives . . . . . . . . . . . . . . . . 61 7.1 Observable signatures of naked singularities . . . . . . . . . . . . . . 62 7.2 Can we test censorship using Astronomical Observations? . . . . . . 64 7.3 Distinguishing black holes and naked singularities . . . . . . . . . . . 67 7.4 Equilibrium configuration from collapse . . . . . . . . . . . . . . . . 70 8 Cosmic puzzles and the new perspective . . . . . . . . . . . . . . . . . . . 76 9 Star collapse: A Lab for quantum gravity? . . . . . . . . . . . . . . . . . . 82 10 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 1. Introduction What is the final fate of a massive star that has exhausted its internal nuclear fuel andwhichthen undergoesacatastrophicgravitationalcollapseunder the force of its own gravity? What are the implication of such a phenomenon on our basic understandingofgravitationtheory,andwhatwillbetheobservationalimplications as far as very high energy astrophysical phenomena are concerned? This is the arena where we in fact come face to face with the regime of extreme and ultra-strong gravity fields, and the answer must be sought within the frame- January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised Gravitational Collapse 3 work of a gravitation theory such as the Einstein’s theory of gravity.This is where the new and unfamiliar universe encompassing the ultra-strong gravity effects ac- tually revealsitself and we must encounter exotic astrophysicalobjects such as the spacetime singularities, black holes, and other ultra-compact entities in nature. ¿From such a perspective, considerable work has been done in past years to understand the dynamical gravitational collapse in general relativity, and many new insights have been obtained. At the same time, several basic issues also re- main unclear or unanswered, and there is a general consensus that the nature of cosmic censorship, black holes and naked singularities remain one of the most im- portantunresolvedissues ingravitationtheoryandblack holephysics today.These issues wouldnecessarilyhavefar-reachingimplications and applicationsfor our un- derstanding on fundamental aspects of gravity theories and applications to high energy astrophysics. Our purpose here is to discuss several key problems and questions on gravita- tional collapse, formation of black holes and naked singularities as final state for a continual collapse, and the related issues regarding the nature and structure of spacetime singularities. These problems are closely related to the nature of cosmic censorshiphypothesisandourcurrentunderstandingonblackholephysics.Theun- derstanding of such questions is also basic to the theoretical developments as well as the modern astrophysical applications of black holes which are being vigorously pursued today. Further, we discuss and consider here certain interesting astrophysical implica- tionsemergingfromthecurrentworkongravitationalcollapsewithintheframework of general relativity. An important question would be, if naked singularities, which are hypothetical astrophysical objects, actually formed in gravitational collapse of massive stars, how these would look observationally different from black holes. A lead that is emerging from the recent work is that the accretion discs around these ultra-high gravity objects, namely black holes and naked singularities, would be significantly different from each other providing characteristic signatures. There- forethere exists a possibilityto distinguishthese two differentoutcomesofcollapse observationally. We discuss some of these current developments here. We thus consider and take up below a series of outstanding questions on these topics, where we attempt to clarify what is already known, while separating the issueswhichremainunansweredasyet,andonwhichmoreworkstillremainsto be done. It is our hope that such a treatment will clarify where the research frontiers are moving on these problems and what remain the major outstanding questions where more work is needed. We intend to review here in this manner some of the majorchallengesinblackholephysics today,andthe currentprogressonthe same. It is emphasized that to secure a concrete foundation for the basic theory of black hole physics as well as to understand the high-energy astrophysical phenomena, it is essential to gain a suitable insight into these questions. This will be of course from a perspective of what we think are the important problems, mainly within an analytical treatment of the Einstein’s theory of gravity in the framework of the January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised 4 Pankaj S. Joshi and Daniele Malafarina general relativity field equations, and no claim to completeness is made. 2. Stellar collapse The stars have a life cycle wherein they are born in gigantic clouds of dust and galactic material, they then evolve and shine for millions of years, and eventually enter the phase of dissolution and extinction. Stars shine by burning their nuclear fuel within, which is mainly hydrogen, fusing it into helium and later into other heavierelements. Eventually,when allmatter is convertedto iron, no more nuclear processes capable of producing energy are possible and no new internal energy is produced within the star. The all-pervasive force of gravity then takes over to determine the final fate and evolution of such a star. Earlier there was a balance between the force of gravity that pulled matter of the star towards its center and the outwards pressures generated by internal fusion processes. This balance kept the starstableandgoing,whileitlivedits normallife spanofshiningandradiating lightandenergyproducedwithin.Oncetheinternalpressuressubside,gravitytakes over, and the star begins to contract and collapses onto itself. A star as massive as ten or twenty times the sun would burn much faster and live only a few million years, as compared to the lifetime of several billion years for a smaller star such as the sun. When the sun runs out of internal fuel, its core will contract under its own gravity, but it will then be eventually supported by a new force within, created by fast moving electrons, called the electron degeneracy pressure. Such an object is called a white dwarf. Similarly, stars up to three to five timesthemassofthesunwouldsettletothefinalstate,whichisaneutronstar,after an initial collapse and losing some of their original mass. These are pure neutron objects created in the collapse under the strong crush of gravity which collapses atoms too. The quantum pressure of these neutrons then support the star, which is barely some ten to twenty kilometers in size. The final outcome of collapse thus depends on the initial mass of the star, which again stabilizes at a much smaller radius due to the balancing pressures generated by either electrons or neutrons. The more massive stars cannot, however, settle to a white dwarf or neutron star state because these quantum pressures are then just not sufficient to balance gravity and stabilize the collapsing star beyond the neutron star mass limit. Then a continual gravitationalcollapse, which no known physical forces are able to halt, becomes inevitable once the star exhausted its internal fuel. So the life-history of a star of large mass is essentially different from the small mass stars, and as the astrophysicistSubrahmanyanChandrasekharpointedoutwaybackin1934,“...one 1 is left speculating on other possibilities.” What will be the final fate of such a continual gravitationalcollapse of a massive star? The answer must be determined by the Einstein theory of gravitation, as gravity now is the sole force deciding the future evolution of the star. Gravitation theory and relativistic astrophysics have gone through extensive developmentsinpastdecades,furthertothe discoveryofquasarsin1960s,andalso January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised Gravitational Collapse 5 other very high energy phenomena in the universe such as the gamma-ray bursts. For compact objects such as neutron stars and for situations involving very high energydensities andmasses,stronggravityfields governedby the generaltheoryof relativity play an important role and dictate the observed high energy phenomena having intriguing physical properties. Several models to explain the gamma-ray bursts, which emit in a few seconds energy of the sun’s entire lifetime, have been proposed in terms of a collapsar, invokingcollapseofasinglemassivestarasthe mechanismrequiredto producethe extreme burst of ultra-high energies. The gravitational collapse of a massive star or much larger matter clouds, lie at the heart of astrophysics of such phenomena. It is the key physical process which is basic to the formation of a star itself from interstellar clouds, in formation of galaxies and galaxy clusters, and in a variety of cosmic happenings including structure formation in the universe. 3. Final fate of gravitational collapse What is the final fate of a massive star towards the end of its life cycle, when it exhausted its internal nuclear fuel and started shrinking and collapsing under the pull of its own gravity? This is one of the most important and outstanding unresolved problems in astrophysics and cosmology today. When the massive star runs out of its nuclear fuel, the force of gravity takes overand a catastrophicgravitationalcollapse of the star takes place.The star that lived for millions of years and which stretched to millions of kilometers in size, nowcollapsescatastrophicallywithinamatterofseconds.Accordingto thegeneral theory of relativity, the outcome of such a continual collapse will be a spacetime singularitywhere allphysical quantities such as densities and spacetime curvatures diverge. The fundamental question of the fate of a massive star, when it collapses con- 1 tinually under the force of its own gravity, was highlighted by Chandrasekhar , when he pointed out: ‘Finally, it is necessary to emphasize one major result of the whole investigation, namely, that the life history of a star of small mass must be essentially different from the life-history of a star of large mass. For a star of small mass the natural white-dwarf stage is an initial step towards complete extinction. A star of large mass (>M ) cannotpass into the white-dwarfstage,and one is left c speculating on other possibilities.’ It is possible to see the seeds of modern black hole physics already present in the above inquiry made on the final fate of massive stars. The issue of endstate of large mass stars has, however, remained unresolved and elusive for a long time of manydecadesafterthat.Infact,areviewofthestatusofthesubjectmanydecades later notes, ‘Any stellar corewith a mass exceeding the upper limit that undergoes gravitational collapse must collapse to indefinitely high central density... to form 2 a (spacetime) singularity’. The reference above is to the prediction by general relativity, that under reasonable physical conditions, the gravitationally collapsing January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised 6 Pankaj S. Joshi and Daniele Malafarina 3 massive star must terminate into a spacetime singularity. While Chandra’s work pointed out the stable configuration limit for the forma- tion of a white dwarf, the issue of final fate of a star which is much more massive with tens of solar masses, remains very much open even today. Such a star cannot settle either as a white dwarf or a neutron star final state. The issue is clearly important both in high energy astrophysics as well as cos- mology. For example, our observations today on the existence of dark energy in the universe and the cosmic acceleration it produces are intimately connected to the observations of supernovae in the universe, which are the product of collapsing stars. It is the observational evidence coming from supernovae, that are exploding in the faraway universe, which tells us how the universe may be accelerating away andtherateatwhichthisaccelerationtakesplace.Attheheartofsuchasupernova underliesthephenomenonofcatastrophicgravitationalcollapseofthemassivestar, wherein a powerfulshockwaveis generated,blowing off the outer layersof the star. If such a star is able to throw away enough of its matter in such an explosion, it might eventually settle as a neutron star. But in the case otherwise, or if further matter accretedontothe neutronstar,there will be a continual collapseagain,and we shall have to then explore and investigate the question of final fate of such a massive collapsing star. But the stars, which are more massive and well above the normal supernovae mass limits must straightaway enter a continual collapse mode attheendoftheirlifecycles,withoutanyintermediateneutronstarstage.Thefinal fate ofthe starinthis casemustbe thendecided bythe generaltheoryofrelativity alone. The important point here is, more massive stars which are tens of times the massofthesunburnmuchfasterandarefarmoreluminous.Suchstarsthencannot endure more than about ten to twenty million years, which is a much shorter span of life as comparedto stars such as the sun, which live much longer.Therefore, the question of final fate of such short lived massive stars is of central importance in astronomy and astrophysics. What needs to be investigated then is what happens in terms of the final out- come, when such a massive star dies on exhausting its internal nuclear fuel. As we indicate here, the general theory of relativity then predicts that the collapsing massive star must terminate into a spacetime singularity, where the matter energy densities, spacetime curvatures and other physical quantities blow up. It then be- comescrucialtoknowwhethersuchsuper-ultra-denseregions,forminginthestellar collapse,are visible to anexternalobserverin the universe,or whether they will be always hidden within a black hole and an event horizon of gravity that could form asthestarcollapses.Thisisoneofthemostimportantissuesinthephysicsofblack holes today. January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised Gravitational Collapse 7 3.1. A black hole is born: The Oppenheimer-Snyder-Datt model Tounderstandthefinalstateofcollapseforamassivestar,weneedtotracethetime evolutionofthesystemoritsdynamicalprogressionusingtheEinsteinequationsof gravity.Thestarshrinksundertheforceofitsowngravity,whichcomestodominate other basic interactions of nature such as the weak and strong nuclear forces that typically provided the outwards pressure to balance the pull of gravity. This problem was considered for the first time by Oppenheimer and Snyder, and independently by Datt, in the late 1930s. 4,5 In order to deal with the rather complex Einstein equations, they assumed the density to be homogeneous and the sameeverywherewithinthesphericalstar.Theyalsoneglectedgaspressure,taking it to be zero. Their calculations then showed that an event horizon develops as collapseprogresses,suchthatnomaterialparticlesorphotonsfromtheregionescape to faraway observers. Once the star collapses to a radius smaller than the horizon, it enters the black hole, finally collapsing to a spacetime singularity with extreme densitiesthatishiddeninsidetheblackholeandinvisibletoanyexternalobservers. For the collapsing star to create a black hole, an event horizon must develop prior to the time of the final singularity formation. Very considerable amount of research and astrophysical applications have been developed on such black holes in past decades, which occupy a major role in astro- physics and cosmology today. To understand how an event horizon and black hole can form when a massive star collapses, let us consider the model for an homoge- neousstarthateventuallycollapsestoasingularityofinfinitedensityandspacetime curvatures.The relativisticcalculationsimply thatasthe starcollapsesthe forceof gravityonits surfacekeepsgrowingandeventuallyastageisreachedwhennolight emitted from its surface is able to escape away to faraway observers. This is the epochwhenaneventhorizonformed,andthestarthenentersthe blackholeregion of spacetime. The infalling emitter does not feel any thing special while entering the horizon, but any faraway observer stops seeing the light from him. The strong gravityofthestarcausesthisone-waymembrane,thatistheeventhorizontoform. Within the horizon collapse continues further to crush the star into a singularity. Such black holes can suck in more matter from surroundings and grow bigger and bigger. The physics that is accepted today as the backbone of the general mechanism describingtheformationofblackholesastheendstateofcollapsereliesonthisvery simple and widely studied Oppenheimer-Snyder-Datt (OSD) dust model, which describes the collapse of a spherical cloud of homogeneous dust. In the OSD case, all matter falls into the spacetime singularity at the same comoving time, while the event horizon forms earlier than the singularity, thus covering it. A black hole region in the spacetime results as the endstate of collapse. Itisofcourseclearthatthehomogeneousandpressurelessdustisaratherhighly idealized and unphysical model of matter. Taking into account inhomogeneities in theinitialdensityprofileitispossibletoshowthatthebehaviourofthehorizoncan January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised 8 Pankaj S. Joshi and Daniele Malafarina infactchangedrastically,thusleavingtwodifferentkindsofoutcomesasthepossible result of generic dust collapse:the black hole, in which the horizonforms at a time antecedingthesingularity,andthenakedsingularity,inwhichthehorizonisdelayed, thusallowingthenullgeodesicsorlightraystoescapethe centralsingularitywhere the density andcurvaturesdiverge,toreachfarawayobservers.6,7,8 Itis clearthat once the lightrays escape,then the materialparticles or the timelike geodesics will also escape from the singularity. Theissueofsuchacollapsehastobeprobednecessarilywithintheframeworkof asuitabletheoryofgravity,becausetheultra-stronggravityeffectswillbenecessar- ilyimportantinsuchascenario.ThispurposewasachievedbytheOSDmodelthat used the general theory of relativity to examine the final fate of an idealized mas- sivemattercloud,namelyaspatiallyhomogeneousballwithnorotationorinternal pressure,andassumedto besphericallysymmetric.Assaid,the dynamicalcollapse created the spacetime singularity, preceded by an event horizon, thus developing a black hole in the spacetime. The singularity would be hidden inside such a black hole, and the collapse eventually settled to a final state which is the Schwarzschild geometry (see Fig. 1). spacetime M 0 singularity 2 = = r r event horizon apparent horizon light ray boundary of the star t collapsing matter r initial surface Fig.1. Dynamicalevolutionofahomogeneoussphericaldustcloudcollapse,asdescribedbythe Oppenheimer-Snyder-Dattsolution. Interestingly,therewasnotmuchattentionpaidtothismodelatthattime,and it was widely thought by gravitation theorists and astronomers that it would be absurd for a star to reachsuch a final ultra-dense state during its evolution. It was in fact as late as 1960s only, that a resurgence of interest took place in such black January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised Gravitational Collapse 9 holes, their dynamical formation and physical properties that they would exhibit for the surrounding regions of spacetime. This was mostly due to some important observational developments in astronomy and astrophysics that happened around that time, such as the discovery of several very high energy phenomena in the universe, like quasars, radio galaxies and such others, where no known laws of physics were able to explain the observations that were related to such extremely highenergy phenomena in the cosmos.Attentionwas drawnthen to the dynamical gravitationalcollapseandits finalfate,andinfactthe term‘blackhole’wascoined just around the same time in 1969, by John Wheeler. 3.2. Predictions of General Relativity According to Einstein’s general theory of relativity, the collapse must proceed to createaspace-timesingularity.Thisis aregionwhere the physicalparameterssuch astheenergydensityandthespace-timecurvaturesblowuptakingarbitrarilylarge values. Thus the usual laws of physics break down near such a singularity. This is the regime of ultra-strong gravity fields, with other basic forces of nature playing only a secondary role.Quantum effects must also become important in suchstrong fields atultra-smalllength scalesnear the singularity,and eventuallywhat is really needed would be a quantum theory of gravity which would possibly resolve the 9 singularity. Specifically, the outcome of a continual collapse in a fully general scenario of a spacetime with an evolving matter field is described by the singularity theorems in general relativity. Subject to the following conditions, namely, (i) An energy con- dition requiring the positivity of energy density for matter fields, (ii) A reasonable causal structure of the spacetime in terms of a causality condition such as chronol- ogy or strong causality condition, and (iii) A condition that trapped surfaces exist or develop in the spacetime, which is a sufficient condition ensuring that sufficient mass is packed in a small enough region, the singularity theorems in general rela- 3 tivity imply thatthe spacetimemustcontainasingularityintheformofgeodesic incompleteness. Itfollowsthat for anygeneralrelativisticgravitationalcollapsedevelopingfrom regularinitialdata,inaspacetimewithoutanysymmetryconditionssuchasspher- ical symmetry necessarily holding, if the above physically reasonable conditions are satisfied then the collapse must create a spacetime singularity necessarily. In all physically reasonable scenarios, the densities, curvatures and all other physical quantities would typically blow up in the limit of approach to such a spacetime singularity. The OSD collapse scenario discussed above would be a special case of such a generalgravitationalcollapse,whichterminatesintoafinalsimultaneousspacetime singularity, which is the final endstate of the collapsing matter cloud. In view of the generality of the singularity theorems, it would be expected that anyphysically realisticgravitationalcollapse,where the massivestarcollapsescon- January 19, 2012 1:8 WSPC/INSTRUCTION FILE IJMPD-revised 10 Pankaj S. Joshi and Daniele Malafarina tinuallytowardstheendofitslifecycle,mustterminateintoaspacetimesingularity of ultra-high densities and extreme spacetime curvatures. 3.3. What the singularity theorems do not predict Itmustbenoted,however,thatthesingularitytheoremsingeneralrelativitypredict only the existence of spacetime singularities, under a set of physically reasonable conditions. The above theoretical result on the existence of singularities is of a rather generalnature,and providesno informationat allof any kind onthe nature and structure of such singularities. In particular, these theorems give us no information as to whether such space- time singularities,wheneverthey formespecially ina gravitationalcollapse,will be necessarily covered in the event horizons of gravity and thus hidden from us, or whether these could also be visible to external observers in the universe. Specifically,thepossibilityremainsverymuchopenthataspacetimesingularity develops in gravitationalcollapse, however,which is no longer covered by an event horizonandmaybecausallyconnectedtofarawayobserversintheuniverse.Insuch a case, the ultra-highdensity and curvature regions would be able to communicate with and send out signals to exterior faraway observers. In this sense, gravity pre- dictsexcitingoutcomesforthefinalfateofamassivecollapsingstar,withprofound implications for fundamental physics. Therefore,whether a strong curvature singularity that formed in a realistic col- lapse would be visible or hidden from a faraway observer in the universe remains very much an open question in the Einstein’s theory of gravity. The key physical feature that decides the visibility or otherwise of the singularity is the interplay between the structure and time-curve of the singularity and that of the trapped surface formation in the spacetime. 3.4. The cosmic censorship conjecture Unlike the idealized and rather special model that the OSD homogeneous collapse scenariodescribedabove,realstarshaveaninhomogeneousdensity(namely,higher attheircenters),andtheyalsohavenon-zeropressureswithinthemastheycollapse. Moreover, the stars also rotate. Would every massive star collapsing towards the end of its life cycle turn into a black hole necessarily, just as the OSD case? The cosmic censorship conjecture supposes that the answer to this question is in the affirmative,namely, that the singularity forming in collapse alwayshides within an event horizon, never to be seen by external observers. Theoristsgenerallybelievedthatinsuchcircumstances,ablackholewillalways form covering the singularity, which will then be always hidden from external ob- servers. Such a black hole is a region of spacetime from which no light or particles canescape.Theassumptionthatspacetimesingularitiesofcollapsewouldbealways covered by black holes is called the Cosmic Censorship Conjecture (CCC). 10,11 Thus,whateverthephysicalconditionsandforceswithinthe massivestarsmaybe,