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The five lectures presented in this volume address very timely
mathematical problems in relativity and cosmology. "Part I" is
devoted to the initial value and evolution problems of the Einstein
equations. Especially it deals with the
Einstein-Yang-Mills-Boltzmann system, fluid models with finite or
infinite conductivity, global evolution of a new (two-phase) model
for gravitational collapse and the structure of maximal,
asymptotically flat, vacuum solutions of the constraint equations
which have the additional property of containing trapped surfaces.
"Part II" focuses on geometrical-topological problems in relativity
and cosmology: on the role of cosmic censorship for the global
structure of the Einstein-Maxwell equations and on the mathematical
structure of quantum conformal superspace.
Manolis Plionis & Spiros Cotsakis plionis@sapfo. astro. noa. gr
skot@aegean. gr Since the dawn of human civilisation natural
phenomena have been subject to observation and investigation by the
humans who initially ascribed to them 'divine' powers. Gods of
'good' and 'evil' werecreatedaccording to the useful- ness or
notofsuch unexplained, atthetime, phenomena. Astheir understanding
of the world developed and deepened, the divine powers, religious
beliefs, su- perstitions and mysticism gave their place to the
knowledge, limited that it may be, of physical reality. However,
many issues have been and still are out of grasp of human
understanding. These issues have always been at the center of
philosophical, theological, and more recently, scientific debate.
It is to us incredible that many of the conclusions concerning the
true scientific explanation of the external world, to which the
ancient Greeks arrived purely on the basis of abstract thought,
came so near to modem scientific ideas and also form the basis of
modem science. We cannot but stand with amazement at the original
thoughts of Archimedes who, among his many extraordinary achieve-
ments in mathematics and physics, calculated (cf. TheSandReckoner)
the mass density of the observable universe and came up with a
figure that is in complete agreement with current estimates coming
from observational cosmology.
This book is written in a pedagogical style intelligible for
graduate students. It reviews recent progress in black-hole and
wormhole theory and in mathematical cosmology within the framework
of Einstein's field equations and beyond, including quantum
effects. This collection of essays, written by leading scientists
of long standing reputation, should become an indispensable source
for future research.
Thisbookisaneditedversionofthelecturesdeliveredduringthe1stAegean
SummerSchoolonCosmology,heldonSamosisland,Greece,inSeptember
21-29,2001,andorganizedjointlybytheDepartmentofMathematics,U-
versity of the Aegean and the Department of Physics, National
Technical UniversityofAthens.
Cosmology,thescienceoftheuniverse,standsatthecrossroadsofmany
?eldsofphysicsandmathematicsandpresentsuswithchallengingproblems of
many forms. Although there are by now many textbooks discussing the
subjectatmanylevels,itistruethatnosinglebookhasthecharacteristics
wehadinmindwheneditingthisvolume. Wehavetriednottoproducea
proceedingsvolumebutmoreamultiauthoredtextbookwhichcouldserveas
areferencesourceofcurrentideasincosmology. Webelievethisbookcovers
atanintroductorylevelmostoftheissueswhichareconsideredimportant
inmoderncosmologicalresearchandcanbereadbyagraduatestudentor
researcherwhowishestoacquireareasonableknowledgeofcosmologythat
will,wehope,continuetobeofvalueforyearstocome. The 1st Aegean
School on Cosmology, and consequently this book, -
camepossiblewiththekindsupportofmanypeopleandorganizations. We
received ?nancial support from the following sources and this is
gratefully acknowledged: the Municipality of Karlovassi, the North
Aegean Regional Secretariat, the Prefecture of Samos, the Ministry
of the Aegean, and the NationalBankofGreece.
TheadministrativesupportoftheSchoolwastakenupwithgreatcare byMrs.
EvelynPappaandMantoKatsianiandwewouldliketothankthem
bothfortheirkinde?ortstoresolvemanyissueswhicharosebefore,during
andaftertheSchool. WeacknowledgethehelpofMr. NectariosBenekoswho
designedandmaintainedthewebsiteoftheSchool.
Last,butnotleast,wearegratefultothesta?ofSpringer-Verlag,resp-
siblefortheLectureNotesinPhysics,whoseabilitiesandhelpcontributed
greatlytothe?neappearanceofthisbook. Karlovassi,Samos,
SpirosCotsakis March2002 EleftheriosPapantonopoulos TableofContents
PartI HistoryandOverview 1 IsNatureGeneric? SpirosCotsakis,PeterG.
L. Leach...3 1. 1 Introduction...3 1. 2
PrinciplesofCosmologicalModelling...4 1. 2. 1 Spacetimes...4 1. 2.
2 TheoriesofGravity...5 1. 2. 3 MatterFields...6 1. 3
Cosmologies...6 1. 4 CosmologicalProblems...8 1. 4. 1
TheSingularityProblem...8 1. 4. 2 TheProblemofCosmicTopology...9 1.
4. 3 TheProblemofAsymptoticStates...9 1. 4. 4
GravityTheoriesandtheEarlyUniverse...11 1. 5Outlook ...12
References...14 2 EvolutionofIdeasinModernCosmology
AndreasParaskevopoulos...16 2. 1 Introduction...16 2. 2
TheBeginningsofModernCosmology(1917-1950)...17 2. 3
Cosmology1950-1970:HotBigBang, SingularitiesandQuantumApproach...20
2. 4
Cosmology1970-Thisbookisaneditedversionofthelecturesdeliveredduringthe1stAegean
SummerSchoolonCosmology,heldonSamosisland,Greece,inSeptember
21-29,2001,andorganizedjointlybytheDepartmentofMathematics,U-
versity of the Aegean and the Department of Physics, National
Technical UniversityofAthens.
Cosmology,thescienceoftheuniverse,standsatthecrossroadsofmany
?eldsofphysicsandmathematicsandpresentsuswithchallengingproblems of
many forms. Although there are by now many textbooks discussing the
subjectatmanylevels,itistruethatnosinglebookhasthecharacteristics
wehadinmindwheneditingthisvolume. Wehavetriednottoproducea
proceedingsvolumebutmoreamultiauthoredtextbookwhichcouldserveas
areferencesourceofcurrentideasincosmology. Webelievethisbookcovers
atanintroductorylevelmostoftheissueswhichareconsideredimportant
inmoderncosmologicalresearchandcanbereadbyagraduatestudentor
researcherwhowishestoacquireareasonableknowledgeofcosmologythat
will,wehope,continuetobeofvalueforyearstocome. The 1st Aegean
School on Cosmology, and consequently this book, -
camepossiblewiththekindsupportofmanypeopleandorganizations. We
received ?nancial support from the following sources and this is
gratefully acknowledged: the Municipality of Karlovassi, the North
Aegean Regional Secretariat, the Prefecture of Samos, the Ministry
of the Aegean, and the NationalBankofGreece.
TheadministrativesupportoftheSchoolwastakenupwithgreatcare byMrs.
EvelynPappaandMantoKatsianiandwewouldliketothankthem
bothfortheirkinde?ortstoresolvemanyissueswhicharosebefore,during
andaftertheSchool. WeacknowledgethehelpofMr. NectariosBenekoswho
designedandmaintainedthewebsiteoftheSchool.
Last,butnotleast,wearegratefultothesta?ofSpringer-Verlag,resp-
siblefortheLectureNotesinPhysics,whoseabilitiesandhelpcontributed
greatlytothe?neappearanceofthisbook. Karlovassi,Samos,
SpirosCotsakis March2002 EleftheriosPapantonopoulos TableofContents
PartI HistoryandOverview 1 IsNatureGeneric? SpirosCotsakis,PeterG.
L. Leach...3 1. 1 Introduction...3 1. 2
PrinciplesofCosmologicalModelling...4 1. 2. 1 Spacetimes...4 1. 2.
2 TheoriesofGravity...5 1. 2. 3 MatterFields...6 1. 3
Cosmologies...6 1. 4 CosmologicalProblems...8 1. 4. 1
TheSingularityProblem...8 1. 4. 2 TheProblemofCosmicTopology...9 1.
4. 3 TheProblemofAsymptoticStates...9 1. 4. 4
GravityTheoriesandtheEarlyUniverse...11 1. 5Outlook ...12
References...14 2 EvolutionofIdeasinModernCosmology
AndreasParaskevopoulos...16 2. 1 Introduction...16 2. 2
TheBeginningsofModernCosmology(1917-1950)...17 2. 3
Cosmology1950-1970:HotBigBang, SingularitiesandQuantumApproach...20
2. 4 Cosmology1970-1990:Chaotic,In?ationary,
QuantumandAlternative...22 2. 5ConclusionsandOutlook ...25
References...26 VIII TableofContents PartII MathematicalCosmology
3ConstraintsandEvolutioninCosmology YvonneChoquet-Bruhat,JamesW.
York...29 3. 1 Introduction...29 3. 2 MovingFrameFormulas...30 3.
2. 1 FrameandCoframe...30 3. 2. 2 Metric...31 3. 2. 3
Connection...31 3. 2. 4 Curvature ...32 3. 3
(n+1)-SplittingAdaptedtoSpaceSlices ...33 3. 3. 1 De?nitions...33
3. 3. 2 StructureCoe?cients...34 3. 3. 3 SplittingoftheConnection
...
This book has grown out of lectures held at a summer school on cosmology, in response to an ever increasing need for an advanced textbook that addresses the needs of both postgraduate students and nonspecialist researchers from various disciplines ranging from mathematical physics to observational astrophysics. Bridging the gap between standard textbook material in cosmology and the forefront of research, this book also constitutes a modern source of reference for the experienced researcher in classical and quantum cosmology.
Manolis Plionis & Spiros Cotsakis plionis@sapfo. astro. noa. gr
skot@aegean. gr Since the dawn of human civilisation natural
phenomena have been subject to observation and investigation by the
humans who initially ascribed to them 'divine' powers. Gods of
'good' and 'evil' werecreatedaccording to the useful- ness or
notofsuch unexplained, atthetime, phenomena. Astheir understanding
of the world developed and deepened, the divine powers, religious
beliefs, su- perstitions and mysticism gave their place to the
knowledge, limited that it may be, of physical reality. However,
many issues have been and still are out of grasp of human
understanding. These issues have always been at the center of
philosophical, theological, and more recently, scientific debate.
It is to us incredible that many of the conclusions concerning the
true scientific explanation of the external world, to which the
ancient Greeks arrived purely on the basis of abstract thought,
came so near to modem scientific ideas and also form the basis of
modem science. We cannot but stand with amazement at the original
thoughts of Archimedes who, among his many extraordinary achieve-
ments in mathematics and physics, calculated (cf. TheSandReckoner)
the mass density of the observable universe and came up with a
figure that is in complete agreement with current estimates coming
from observational cosmology.
This book is written in a pedagogical style intelligible for
graduate students. It reviews recent progress in black-hole and
wormhole theory and in mathematical cosmology within the framework
of Einstein's field equations and beyond, including quantum
effects. This collection of essays, written by leading scientists
of long standing reputation, should become an indispensable source
for future research.
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