Summary Talk on Cosmology and Gravitation
XXII Brazilian National Meeting on Partiles and Fields
M.J. Rebouas
CentroBrasileirode PesquisasFsias
Departamento deRelatividadeePartulas
RuaDr. XavierSigaud150,22290-180,Riode Janeiro, RJ,Brazil
Reeivedon29Marh,2002
Theplenaryletures,paralleltalks,oralpresentationsandposterontributionsonCosmologyand
Gravitation presented during the XXII Brazilian National Meeting on Partiles and Fields are
brieyreviewed.Somegeneralremarksarealsopresented.
I Overview and introdution
After four days of listening to two plenary letures,
two parallel talks, a general publi leture, seventeen
oralpresentations,andreading morethanftyposters
related to Cosmology and Gravitation, my hief
im-pression is that the XXII Brazilian National Meeting
on Partilesand Fields(XXII BNMPF) wasa
notie-able sienti meeting, whih overed a great variety
of issues on Gravitation and Cosmology. It brought
together perhaps most of the researhers and
gradu-atestudentsthat haveworkedin thisareainBrazilian
UniversitiesandResearhInstitutes. Thesessionswere
verywellattendedwithafairnumberoflarifying
ques-tions. Ingeneralthespeakersexplainedtheunderlying
ground, approahesand resultsin alearmanner and
keptto the time limits. I thank to them allfor their
quitegoodtalks.
From this and the previous meetings I support
the view that if one onsiders the ontributions
pre-sentedin, e.g.,two suessiveBNMPF meetings they
are rather representative of the researhes that have
beendonein this areain Brazil,and mostofthe
on-tributions reveal a lear emphasis on theoretial and
(or)mathematialaspets ofGravitationand
Cosmol-ogy[1℄.
Theresearhesinmodernosmologyanbebroadly
groupedinvedomains:
i. Astrophysialosmology;
ii. Observationalosmology;
iii. Theearlyuniverse;
v. Cosmitopology(more reently).
Mostof theontributionsto theXXII BNMPF
(orga-nized by the Brazilian Physial Soiety - SBF) were
in the last three families. On the other hand, as far
as I am aware agreat numberof the
observationally-orientedworksonosmologyareoftenpresentedinthe
annual meeting of the BrazilianAstronomial Soiety
(SAB).
I do not share the view that theoretial (and
mathematial)osmology should be stritly relatedto
the observed universe, otherwise it beomes a
point-less exerise. In my evaluation the frontier between
theoretial (and mathematial) osmology and more
observationally-oriented osmology is not and should
not be well-dened, and it is very important that we
have people working on both generalaspets of
mod-ern osmology. However, I feel that a loser
intera-tion between theoretial and observationally-oriented
osmologists is more than desirable | in my view it
is reommendable| forthebenetofboth(physiist
and astophysiist) ommunities. The reentworkshop
alledNewPhysis inthe Spae isertainlyagood
ex-amplein thisdiretion[2℄.
Aonsiderablenumberofabstratsweresubmitted
to the organizers. I envisage how hard was to selet
between oral and poster presentations. A number of
relevant subjets seemed to them to be of interest to
motivate oral presentations, but no doubt other
orga-nizerswould havemadeaquitedierent, andperhaps
equallygood,seletion. Iwillsummarizethepresented
ontributionsbelow,withapologiestotheirauthorsfor
misrepre-II Plenary and parallel talks
The GeneralRelativity(GR) preditstheexisteneof
gravitationalwaves,andanalysesofexperimental data
obtainedfromobservationsofbinarystarsystemsseem
togivealearevidenethatthesesystemslooseenergy
throughgravitationalradiation[3℄.
Gravitationalwavesare predited notonly by GR
but alsobyothermetrigravitationaltheoriesofsome
generality and sope. However, the harateristis of
gravitational wavessuh as propagation speed,
multi-polarstrutures and polarization statesvaryfrom one
theory toanother. Thus, itis expetedthat its
dete-tionwillprovidearatherrelevanttooltoseletthemost
suitable theory of gravitation [4℄. Further, the diret
observationofgravitationalwavesalsooersthe
possi-bility of testing GR(as well asother metri theories)
in astrongeldlimit,wheretheeetsarenotmerely
a orretion of Newtonian Gravitation. Obviously at
Earththewavesareexpetedtobeweakperturbations,
howeverthey an in priniple provide information on
theonditionsattheirstrongeldsoures[5℄. Further,
thetehnologyneededtodetetaswellas theanalysis
of gravitationalwavesis expeted to open anew
win-dowforobservationoftheuniverse,thusgivingriseto
aremarkableperiodin astronomyandosmology.
BarryC.Barish(CaliforniaInstituteofTehnology)
deliveredalearplenaryleturein theXXII BNMPF,
in whih hepresentedagoodreviewofthenew
gener-ation ofdetetorswithsuitablesensitivitiesfor
detet-ing gravitational wavesfrom avariety of atastrophi
events,suhasthegravitationalollapseofstarsor
o-alesene of ompatbinary systems. He pointed out
that more than forty yearsafter the beginning of the
searh for gravitational waves, several resonant-mass
wavedetetorsare monitoringthe moststrong
poten-tialsouresofsuhwaves(inthekHz band)in our
galaxyandin ourloal group. Thegravitationalwave
detetionoflowfrequenies(inthemHzband)from
spae wasalsobrieydisussed in histalk. Contrarily
to theearthbaseddetetors,forthis typeof detetion
there is anaturaladvantagewhih is thefat that
es-sentiallyallthenoisesduetothegroundareeliminated
(formoredetailsee[6℄).
For some deades sine the disovery of the
os-mi expansionby Hubble [7℄ it wastaken for granted
that thematter ontentof theuniverse wasomposed
of theforms of energy we anreadily detet, i.e., the
ordinary matter and radiation. Suh universe would
expand with a negative expansion rate due to
gravi-tational self-attration of the matter. However, some
yearslater,theoretialaspetsofthestabilityof
galax-iesand starsand surroundinggalaxies) indiatedthat
most of the matter in the universe does not emit or
absorblight (darkmatter). Thedarkmatter lear
in-diationfoundresonanein the1980'sbythe
ination-aryuniversesenarioin whih theuniverseistaken to
be at | the total energy density equal to the
riti-al density
= 3H
2
0
=8G 1:710 29
g=m 3
.
How-ever,measurementsmadeby that time oeredalear
indiationthat the ordinarymatter and the radiation
ouldonly aountfor about 10%of this value|
in-ationseemed to requiredark matter. The new
on-sensus model beame that in whih the universe
on-tainsprimarily old,nonbaryonidarkmatter, and
al-thoughobservationsatthattimeindiatedthatthe
to-tal massdensity wassmallerthan the ritialdensity,
manyosmologistsassumedthattheatmodelwas
rea-sonablywell-established. However,furtherobservations
stronglyindiatedthatthetotalmatterdensitywas
in-deedlessthanhalfoftheritialdensity. Theonlyway
ofhavingsuhalowmassdensityandaatuniverseis
ifanadditional, nonluminousandnonlustering \dark
energy"omponent dominates the universe today,
al-thoughit must havebeennegligible in thepast soas
topermitstrutureformation. Thegeneralrelativisti
Friedmann-Lema^tre-Robertson-Walker(FLRW)
stan-dardmodelingapproahrequiresthatthisdarkenergy
hasanegativepressure,and the reentmeasurements
ofdistantexplodingstars(supernovae)supportthe
ex-isteneofanegative-pressuredarkenergysuhthatthe
(total)energydensityandthe(total)pressurepobey
therelation +3p<0,whihleadsto anaelerating
expansionfortheuniversetoday(forafairlistofbasi
referenesonthetopis I havebriey mentionedhere,
seetheverygoodreviewbyBahalletal. [8℄).
Lua Amendola (Osservatorio Astronomio di
Roma)presentedaverygoodplenarytalk inwhihhe
reviewedhowthereentindependentosmologial
ob-servationsonstrainthevaluesoftheosmologial
den-sityparameters,andhaveindiatedthattheuniverseis
lledwithdarkmatteranddarkenergyandundergoes
anaeleratingexpansion. Hepointedout howreent
supernovae Ia observations [9, 10℄ all for an
aeler-ation expansion of the universe, whih together with
reentosmimirowave,large-salestrutureand
lens-ingdatagivearatherstrongindiationthatthematter
(energy)ontentof theuniverse is basiallyomposed
of darkmatter ( 30%), darkenergy ( 70%),
bary-onimatter (very few perent). For moredetails and
referenesseehis reviewpaperinthisissue[11℄.
OdylioD.Aguiar(INPE)toldusaboutthestatusof
theMarioShenberg gravitation wavedetetor, whih
erate in 2004. This detetor has a spherialantenna,
willoperateat temperatureoflessthan0:1K,andwill
besensitiveto signalsof amplitude h>10 21
Hz 1=2
inthebandwidth3:0{3:4kHz (formoredetailsonthis
talksee Aguiar'spaperinthisissue[12, 13℄).
It is well known that general relativity is a loal
metrialtheoryandthereforeitseldequationsdonot
xthe topologyof thespaetime, sinegeometry does
notin generalditatethe topology. This freedom has
resulted in a great deal of reent works in whih the
possibilitythat theuniversemaypossessaspatial
se-tionwithanon-trivialtopologyis examined. Whether
weliveinanite orinnitespaeandwhatisthesize
and the shape of the universe are open problems of
topologial nature. Inhis talk HelioV. Fagundes
pre-sented a brief introdution to osmi topology in the
ontextofFLRWmodels, andreviewedthework done
by his group and ollaborators at IFT/UNESP. The
works hedesribedrangefrom early attemptsto solve
aontroversy aboutquasars throughthe multiple
im-agesproduedbynontrivialtopologies,tomorereent
issuessuhasosmirystallographyandquantum
os-mologyinompatuniversemodels(formoredetailson
thistalksee Fagundes'paperinthisissue[14℄).
Before reviewing the oral presentations I remark
that one partiular objetive of the organizers was to
involveasfaras possibletheloal generalpubliwith
themeeting. TothisendtheyinvitedI.Wagatogivea
publi generalleture onosmology, and hepresented
alearandmotivatingleture ontheexpansionofthe
universe[15℄.
III Oral presentations I
The rst oral presentation was of an
observationally-orientedpaperbyM.O.Calv~ao,J.R.T. deMello Neto
and I. Waga [16℄, where it was disussed, through
Monte Carlo simulations, how the Alok-Pazynski
test, as applied to quasar lustering, an be used to
probe the osmologialdensity parametersspae, and
also the equation of state parameter. The approah
disussed in this ontribution may beome a relevant
strategy to narrow down the osmologial parameter
spae.
H.P. deOliveiraand S.E.Joraspresentedanearly
universeontribution,wheretheystudiedtheevolution
oftheentropyandadiabatiperturbationsandshowed
thatforasmallamountofdissipationtheentropy
per-turbations an be negleted, and so the purely
adia-bati perturbations willberesponsible forthe
primor-dialspetrumofinhomogeneities[17℄.
Araujo,S.R.M.M. Roveda andW.Stoeger[18℄)
spher-iallysymmetriperturbationsofFLRWmodelsinthe
so-alledobservationaloordinateswereexamined. The
FLRW (spherial) models areused asthe bakground
spaetime and apartiular ase of spherialdeviation
from this bakground is studied (for more details on
this \observational program"I referthe readerto the
paperbyElliset al.[19℄).
Usingreentobservationalonstraintson
osmologi-aldensityparameters,togetherwithreent
mathemat-ial results onerning small volume hyperboli
man-ifolds and a topologial detetability indiator
intro-dued in [20℄, G.I.Gomeroreportedonaontribution
on osmitopologyin whih itis argued that,by
em-ployingpatternrepetitions, thetopologyofnearlyat
smallhyperboliuniversesanbeobservationally
unde-tetable[21℄. Thisisanimportantresultinviewofthe
fatthatquantumosmologyseemstofavouruniverses
withsmall volumes,and fromtheexpetation,oming
frominationarysenarios,thatthetotaldensity
0 is
likelytobeverylosetoone.
By onsidering that the urrent expanding era
is preeded by a ontrating phase, in other words
by assuming the existene of one boune, N.
Pinto-Netoshowedhowoneanonludethat noobservable
bouneouldpossiblyhavetakenplaeintheearly
uni-verse if GR together with hydrodynamial uids
de-sribe the evolution of the universe, thus under these
onditions theuniverse hasalwaysexpanded (see [22℄
formoredetails).
Therstsetoforalpresentationwaslosedwiththe
presentationbyS.E.JorasofaartilebyR.H.
Branden-berger,S.E.JorasandJ.Martin,inwhihthespetrum
ofsalareldutuationsinabouningasymptotially
atuniversewasalulated,andthedependeneofthis
result onlengthsales shorter thanthe Plank length
wasinvestigated(formoredetailssee[23℄).
IV Oral presentations II
Topologialdefetssuhasmonopoles,stringsand
do-mainwallshavebeenstudiedindierentontextssuh
astounderstandtheprimordialuniverseandstruture
formationin theearlyuniverse. Theirnature depends
uponthetopologyofthevauum manifoldoftheeld
theoryunderonsideration. Theseondsetoforal
pre-sentationsbeganwithaontributionbyR.M.Teixeira
FilhoandV.B.Barbosa[24℄,wheretheyhaveobtained
intheontextofsalartensortheoriesthegravitational
eld of a global monopole, in the weak-eld
S.S. e Costa delivered a ontribution related to
osmi topology in whih general solutions of the
Helmholtzequation, inseveral oordinatessystemsfor
twoandthree-dimensionalhyperboli,spaeswere
pre-sented[25℄.
Another ontribution related to osmi topology
was an artile by D. Muller, H.V. Fagundes and R.
Opher[27℄,wheretheyhavestudied,throughnumerial
alulations,theCasimir(vauum)energyfora
onfor-mally oupled,massivesalareldin astatiuniverse
whosespatialsetionsareendowedwiththetopologyof
the smallest known hyperbolithree-manifold (Weeks
manifold). Theyhaveonludedthatthereisa
sponta-neousvauumexitationoflowmultipolaromponents.
A. Bernui alsopresentedaosmi topology
ontri-bution in whih the osmi rystallographystatistial
approah to the topologial signature of the universe
wasused inhis numerialsimulationswithinomplete
atalogs.
R.Androvandipresentedaninterestingontribution
(R. Aldrovandi, J.Garieland G.Marilhay)onwhat
theyallthepre-nuleosynthesisperiod(PNS period),
betweenz 10 10
and z 10 15
, and where our loal
physisdoesnot neessarilyhold. A generaloverview
of physialproblemsappearinginthePNSperiod was
given,andpossibleunderstanding forthestriking
out-omes weredisussed. Formoredetailssee [26℄.
V Oral presentations III
Condensed mattersystemssuh aslightinmoving
di-eletrisand quasipartilesin amovingsuperuidan
beused tomimi kinemati aspetsof general
relativ-ity. The omparative study between the kinematial
aspetsofGRandotherkindsofinterationshasbeen
alled analog model for gravitation or simply analog
gravity. Thesetypesofanalogmodelsarerather
impor-tantin that, e.g.,theyprovideblak holeanalogsand
mayleadtoexperimental testof quantum eld theory
in urvedspae. Thelast set oforal presentations
be-ganwithabriefreviewtalk,deliveredbyR.Klippert(a
workinollaborationwithV.A.deLoreni)where
ana-log gravitymodels were disussed in several ontexts,
ranging from eletrodynami in non-linear media [28℄
to movingdieletrisandaoustiperturbations(fora
fairnumberofreferenesonthistopi see[29℄).
AworkbyJ.M.FMaiaandJ.A.S.Limainwhiha
proeduretogenerateosmologialsolutionsinthe
on-text of GRwhose matter ontent is given by asalar
eld plus a perfet uid waspresented. Appliations
to inationary and quintesseneosmologieswere also
A.Y. Miguelote reported on the results of an
ar-tile in ollaboration with M.F.A. Silva, A.A. Wang
and N.O. Santos, in whih some properties of the
Levi-Civita(LC)typeofsolutionsofoupled
Einstein-Maxwellequationsarestudied,andsomelimitsofthis
type of solution are obtained together with an
inter-pretationofthefreeparametersinvolvedinLCtypeof
spaetimes[31℄.
I.D. Soares presented a interesting paper
(homo-lini haos in the dynamis of a general Bianhi IX)
ofa work in ollaborationwith H.P. Oliveira, A.M.O.
Almeida, and E.V. Tonini, in whih they have
stud-ied the dynamis of anisotropi (three sale fators)
BianhitypeIXmodelwithdustandosmologial
on-stant(positive). Theyhaveexaminedthe existeneof
haosin thismodel,andhaveshownthat itishaoti,
andthat the haos hasahomolini nature. The role
playedbytheosmologialonstantinthephasespae
is shown to be ruial in that it determines both the
existene of a saddle-enter-enter ritial point, and
theritialpoints atinnityorresponding to the
De-Sitteronguration. FormoredetailsIreferthereader
toref.[32℄.
The interation of Hawking radiation and a stati
eletriharge was aontribution deliveredby L.C.B.
CrispinoofaworkinollaborationwithA.Higuhiand
G.E.A.Matsas,in whih theyhaveinvestigatedintwo
interating situations whether the equality found for
theresponseofastatisalareldismaintainedinthe
aseofeletriharges(see[33℄).
The last oral presentation was by J. Casti~neiras
(a work in ollaboration with L.C.B Crispino, G.E.A.
Matsas and D.A.T. Vanzella). They have studied
\free partiles" for whih E < m 2
outside
Reissner-Nordstromblakholesandin aspaetimeofastar(for
moredetailssee [34℄).
VI Panel ontributions
Morethanftyontributionswerepresentedasposters.
About twenty per ent were related to the physis
of the early universe. F.G. Alvarenga, J.C. Fabris,
G.A. Monerat and N.A. Lemos presented two
ontri-butions on quantum osmology [35℄. N. Pinto-Neto
and E.S. Santini also presented a poster related to
quantum osmology (see in this onnetion the
arti-le [36℄). Three works onneted to the preheating
proess were presented as posters: one by S.E. Joras
and V.H. Cardenas [37℄; a seond by A.H. Campos,
R. Rosenfeld and J.M.F. Maia; and another by R.O.
a seond by H.P. de Oliveira alone [38℄, and a third
by J.C. Fabris, A.M. Pelinson and I.L. Shapiro [39℄.
A.H.Campos,R.Rosenfeld, J.M.F.Maiaand H.Reis
disussedin aposterthepossibleprodutionof
super-heavy primordial partiles. R. Aldrovandi, A.L.
Bar-bosa,M.Canadaand J.G.Pereirapresentedaposter
onkinematisofaspaetimewithinniteosmologial
onstant(!1) andspeedoflight(!1),whose
results may be of someinterest to early universe
os-mology[40℄. Aposterwithsomeontatwiththeearly
universe was also brought to the meeting by M.G.C.
Batista.
Nineontributions relatedto topologial defets in
dierent ontexts were presented as posters. Three of
themtreatedthesedefetsinsalar-tensortheories: one
byV.B.Bezerra,L.P.Colatto,M.E.X.Guimar~aesand
R.M.TeixeiraFilho[41℄;anotherbyV.B.Bezerraand
C.N. Ferreira [42℄; and athird by V.B.Bezerra, R.M.
TeixeiraFilho, G.Grebot andM.E.X.Guimar~aes[43℄.
Thebehaviourofnonrelativistiquantum partiles
in-terating with dierent potentials in the spaetimes
generated by a osmi string and also by a global
monopole weredisussedin aposterbyG.deA.
Mar-ques and V.B. Bezerra [44℄. Two posters on osmi
strings were presented: oneby A.A. Moregula in
ol-laboration with M.M. Som, and another by V.A. de
LoreniandE.S.MoreiraJr(see[45℄). Thesolutionsof
Shrodinger equations for the Coulomb and harmoni
osillator potentialin the osmi-stringonial
spae-times of N dimensions were presented in a poster by
J.L.A. Coelho and R.L.P.G. Amaral [46℄. T
opologi-al defets in the ontext of(or related to) ondensed
matter were disussed in two posters: one by C.A.L.
Ribeiro,C.FurtadoandF.Moraes,andanotherbyJ.F
deAssis,V.B.BezerraandC.Furtado.
BesidesFagundes'paralleltalkandtheoral
presen-tationsbyG.I. Gomero,S.S.eCosta,D. Muller etal.,
and A. Bernui, wehad an additionalposter
presenta-tion by G.I. Gomero of a work in ollaboration with
M.J. Rebouas and R. Tavakol [20℄ on the
detetabil-ity of osmi topology of nearly at FLRW universes
in the light of the most reent observations (Sne Ia,
largesalestruture(LSS)observations,MAXIMAand
BOOMERANG).
In addition to BarryC. Barish'splenary talk,and
O.D. Aguiar's parallel talk, four posters related to
gravitationalwaves were presented: K.L. Ribeiro and
O.D. Aguiar; S.R. Furtado and O.D. Aguiar; and
L.A. de Andrade, O.D. Aguiar andK.L. Ribeiro; and
also C. Frajua, N.S. Magalh~aes, O.D. Aguiar, K.L.
Ribeiro, L.A. de Andrade, W.F. Velloso Jr and J.L.
Melo(see[47,48℄).
One by T. Vargas on Regge Calulus in teleparallel
gravity,andthreeothersbyA.A.SousaandJ.W.Maluf
(formoredetails see[49,50℄).
Itseemsindisputablethatmostoftheoretial
physi-istsspendalargeamountoftheirtimeinarryingout
nonnumerialulationofonesortoranother,mostof
whih are algorithmior semi-algorithmi. Today the
omputer algebra(CA) systems are standard toolsof
theoretialphysiistsforperformingsymboli,although
inmostasesperhapstheysimplydonotmentionthis
fat. We had three CA poster ontributions in the
meeting, all related to the Maple system. One dealt
with the symmetry groups in GR (by J.A.F. Roveda
andJ.E.F. Skea), whih isarelevantpiee of
informa-tionneededin theinvariant(loal) haraterizationof
spaetime;andanotherwasabouttheusageofMapleto
alulate quasi-normalmodesofradiatingsystems(by
P.C.C.MonteiroJrandJ.E.F.Skea). F.D.Sasse
deliv-ered a ontribution in ollaboration with R.F.
MLe-naghan and S.R. Czapor where the Maple pakage
NPspinor was used to prove the Hadamard's
onje-ture for the salar wave equation in Petrov type III
bakgrounds.
Dierent aspets and ontexts of blak holes were
disussed in a series of four posters. G. de Oliveira
Neto studied exat solutions of Einstein's equations
in (2 +1)-dimensions whih, depending on the
val-uesofertainparameters,mayrepresenttheformation
of blak holes [51℄. A.A. Sobreira and V.B. Bezerra
examined rotating blak hole in Einstein-Fokker
the-ory in (2+1)-dimensions. Holonomies in the (2+
1)-dimensional geometry of blak holes were the ontent
ofaposterbyA.Carvalho,C.FurtadoandF.Moraes.
A blakhole typesolution ofEinstein equationsin
2-dimensionswasdisussedbyD.G. Delfrate.
There were four posters whih I broadly grouped
asgravitational-relatedworks. M.Caladapresenteda
posterongravitationandtheloalsymmetrygroupof
spaetime [52℄. A.A.Sousaand J.W. Malufpresented
aposterwhere theyproposed anexperimentaltestfor
the gravito-magneti eet. R.C. Rigitano disussed
inaninterestingposterthegeometrirepresentationof
generallineartransformations,andthepossibilitiesand
limitations ofthe representationof ovariant
transfor-mations. C.R.Munizexaminedgeometripropertiesof
thespinintheontextofGR.
Two posters were related to Astrophysis. In one
the third post-Newtonian dynamis of ompat
bina-riesequationsofmotionwasdisussedbyV.Andrade,
L. Blanhet and G. Faye (for detail see [53℄). In
librium ongurationswith spherialsymmetry (King
models)[54℄.
M.D.Maiapresentedaninterestingposter(related
totwoworksinollaborationwithE.M.Monte [55,56℄)
in whih he showedhowbrane-worldosmology oers
aquitesimpleexplanationfordarkenergy.
M.E.X.Guimar~aes,L.P.ColattoandF.B.Tourinho
presentedaposterin whihtheyextendedto the
on-textofsalar-tensortheories[57℄(wheretheparameter
! in no longer onstant) a proedure, devised by A.
Barrosand C.Romero[58℄, whih makeslearhowto
obtain solutions in the Brans-Diketheory from
solu-tionsinGRforthesamematterontentwhenone
on-siderstheweak-eldapproximationsin boththeories.
In an interesting poster by S.O. Mendes and R.
Opherit wasdisussedhowthe1=r 2
gravitationallaw
onsubmillimetrisaleanbeusedtotestthemodied
Newtoniandynami theory(MOND)[59℄.
Besidesthebriefreviewtalk,presentedbyR.
Klip-pert as an oral presentation, Analog Gravity also
ap-peared in a poster by V.A. De Loreni and R.
Klip-pert[28℄.
AninterestingposterwaspresentedbyF.P.
Deve-hi and G. Kremer in whih the kinetitheory of
rel-ativistigasesin two-dimensionalspaewasdeveloped
toobtainthermodynamialquantitiesin2-dimensional
osmologialmodels[60℄.
H.P.deOliveiraandI.Dami~aoSoarespresentedin
aontributiontheresultsoftheirstudiesofthe
dynam-is ofspheriallysymmetrigravitationalollapseofa
masslesssalareld [61℄. H. P. deOliveira,I.Dami~ao
Soares and E.V. Tonini also had a poster where they
presentedananalytialmethodtodesribetheunstable
periodiorbits oftheenter manifoldfor Hamiltonian
systems. Anotherposterwithsomerelationtothiswas
presentedbyO.C.Castellani,G.A.MoneratandJ.F.V.
Roha.
M.M.deSouzalaimedinaposterthattheonstant
anomalous radialaelerationobserved in thePioneer
10and11spaeraftsanbeexplainedintermsof
dis-reteinterations(fordetailsee[62,63℄).
J.F. Villas da Roha presented a poster in whih
solutionstoEinstein'seld equationsinN-dimensions
withspherialsymmetryweredisussed[64℄.
L.SandovalJronsideredinaontributionthe
on-straints on generalized metris (with both symmetri
and antisymmetri parts) desribed throughvierbeins
imposedbybosonistringsinurvedspaetimes.
M.L. Bedran presented an interesting pedagogial
posteromparingtheDoppler(speialrelativity)eets
withtheosmologialredshiftofgeneralrelativity.
F.D. Sassereviewedthedierentinterpretationsof
fermions in a storage ring in a Serret-Frenet tetrad
frame,insteadoftheusualHehl-Niframe.
M.J. Lazo and S. Ragusa showed how to
alu-latetheeletromagnetiangularmomentumemissionof
fourthorder,extendingthereforethealulationsmade
in the Landau-Lifhitz book for eletridipole. They
intend to use a similar sheme to examine analogous
gravitationalemission.
Tolose this setion I remark that a onsiderable
numberofextended versions oftheworkspresentedin
theXXIIBNMPF willbeavailable(proeedingsofthe
meeting)andanfairlysoonbeobtainedviadownload
fromtheBrazilianPhysialSoiety(SBF)webpage. So,
formoredetailsonsomeofworksbrieyreviewedhere,
Ireferthereadertothat site[65℄.
VII Closing remarks
The large number of abstrats submitted to the
Cos-mologyand Gravitation sessionsof theXXII BNMPF
isertainly indiativeof the robustlevelof interestin
the area. The meeting was a lively one and
demon-stratedthevitalityofaextensivesetofresearhtopis.
Italsowasveryinformativeandmanydisussionstook
plaeintheregularsessions,andalsointheoeeand
othersbreaks. Thespirit ofollaboration,essentialto
theprogressofsiene,waspresentinthesessionsand
disussions.
Let me lose my review by strengthening a point
I have indiated in the introdution, whih is that
the interation and ollaboration between
theoreti-alandobservationally-orientedgravito-osmologistsis
stronglyadvisablefortheadvaneofthearea,the
ben-et of our ommunity as well asfor the formation of
Brazilian young sientists in Cosmology and
Gravita-tion.
Aknowledgments
IwouldliketothanktheOrganizingCommitteefor
theinvitationto deliverthesummary talkon
Gravita-tionandCosmologyoftheXXIIBNMPF.Ialsothank
them for the large amounts of eort put into the
or-ganizationof a very suessful meeting. I thank Ioav
Wagafor hishelp in thelassiationofthetopis for
my summary talk. Some authors provided me with
preprints, reprints or referenes related to their
sub-mittedabstrats. Theadditionalinformation material
provedto be veryuseful forme, and I thankall these
olleagues for their helpful gesture. I also thank
thank CNPqfor thegrant under whih this workwas
arriedout.
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