• Aucun résultat trouvé

Relativite Generale et champs quantiques: quelques aspects de physique des trous noirs et de cosmologie en gravite de Lovelock, espaces de Sitter et dimensions supplementaires

N/A
N/A
Protected

Academic year: 2021

Partager "Relativite Generale et champs quantiques: quelques aspects de physique des trous noirs et de cosmologie en gravite de Lovelock, espaces de Sitter et dimensions supplementaires"

Copied!
252
0
0

Texte intégral

(1)Relativite Generale et champs quantiques: quelques aspects de physique des trous noirs et de cosmologie en gravite de Lovelock, espaces de Sitter et dimensions supplementaires Julien Grain. To cite this version: Julien Grain. Relativite Generale et champs quantiques: quelques aspects de physique des trous noirs et de cosmologie en gravite de Lovelock, espaces de Sitter et dimensions supplementaires. Cosmologie et astrophysique extra-galactique [astro-ph.CO]. Université Joseph-Fourier - Grenoble I, 2006. Français. �tel-00104399�. HAL Id: tel-00104399 https://tel.archives-ouvertes.fr/tel-00104399 Submitted on 6 Oct 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) 

(3)     "!#

(4) $%'& (*),+.-/(102+3)546+,7989-/(:0;(:<*=?>A@CBED,F;( G H I JI EK LENPM OQNSRUT NSM N KWVYXELZV\[ T]NSRE^ L _ N`TQ^aT L N/bcN d#feCg hjife SeZ lk%\mn

(5) o p qr . s KtNvM u^xw _ ^yT N{M z}| V OQ~ VY_aVY ^€N\c‚OnT L]V\K„ƒU OQ^€† X N‡bcNvOZˆ

(6) w L TQ^xu XE_ NPO "‰ ŠŒ‹]rŽ{‘’“Ž•”Š –—Œ”Š ˜™Œ”Š š›•‹œŠŠžŽ Ÿ6¡*3¢ £¤¦¥¨§5’˜Ž/n¥¨§Šf¤ © ª¬«

(7) ­¯®€ª¬«

(8) ­±°;² °±³C­µ´›¶U°9·Z­¸³Z¹gº

(9) °›»€ª¬«

(10) ­¨·Z­µ°•¶½¼¿¾‡« °2À

(11) ¾`»‘¼°•­±¶’·Z­¨´¾Á°±ÂA¾‡®€¾ÁÇ»x­?­ÁÀ ì¼²gÄZ»a¶Z­AÅ ·Z­ÇÆÁ¾ÁÄ

(12) ­Á®a¾q´¯ÈCɇ­±°±³²

(13) ´­±°9·Z­ËÊ»a¶\¶U­Á¼­›¶’·‡»‘ÂA­¯À °›»x¾`À °.°±«Z³Z³Z®Ì­ÁÅ ÂA­¯Àg¶Í²Z»Î¼¿­µ° KwL ÏtÐÑQҜӵÔÖÕ37983BU× s VYX TQNPR X N _ N{Ø V u¿T VY[EL N¬Ø\Ù\ÙYÚ{bcNPÛÜw\RUT _ N¬Ý XELQ u V ~ K½V O N‡M bcNz ‚{â ބÞWßtßÁw NvL]OQL w\w R

(14) X u ã V R åé Þ„ß V\X u ƒ NT 䬈 ބÞWބˆ ˆ

(15) êNSw NSTQLR N NSLL RU^ T]w\RE^. àä w^ L KENPK½uTQV\N L XETQNL X„bcL N‡T ƒ±NPá OQN æˆ çcLENvw\M On~p^xbc^aNPR„RYwèT TQN XEL æä çcw w\KE~pK½V\^aR„L TQwèN TQX„N LXEL. ë w [WVYL wèT V ^ L NqbcN/ˆ ƒÍ OQ^x† X N s XE[ wÌT V ~p^x† X N`NSTbcN| V OQ~ V\_€V\ ^aNYc|Cìqä s„íÜî ì`ØèˆÁï{ð¯ñqÝ å.

(16) Ø.

(17)     

(18)  u&0. ^€NS/2~p1 ‚#3NS45RU_ w/-6T]7O ~$΁ REwè_aN¬VYRELO ^ O]NVá † LRYNX T N bE† NP_X O VN NPR5M _u  LNS~p^€ç ÛÜNKEw\L ^abcRWNvNSOQO¯~OQ^O V XEwèR±RWLQL„cbcNvMO Nžw KW_ bcV ^€OnRYNTQTNvbcwèO

(19) ^R L† NSN8M X N\^}c9OQbcN#Nv-:O _ )wè K RWÞµN u ‚"L Ná O L V bNPR„RYN#M RE;T¯w NPb„X OwèT¬R„bO =NS_< nT NvM L u NL ^yu T VXERÍL !N Û\"NPO #RUK½%$TQV '^ VRU&(RET]*w\RER N )NS_ M +,OPNY›YuuS-¿NvNP„O O uSN LL LNPNPT]~~wè^€NN R„LL Oðð _u ^€^aNS~~pw NS RUN¬T]ObcN O V _ NRUXET{L On^€w R„X u TQNá N L XENPL OPÞ ›NTuSN L T]wè^€R„O¬~ NP< ~pN^aRUTQNP~ KWVYL N _ OP±~wè^xO  w L bEN L]V RUT X RENfuSN L T]wè^€REN KEX bcN XEL  wá uNƒEç VKEOQñ L N\NPR3ÞÍO]Onæ¯^ b V OnV\RATnXð‘^ ç’7_ /BÛ NC1L XEwè:KE^€DE~ƒtF36NSMNP$G~pRUHTÁ^x4IOnR ~p&JNv3LM NuNvKMKWOQLO]VYwèXE^ LL N(N $u bEV 4!N`~pNJ~p~-LN,NPOR„> D6X u4"OnN TQ-6L ^=7Þ

(20) ?„ÝYN L"N -L@ L )PNPÝ\L~N`NRE!L N`uSR^a~NrQLN‡~p-:uSNP#wYO3Pu 3#ƒ KN I3w L ¿LwèÞ±NS^ RUÝYK T]NpwYOP

(21) OÁREuNbcN N __ LQNvw L O¬^ KNá u L w\ƒ N O]N OQ_ L Nrw¬u ƒ T wÜNL]ÛÌV\wèK K RUwYTu OSN }M T _ VYTNá V\X[EX TQL NNT On^€~ KE_ NP~pNSRUTPÞ„Ý X OnTQN X Rr~pNPO]OQw  N‡NSRUT L N _ NPO _ ^  RENPOPÞ â V Rrw <T R NSM NYUb V R„u`~ V Rr~ V b Ná _ N\ÞEì NPM uSNPO]OQw\^ L NS~pNSRUTvÞc|ÁN _a_ N¬† X ^±Û VYX OC^aR„O K ^ L N \ Ý N S N p ~ N  u € ^ q N  ~ p w : O S Þ L L E X L OQw\R„OtÛ VYX O \X ^xbcN L E† X ^±Û V\X OU; VYL ~pN¬OQw\R„OtÛ VYX Otb NM ; V\L ~N L Þ O† XEX L N Ý\T]_N N NL]L L NS~ N~pVZ±NR„O]L uSbcuw\N^€R„NC†bEÝ X w XE^Z_ _ N ^a~NYX MOn NPVpNS~pRUOQT uPNSVYwèRUXER„T L b„NYKEw Þ

(22) LE_ NPNÝ\M OQXN NSOQRUNS_ TQw ~pNLNSb NSRUXE~pT L [N wèL NRUuS_aT‡_^aNXN T WUV\KWYHX VYO¬ZYXEOQL\uuPNPwèN<O‡R„T L~ bEN w V __ ~N w*X NPOQOQRUNSN T]~pXEO‡_ NSN NRUT/wŒTá w K uX w\L]OQO]V OQOn^^Î^L  V NY[R g^aNSM†NPN[RX Zè^ZO]KEuSNv_awèXOœT RWO bEK NSM w ÛÌw _ wèLN ; R„X V NPOQ^€NSO]O u~pNSKENPRU_€XRYT]NOT ^a~ K½V\L T]wèRUT † X N/O]wÜÛ V ^ L U† X N _ N‡~NP^ _€_ N XEL K„ƒU OQ^€uS^aNPRrO XELR] N L]L N‡R  NPOnT w X T L N¬† X N¬~ V ^ÎÞ V R„u _Ý\NvN OS\L T]NSwè~pRUNT]NPL uOP^€YNu VYNSX ROQ?„^aR„R•OPYT V\u XV\XOOQuS^€REN XNPO¯ç’NbET NX R ~pK w^NSTQ; w\^aT ~p[½^ V_€_ RN ƒ„† V X ~p^Z~p~ N\ ÍV b RUN_TfM > w‡á O V\NPX RT]; NSwèR RUX TQð‘Onz¯T]w ~L¯NvK O w \L L uwèNvRWO bEL OœNSð ~pK w N L L NPuRY^€NST~pOSNS~pRUTNPOSO Þ â â KWX RVYXEOQL uSNOnN NK L uT]K„^€^ uS_ wqwYá ^€OQu‚ ~pN L XEN LEw N_ XM ^ _ [Eð“^aNPbcL R±N¬N _“ÜwqÛÍá b ^€bEVOnð RUN wÌá T uð‘ÛU_N  ^xNSOZ† RUXabcT ƒ„Nv^ _ V\O ;X KEw\OQ^yL]^€TvV\wYYK½Onw ~pV X OQNCð‘^ybcT]OQ^ N uSV _‘^aR„w`áNPOZRYbcT]ON ^`XE?½uSL† N X _ †N/NÁX ~Nv^cOœNPVT

(23) OnR„uT¯bEN bcLN\T^yETvwèNSÞ\^€TREˆ NSNSV\~pRX„?WLNSRRU~ T bc u wÜN/V Û RUREV TN^ wL K NS^€w\RWN OZuX V\ç}~ X„Þ L wÜw Û 

(24) w\V N ^€M ^ O L wá O bXEwL FTL3cV\bc#X N TL ~b)O&NPM dEu wÜSV\Û ÞYX V ÝYÛ ^ LNtL NqTQu N V NSRT L NS? KE~pL LQ~ V N bL NpM uSX ^a† ^yN TvX ÞK½NV\TXEVYL X T T{V RO]uO^€NSVYRUX TQTQ^=^€?WNS†RpX NSNfT

(25) OQT]Nžw [bc^€NSNSÛÌRÍw\Û\^yT{NP^ _€b _ wèeNS< R„T uSL N\N ÜƒUT]w\X RU~ T [EKE_ LQNV N; NPT O]OnƒÍ^ X V ~R„REw\N ^aR^_ O

(26) ;† w\XauS NžƒÍX w ~X w\O]^awÜR„Û O V NS^ TL K½† V\XaXE ^ L _ â s K w\O]O NM ðn|Cä 毂 â KEL„NvM OnNPRYTQð sIf ‚ \ Ý N S N p ~ N  u € ^ N P N U Û x ^ c b P N  ~ p ~ P N Y R f T T O P N ž O p ~ P N ~ P N ž O b N ‚ L L M \ V X _ E [ L ; X \  ] L \ V E X K n î s ë â ;X X RET N XEL NSðM REN LQ ‚¨^aN5wÜ†Û XV\LNLT NY>œM N5Þ RE^€N u ƒ KWN VY_ X XÛÌwèR ^xOru ƒ ^a~N;w wè RU^aR„TQ^aN ðÎL~pZ Nvbcë N#w ;XEbL NSV RURYTPT  _ _Nvw.O NSOQ~N XEKE_ N _€VÌ ¯K NPNM OtL O R„V N{REREO VNŒRU†T X K ^‡w\O Û VYb„X wèO R„O K w_ w L]_ L]N5X bN\½œNM wÜT]Û\wèNvT]uO †† XX ^awèRIRUgPTQN ^x† ƒ X N NPXEOL ^€NPRYO`T LNS^xT¬† Xt† NvX M O ^[?Wwá R„V w RI_ NSgP~pN NSƒ RUN T¬XEÛL NPVYOPX 

(27) O‡bcO N VYL K½T V\X _ ^aRETQ^xN † X K Nr^ _ NpNSçÍbET N N M L K„^€NƒEXEV L T N V u wá V\K T]^€w NP[EO¬_ NYbEN bc_N ‚ O [EXEL K„wèKW~ VYVJL Th ^a~ T:gNPM uPi wèREs ^xTQ† N X \N X Rwá â TOj ƒtXEX L`N M wèV\_ RUL NP^aTQO NZ^x† ; † VX X R„N{w\uRYNSTQT/T]^ V ^€† OQR„wX O‡N [ bcbE^aNpNPNPRÍßCO¯Û\uNPNSƒO]^ On_€wè_ N w\~ _ R„KwÜuÛÌO

(28) Nw\NSZ›RYT¯O]T‡wèNSbcR„RN?WO R V\L NPXEf RY[„TV _ L ^€OœNN T]LL^€w„âwá  K½_w wV\L XEuS~^€L w\wèOQR NP^xVO O V C_aRHXk ~pZ _ ^€ÛÍ^€RE^awN N LL X ^€Onw\NSNvT¬REO¯N ä bcK½NS^xM OQV\~ u XEX L O]Þ}OnOQæ

(29) ^ NPV T OqR„[O¯Nç^aO NPKEXER*_ L¯^€uPO _ XEwÌw< TQL â^ WV TRWNPM V\uSOqX w\OT¬REXE^xuL‡† N X __ wwN bEwèR„O X REN‡T LPNPá O [½V RER„N/wè~ [ ^€w\R„uNYÞ Ý\N L NS~pN L u^€N _ NvO  NPR„O wÜÛYNPu‡† X ^>  wè^±N X_ wl> V ^aN/bcN‡T L wÜÛÌw\^ _€_ N L zWˆ

(30) w\R„w  ^ V T]w f w\RUTQ^΁ KWV ^aRUTbcNb N M K w L T monqpsrXtvBu w t v_xy p{zE|} ~q'€6s‚qƒ„€6s ^.

(31) ^a^ b_ w X X REb„N w\\uNL wèäR„bEX N O]OQK NLw L; wYT]^auNZNbcw NvX O ç T L NPwÜM †ÛÌXw XwÌçT]^ V K„R„LEONvM OnLNPNvRUOQT O NvMV\OL bETQ^€w\NPR„O O

(32) K uw NSL TnT]â NtT ‚qƒ±ˆ Nvá Onë NæZ s T]w w\_aO¯_ N‚ g _ VNçcR’NSNPOQÛ½^a~ è†KEX_ ^`^„?W~NuSw NPO; wè^abcT¯^aç b NvM K u wV\X NPÛ OL 5^ L Z ˆNSR^€N?„L]R L N â s wèw çc_ wè^a~ TQ^΁½f ä ƒ„^€u_aVYƒ KWw V L Û}b Þ ] wè^ _€_ NSTNT à wÜÛÍ^xb â w X„L ^€R± YL w\R„b~w <T T L N/bcN _ w K„LQVYK w  wÌTQ^ V R  w _ w\u¿T]^€† X N[Z½NT ë ˆ s |qtÝ VYƒ wèRER?| VY_a_€V Tv K½V\XEL ~  wÜÛ V ^ L w KEK½V\L T N M O V R \ Ý N S N p ~ N S u a ^ N w ] O n O ^ \ w  u T N c b ^ v N ¿ u ] T N b L L X  _  X _ L E X L X Ow{VYT X V\TQX ^€NSTRrbEb N¬NPá ~ O _NS< N`~pb N¬N M [Eu ƒ X wèTtR bc

(33) N`NqM ~ bEN‡V R TQ^aàT L æ¯N/‚ † X NwÌT T L KWN VY;XEV L ^xOSwÜÞ Û V ^ L T V\X > V\XEL OÁO X ^€ÛÍ^ _ NPO NPM Û V\_€X T]^ V R„O¯bcN‡uNSTnT]NT ƒ›NPá OQN\Í† X ^ â w L u`ßCNPO]wèR

(34) u ã V RrNTˆ

(35) wèT L ^€uˆ NT]N L b  wÜÛ V ^ L wYuSuN K T N M \ Ý ` N Q T € ^ S N W R. O w ] O Q O ^ w S N p ~ N S u a ^ N u w N N Q O S N p ~ P N Y R T X á L L L ƒ _ E X L X __b Nw =N< K„KET _ LL]w\NV ^€OQOQ_ N/^NPL O b bcL  N Xw KERu K½V w R„V\X LOnT]^xTQbNN XEX„N M LL L N O†L bEX ~Nq^NvuwpO

(36) NqN T ~X L wÜwèOÛÌRV w XR X O]ç[u L wYbc^yu¬TvN YOL wèXENP^€uL R„ƒT OQVYN ^½XL † u T Xƒ YNN\LXÞ _wY< î  uNS_ ON‡RWOnV w NPRUX ~ T¯O][Ew\u_^a^€NqR„NSOQR„bc^EuSNvN NPOXOP~pÞE_ w/æ

(37) NS~ çEu ƒu [EX wèL OQR„NPNOCuSgSN\ðÎb è~ X NSVT > ^XE_ NL]KW VYu V\XE† XEL X L ^W_ w w ~  _aN\VYVèXERUbcL TN bE; _N w\^ XEL ^yNTL bcNPOtT V\XEL R XEL NPOCNT ~pN L u^ K½V\X„LZ_ N‡T]NS~ K O wYuSu VYL b N\M Þ ë ˆ s |;wÜÛYNPu¬† X ^guNH; X T X R KE_ wè^xOn^ L bcN K„L NPR„b L N X R uSw(; N\M   æ  R „ ? µ R „  p ~ N  u ^  w T ] T P N O v N O N O E R E R P N  O b L á \ V X _ K L V X s ë bcOnN ^€O]uL NX T TQLQN VYL X  Û\NPM N u L ƒ w w\R [  ^€NSN RUL TÞ V < Tw¿Þ TQëNPw\Nv~hO L ‚NPR„ä u V|CRUêT Læ'NPk`O¬ˆ bc^€Û\N T LVYOQX NPTqO‡b NPR„w O [½X V\^yT]L NPbŒOžzWzÝ Ý X XEwè_ Rµ^€NS}R±|  NvM é u^ ^ _ X NYOQ N à K„Kw\RENY^€N ßC_ NSNRJTq>nÝw\V~pR„^awèR±T  ƒ â w\Rw _ NV }R  Ý\NvwèRcð“ˆ^€N L]L NYU‚ L RWw X b› s Í_ ÛÌwè^€RrNTZT VYX OZuN X çr† X NU>  wè^ VYXE[E_ ^ NM ÌÞ ë Ý\bcNZN‡T]ÛU^a^€NPN\w¬R„cbOC^€R„XEb L„bcV NP^xM R„O]N uO bV wá u X ^xL w RENP[„N ~p_ NvT N ƒ›OZL NPáubcOQ^€N`N N L T RETV\NqV\X X OnTQNNO¯L„~KENvM L]NvO V XOÁb ~pw\X ~pNu¿T]^€K ^ OÁV wYRr† O¯X †O]^IuXa; ^€VNSw/á RURUTQTtbc^=N ?W† †X_ w/XNN¬O]uuNv† ^€O

(38) NSX R„T^›LuSNPwÜN\OnÛ́YTPw NSEXRbEçcNHT V\; ; V X wèRUTÁ^aTPTCuPcw w\NSX O¯R O]NSOnK Rž^Ww NPuL u NqT]ƒE^aN† VfX K w/á ^WN ~pbEL ONPNV OÁREu ~ REV R„NV _€~puS_ NN\NSLÞERUREæ

(39) T]N\TO Þ KEX ^xO[>œN L NP~pN L u^€N`† X ^>œN¬ÛYN X ç. â ë VT\V\X X ÛYT Ý\N LN K½T V\L _ XENSNP~pLtO XKWN LRVYuSL ^aR T]NfNPV Ot~b Vb [ER„ LX užNRrT^€R„~V\uSX V w T R„_ u KbcXEN`w _ Lw ^aT]~[E^€u_ wNqXE _ b ^^€NR„á ^aL wèRWNP^ Oœ~L TNYwèNP RURU_ T]wT OtLEb NvM wN wèƒ_ RU^yTbET N Mƒ„^  V\ÛÍà_€^ V\L LT ^xX ^€OQNN OP_€NS_ N Ttk _bE_ w ^€N Û\KEN\[½_€gVX ßCROCƒ N ÛÍNL ^aTXENPV ^ L _€Þ_ NSN‡â T b N X L X u~ uS^ wEVwá  R„_ K½bEwV\N\bEXEÞ ^aâLÛÍ^€~REwè^xNSOt ~pwÜOÛ NSX„V RUL^ TLð uå ƒ L wèw R„V TQuS^xN † XNTÁNfwYR bcN MN [EK XETQ_NN XbcOQN N _ w êq; w\L bw\LR„wEu Þ ƒ ÝYVYN X ^L _aNS_ w~pL Nb L “uN ^€NfuPwèßC~NSwRµL  w\uSbEN N _€L _aX„^aNt_ N NSRpK OT] N L]u L ƒ„wYV\OQ_€OQV\N‡ ^xz\† T X X Nf?„w REX ^ L w\êqOØEw  X KEˆ

(40) L NPwè~pRUT ^aNƒtLN M V [ RµNPÞ w â X ;qN L bcuN ^ s Kw*á N ÝYL ONPV w\RERAR„iÖNPOZ†Ý XEX _NU^aN>  w\wè^µ^€R„u OQL]^ZV ^x† O X NSM Nvxwá OÁwÜÛYV\NPK„u ƒ [W^aN V R K½ƒ V\N XEX„LpL Þ_ N XEL O V\X T]^aNPR w5á bc^xOœTwèR„uSN\Þ

(41) ñ R \L wèR„b.~pN L u^ wá T V\X T]NPO _ NPO w X u æ

(42) V Tg~ O KXETL VT VY^ L X TPO>œN L NP~N L uS^aN¯T VYX OuSNPO u V ~ K w  R V R„ObcNTw [½V\XKWVYXEL uNTQTQNtOn^€R„u Ná L N¯wè~p^aTQ^ N\M ÞÜäZNPR„bcNgSðÎÛ V\X O Ku ƒ ^=gw gP_€Ý\wè_ NNPðR; T]L  ^a^yT]NPNvNPR„OqOPOO  V NS[ RURNPT ?„^  RKWREV NwáOQTOQOL^ [ENPbc~p_ NvNO‡N LuSbEuw wè^€_ N wèR„L{~O‡_ uSwNfNL ê`On_ð ^aLØ N ^eXgf† XwÜbEÛ\^CNNv~ uu XE wO]_ T]w N R_ w\VY bcXEw\NSL]Onð LT[ ^L]w V K L R NPVNSR„Tp~pbEwèT]^€† wRUXL TTQNYNT Þ½L]ßCwV X^x^ O{ uwèb ^aRWT NPM L]OSbcV Þg^xR•uSß wYL~puw\NNOQNLw ^aL]X R V \ð‘s ~pXtwèNPM^^€N_€RY_ TNPz Onå ðT ; V\NNM _XX ^xuO^ _€^€_ NS_NPNPR±OPO  bcN L RE^€N LZL NS~ K w L T bEwèRWO _ wpu VYXEL OnN‡w X ÚEÞ Ù

(43) W L Nvu V\L bž~ V R„bc^xw _ bcN _ wpbc^€O]u^ KE_ ^aR„N\Þ ˆ L Þ é L èw ^€R. 1 % (23 (4v vu y( vt sv x r v% u  #p v p -x3X(6v5   v v p x #y y tr  t v Xv!_v"(v t "y pXp v#" p v$&% y p x')("*+( t  v u z y,-"*"./ v v p 0x Xv.

(44) H

(45)        H

(46)    ë NPOCT L wÜÛÌw X ç KELENPM OQNSRUT NPM OÁbEwèR„OZuSNTQTQN‡T ƒ±NPá OQN V RUT b V RER N M _ ^€N X,wá KE_€X On^€N X„L OZw L T]^€u _ NvOZbcN L Nvu ƒ N L u ƒ N‡b V RUT Û V ^xu^ _ w _ ^xOnTQNz.

(47)   !  ÝW*,Þ é +.L -0w\^a/#R8*iË4M‚{4"-:ބNßt&E)2w 1*L]L $ow N4X c3"ì )P&(X /=&Ju _- ÞW5 ˆ ƒÍ /=KXOS37ÞEß#698J"%5&$'(& cØè)#ÙY3 Ù\7Ú2;:Á[Ø)(èï-6JOK.3(4!&M)P=<>a79 ÝWC Þ D„é &E)#L $Ew\D ^aRµ6E36‚// ބ$3GßtF#w N(L]- L w C X Xi&P4IN(ˆ -:Þ &Jf$7{dwèRUTQ/ ^΁E/=&Mˆ )IƒÍH9 JcOPÞENJäZ/=#NS3HÛ}7Þ K3à ""?!& &J-:Ø\PKÙ\<LÙ!:q( A-6@PJÙ &J

(48) U$ÙB@v-:AÚ M NJJ/=N)IHONU-O&Js7$8

(49) P NR&J„3P3L< / NJ!"#$ N'-:Q8RPNsKS85 &M)$oNJ-P3 ˆ / Þ f / Hcw\&JRY5KT]^ E/ ÝWÞ-:&Jé "L Vwè6b^€R\Pi)P&S8 ‚/NWބF ßt&

(50) w LQXZY'L w [ X \Íˆ <6 ƒÍ 79OPÞE#äZ!3PNSÛ}N(Þ 5&à (/]"U3"T )I1^ Ø\&(Ù\-`Ù!_6( 3A)I1„@P7Ù /=

(51) UK <2Ù\KMÙU7Ø 357$$o- / /=&E)2HaJcNJ/=7P 3C)O&(/=&J-AD &MK(&J$NJ ‚{* 3Pބ$ßt-:NPw 4BL]1L w8XX36c)P|q&J/cÞ f'å -:N MNL]K(V !R )#$i NJÝ„Þ Ngé FiL h0w\^aR±)-:ENX‚q3)POœTNOLQ4"VYKE) ƒÍ/ /=OS&EÞc)2ÝWH9ÞcJ bcNJd?/ee 63lØ\7 Ù\Ù!&a( AM NS@P^jÙB@fU( /=&(5)IHS<k3C)P&J/= + N(-6/=K ‚{NRބ&J„ßt3Pw 3LL]< L/ w NJX !U"ÝW#Þ $ é / L /ewè&M^€)IR\Hni JcNJs /=ބ#3c‚ _&JNS$,çÍ$ZN 1! 7NPÛ½MEJ.ˆ :oƒÍ P OP/Þ ë QNS8MTnN(TP5KÞ½Lß#$Z1!lc m%$6 7ÎØèÙ\Ù I3

(52) 26AN(@5&@J

(53) /`7$8 NgFa3(4!&M)P â ÞBp X Þ f ƒE_€V\K½V Û}Í‚{ބßtw L]L w X i Ý„Þ é L wè^€R±½| _ w\O]OSÞ j X w\RUT X / ~ é L wÜÛ C &c:Bd NJ!36Ø\$Ù\-:&(Ù\7Ú2!$q3 @r!N(s(o$x1IN'7-:y6&(]1I7$NJ75N9tNOdEfU-:!Ns7KJ$z8 !)NW$FHN($xuR1I =C 8v&(fU-6/{-68}7| N(%-:7KJX&(-P/ 3 /=&E)2HwJ N(/= X&P4IN(-:&J$NJ &J"K ‚{äZNPÞ\Û}ßtÞ w à L]L w "cX & Ìˆ ÎØèÞ ÙYs Ù)w ( _ CwÌT]ÙY^ Ú\ ï)é (\Þ Ù!s s N L ÛÜw\RUTP å Þ àqV R„wèT V èÝ„Þ é L wè^€R± à Þ â w XEL ^€Ri?ä¬Þ ] wè^ _€_ NSTP\ˆ ƒU OPÞ - &J/`)_& < - /=#7~6c&(-`H4h &($$o#- &(5KON &(/=&M)$) * !$ 45-:N($GN(I3.

(54)  4€E ! ] S] ‚c ÝW/ Þ é / HOL w\NU^aR-O&Js$'7$GN(&(/„ƒ€EC NSbR FKE3PL„3PNM N(K Rw L =wÌ8KT]^ V NRR &J„KW3PVY3LXE< L/ ˆN(!ƒÍ" #OQ$^€uP/ O /eë &MN)ITQHnTQN JcL ONJ/=#3 ÝW† Þ !é &J%$L w\^aR8 iË/ ‚{N(ބ5Kßt4w L]35L $Gw &(X $G#Í3NSR &J-:KEN(LEN M5KK w L/ wÌ&MTQ^)IV HR J KWN(VY/=XE63L ˆ ƒÍ On^xuSw _ äZNSÛÍ^€N h ÝWNRÞ é 5L w\-:&J^aR8/B5 iËN(-6‚{ބ&(ßt/ F36w oL]L w F#X NJ-AÍNS3"R cKELEN)M K/=&Xw 3PL 36wÌ)PTQ&J^ V /‡R 3CKW)O&(VY/=XE&JL- ì + X &(u X_ Nviw 5aL ˆ 5)ƒU $OQNJ^€I3uPOR7t:[-6XPK / &M)IHdM-:NJ"K. ^€^a^.

(55) ^aÛ.

(56)         

(57)     9‚?c‡ ‚?E.! .‚?E %‡   ‡ = S‚ G E ‚c.   U. B

(58) -    Ò cÒ¯Ô

(59) ԯРUÓ!#Ó"   $ T % 'K)(4 ‚?+-* ,7G  & d & .ØcÞ 1 @ 0 ë Nv]O KE2 LU^€R„ uS4  ^ K 3#NPOZ bc9N ! S_ wpBäZ N _ wÌT]^aÛÍ^aT N M é NPM R N M L w _ N,ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 56 / ØcØcÞÞ @\@\ÞÞ Ø@ ë] NvNPR„O OQKEN L XE^€R„L O`uS^ Þ`K NPÞ¬O Þ¬bEއN Þ¬L N އ_ wèÞ¬TQ^€Þ‡ÛU^aÞ¬T NqM Þ¬NSއTÞ¬b œÞ`NPM † Þ¬X އ^€ÛÜÞ¬w _ Þ¬NPR„Þ‡uNެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ @P6Ù ØcØcÞÞ @\@\ÞÞ

(60) ï îæ¯RU† TQXN L]wèKETQ^LEV NM RTwÌbcT]^NPV O R 

(61) 

(62) N M NV M V b ~ NvM OnNSM^xT† L X ^€†NPOÁX N NT NvÞ¬M † Þ`X wÌÞ¬T]^އV R„Þ¬OtÞ¬b އ æ¯Þ¬^aRWއOœÞ¬T]NSއ^€R"Þ¬Þ¬Þ¬Þ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ @v@

(63) Ø c Ø Þ @\Þ ( àN M L ^aÛÌwÌT]^ V RrbEN ë ^aN¬NST Û\Nvu¿TQN XEL bcN f ^ _a_ ^aR  އެއެއެެÞ`ެއެއެެއެއެÞ`Þ @

(64) ë ØcÞ Ø ØcÞNvØcOCÞ @ T L]V\X ë OtwR ~ V ^NML T O'L ^x† Þ`X N¬Þ¬bcÞ¬N އs Þ¬u ƒ„Þ‡h Þ¬w އL gvÞ¬OQu Þ¬ƒ ^އ_ b2Þ¬Þ`Þ`ެެއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ @P@Ús ØcØcÞÞ ØcØcÞÞ ïØ ]µs ^€L]R V\\X XEOt_ w R L V ^a^T L NYM OZ wƒ„X V\L bE^=g N V _“wRrá bENNTO_ wp OnäZT NSá N ~p_ wèNPTQOt^€ÛUbc^aT N¬N M u é VÍVYNSM LR b N M V L wRE_R N'NPM NPO{އެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ Øè@76Ù d ïEÞ @8 Gâ !9 wè4* ^xO GOw† 7 :n^ ‚% SÞ` Þ¬ <Þ¬;=, އÞ¬Eއ Þ¬އ ެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ &cØèlÚ ïEïEÞÞ ïØ æ¯]tOƒtK N M w\V\uSL K½N`^aN`V\wÜXEbcÛYL N NPu`XEë VuV V ÛY@R„N Oœ_€V TwèuRUTQbcN¬N u _V w OQ~ \L VYwÜ_aÛÍVY^y T^xw̆ TQX ^ VN R Þ`Þ`ެެއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ Ø)Ø)ss ïEïEÞÞ ïEïEÞÞ Ø@ ]]tN ƒtL N M~pV\LN¬^aN‡bcNbcN é ë w V X ÛYOQNOnð“_€Vß uV  REREއNST?ެެެއއެެÞ`Þ`ެެއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞ ØØ rr ïEÞ

(65) ]tïEÞ ƒt

(66) „NÞ M @ V\L ^aN`ë wÜwÛ\TNPVYu`XEbcL ^€~pbcN NSR„f OQ^w V _aR„X O gvwÌO ð XEf KE_ KENP_S^aNPR M ~Þ¬NPRUއT]Þ¬wè^ Þ`L NPÞ¬OއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞÞAï\Ø>6Ù ïEÞ

(67) „Þ Ø ë N¬~ V b Ná _ N‡‚ à`à NST _ N KEL]V\[„_ NPá ~pN`bcN _ wê ^ N M L w L u ƒ ^€NpÞ¬Þ¬Þ`ެއެއެެއެއެÞ`ÞAïB@ BcB. ?/Ó!" @

(68) ÔÒAtÐÓËD.Ð ÔBEÒAtÐÓ2Ó  C¯Ð.Ô¯Ò $E.  = S‚cG.G‚c 4F=; ) B ] ‚c S‡. DD. d?l

(69) „Þ @ j X wèRUT]^`?WuPwÌT]^ V R b X u ƒ w\~ K O]uSw _ wè^ L N¸Þ‡Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞAï)( „

(70) „

(71) ÞÞ @\@\ÞÞ Ø@ |j ƒEX VN ^a_ ç† X bcNPN OZ_u œVNM TR„wÌOQTZ^xb ÛÍN M ^€L bcwÌN T]^ V R„Þ‡OCÞ¬bcÞ¬N/އO Þ¬~ Þ`NSM Þ¬T L އ^aNhެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞAÞAï\ï\ÚÚ „

(72) „

(73) ÞÞ \@\@ ÞÞ

(74) ï jj XX wèwèRURUT]T]^`^`?W?WuPuPwÌwÌT]T]^^ VV RR K½K½V\V\XEXELZLZXX RR VYVY[[ OQOQNN LL ÛÜÛÜwèwèTQTQNN XEXELtL _aNSV R^aRUu T]ƒÍw\X ^aR#TQN Þ¬_ ^ [EއL NÞ¬Þ¬Þ¬Þ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞAÞAï!ï!ss

(75) „Þ Ø ë N¬O K Nvu¿T L N¬b œNSM ~p^xOQOQ^ V Rrb  X RrT LQVYX R V ^ L Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞAïr „

(76) Þ ØcÞ @ àN#M ?„RE^aTQ^ V RbcN¬uSN/O K NPuT L N:ެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞAïr. Û.

(77) ÛU^.  

(78) .

(79) „ë Þ ØcÞ Ø ë wT L wèRWO_; VYL ~wÌT]^ V R bcN/ß VY\V\_ > XE[½V Û Þ‡Þ¬Þ¬Þ‡Þ¬Þ‡Þ¬Þ‡Þ¬Þ¬Þ`ެއެއެެއެއެÞ`ÞAïr

(80) „Þ ï ë œNM TwÌTZ† X wèRUTQ^x† X N ެެއެއެއެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ Y

(81) Ù

(82) „Þ

(83) œNSM ÛÌw KWVYL wèTQ^ V RfbcNvOCT L]V\X OtR V ^ L O#ެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ Y

(84) Ù

(85) „Þ ( ]tƒ N L ~ V b R„wè~p^x† X N`bcNvOtT L]V\X OtR V ^ L O:Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ

(86) %@

(87) „Þ c( Þ @ 

(88) ë N L O _ wT ƒ N L ~ V b R„wè~p^x† X N‡bENPOCT L]V\X OtR V ^ L O1އެއެެÞ`ެއެއެެއެއެÞ`Þ

(89) %@

(90) „Þ c( Þ Ø s NvO KEL ^€R„uS^ K NPO bEN _ wT ƒ N L ~ V b R„w\~p^€† X N އެއެއެެÞ`ެއެއެެއެއެÞ`Þ U

(91) Ø

(92) „Þ c( Þ ï NPu V R„b KEL ^€R„u^ K N 

(93) NSM R N M L w _ ^€O NM އެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ Y

(94) ï

(95) „Þ Ú ä NvM O X ~ NoM އެއެÞ`ެެއެއެއެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ

(96)

(97) l ! 7:G ‚ E j 2)B  'E  GB)O‚?E   $‡" (cÞ @ æ

(98) T X bcN¬bEwèRWO _ NPO K w\uSN¬bcN/u V R? \X„L wèTQ^ V R wá X R„N K w L TQ^xu XE_ N އެެÞ`ެއެއެެއެއެÞ`Þ

(99) s c( Þ \@ Þ @ î毆 X wèTQ^ V Rb  V R„bcN L w\bc^xw _ N"ެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ

(100) s c( Þ \@ Þ Ø RUTQN L]KELENM TwÌT]^ V R OQNS~p^yð“u _ w\O]OQ^€† X N¦Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ F

(101) 6 c( Þ \@ Þ ï äZNPO V\_€X T]^ V RrOQNS~p^að‘u _ wYOQOQ^€† X N1އެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ (]@ c( Þ Ø ‚ KEK„_ ^xuSwès TQ^ V Rw X çfNvO K w\uNvOœðÎTQNP~ K O wpá u V\X„LQ[EX„L N`R N M  swÌT]^aÛYN6ެއެެÞ`ެއެއެެއެއެÞ`Þ ( r c( Þ ØcÞ @ K NPu¿T L N¬NPR NSM REN LQ ^aN‡bEwèRWO X Rñ RE^€Û\N L OZs ‚qb s ެއެއެެÞ`ެއެއެެއެއެÞ`Þ ( r c( Þ ØcÞ Ø æ

(102) TwÌT]OZ† X wYOn^að“OœTwÌTQ^ V R„R„wè^ L NvO¯NPRNPO K w\uSN ‚b އެއެެÞ`ެއެއެެއެއެÞ`ÞAÚ

(103) c( Þ ØcÞ ï | V R„u _aX On^ V R ެއެއެއެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ ès Ø b % )  c‚%G  j‡ n  j Is %  'G GBG. ;„G% G  :G } "cl ÚEÞ @ äZN K„LENvM OnNPRUT]wÌT]^ V RfbcN u ƒ„L"V! bc^aR  N L NPRfs T ƒCN M VYL ^€N‡bcNPO u ƒ wè~ K O`އެެÞ`ެއެއެެއެއެÞ`Þ s ( ÚEÞ \@ Þ @ 毆 X wèTQ^ V R ; Vå R„uTQ^ V REREN _a_ N¬bcN u ƒEL#V! bE^aR  N Ls އެއެއެެÞ`ެއެއެެއެއެÞ`Þ Ìs Ú ÚEÞ \@ Þ Ø æ¯O K w\uSN¬bcN V už NSR L N KEL„NvM OnNPRYTwÌT]^ V RfbcN u ƒEL#V! bE^aR  N L Þ¬Þ`ެއެއެެއެއެÞ`Þ ss ÚEÞ \@ Þ ï ˆ L]V\K w  wèTQN X„L † X w\RYT]^€† X NެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ \r Ù ÚEÞ Ø àNSM Û\N _aVYKEK NS~pNSRUTZOnNP~^að“u _ w\O]On^x† X NެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ rB@ ÚEÞ ØcÞ @ ˆ L]V\K w  wèTQN X„L‡wá _ VYL b L N¬OnNP~p^yð“u _ w\O]On^x† X NÖެއެއެއެެÞ`Þ¬s އެއެެއެއެÞ`Þ rB@ ÚEÞ ØcÞ Ø ‚ KEK„_ ^xuSwèTQ^ V RŒz„u ƒ w\~ K O]uSw _ wè^ L N _ ^ [„L N‡NSRNvO K wYuN KE_ wÌTZNTbEN ^yTQTQN L ެއެއެÞ`Þ r)( ÚEÞ ØcÞ ï ä Ná \_ N`bcN/† X w\RUTQ^=?WuSwèTQ^ V R5z KELEN M _ ^a~p^€R„wè^ L NPO"އެއެއެެÞ`ެއެއެެއެއެÞ`Þ r 6 ÚEÞ ï à ^xO]u X O]On^ V REð‘‚~ N M _ ^ VYL wèTQ^ V í Rc𓈠N L O K NPuTQ^€Û\NvO‡Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6YØ ÚEÞ ïEÞ @ ˆ

(104) w\O]OQw  N`bc^€O]u L NT u V RUTQ^€R X ެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6YØ. ÚEÞ ïEÞ Ø |Cw _ u XE_ bcNPO KEƒ w\OQNPO¬Þ‡Þ¬Þ‡Þ¬Þ¬Þ‡Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6YØ ÚEÞ ïEÞ ï |ÁN/b NPM Û\N _€V\K„K NP~NPRUTCNvOœTQðÎ^ _±KELENPM bE^€uTQ^ [E_ N @ ެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6\ï ÚEÞ ïEÞ

(105) ˆ N L O K NPuTQ^€Û\NvOqެއެއެއެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6

(106) 5l " ,B] å ‚% S] ‚? %$ E1* GO10 B 2U   3# 9! SB sÍÞ @ wYu¿TQN XEL OZbcN¬u V\L]K O YL ^xO`z 

(107) NPM R N M L w _ ^aT NvM OlÞ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6)( sÍÞ @\Þ @ àN#M ?„RE^aTQ^ V RhެެއެއެއެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6)( sÍÞ @\Þ Ø æ

(108) çcNS~ KE_ N¬b  X R u ƒ wè~ K OQuPw _ wè^ L N‡O]wèR„OC~w\O]OnN`ެއެއެެÞ`ެއެއެެއެއެÞ`Þ 6\Ú sÍÞ @\Þ ï ˆ

(109) w L TQ^xu XE_ NPOtwÜÛYNPu`O K ^€R އެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙ%@ sÍÞ @\Þ

(110) |Cw\OZbcNvO bc^€~pNSR„OQ^ V R„OZO XEKEKE_NSM ~pNPRYTwè^ L NvOÖެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙUØ sÍÞ Ø å wYu¿TQN XEL OZbcN¬u V\L]K O YL ^xO`z„uSw _ u XE_ OtR X ~ N M L ^x† X NPO`ެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙ

(111) sÍÞ ØcÞ @ ˆs L ^aRWu^ K N 

(112) NSM R N M L w _ b XrK„LQVY\L wè~p~pNrެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙ

(113) sÍÞ ØcÞ Ø KtNvM u^=?Wu^aT NPM OtOnN _aV R _ NPOZuPw\O NSM T X bE^ NvM OfެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙYÚ å sÍÞ ï wYu¿TQN XEL OZbcN¬u V\L]K O YL ^xO`z LENPM O XE_ TwÌTOÁé NSTO K NPuT L NPO3ެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙ)r sÍÞ ïEÞ @ ä NvM O XE_ T]wèT]OZwÜÛYNPuTQN L ~pN¬bcN w X O]Onð‘ß V R„RENT އެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PÙ)r sÍÞ ïEÞ Ø ä NvM O XE_ T]wèT]OZwÜÛYNPu`u V RWOœTwèRUTQN¬u V On~ VY_aVY ^x† X N’Þ‡Þ¬Þ‡Þ¬Þ‡Þ¬Þ¬Þ`ެއެއެެއެއެÞ`ÞE@vØ\ï sÍÞ ïEÞ ï ä NvM O XE_ T]wèT]OZOQNS~p^að‘u _ wYOQOQ^€† X NvOއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@Pï!( sÍÞ

(114) | V R„u _aX On^ V R„OCNST K N L O K Nvu¿T]^aÛYNPO އެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PFï 6 sÍÞ

(115) „Þ @ | V R„u _aX On^ V R„OŒÞ¬Þ‡Þ¬Þ‡Þ¬Þ‡Þ¬Þ¬Þ‡Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@PFï 6 sÍÞ

(116) „Þ Ø ˆ N L O K NPuTQ^€Û\NvOqzI; w\u¿T]N XEL OZbcN¬u VYLQK O \L ^€OެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@

(117) UÙ sÍÞ

(118) „Þ ï ˆ N L O K NPuTQ^€Û\NvOqzET ƒ N L ~ V b R„wè~p^x† X N¬bcNPOCT LQVYX OtR V ^ L OtÞ¬Þ¬Þ`ެއެއެެއެއެÞ`ÞE@ (\Ù.

(119) UÛ ^€^ m .rEÞ @  =ë SNv‚cOZGu .V GRUT ‚cL w\ ^a4RUTQ)Nv‚ OC Nç ;KtN MqL ^€ ~p‚cNSRU GT]w_ Nv EOÁOwYu¿GT ‚?X !N _€?_ Nv!O#އnÞ¬Þ¬:  އ Þ¬'އGÞ¬ އެެÞ`ެއެއެެއެއެÞ`ÞETB@ l%(\d ï rErEÞÞ @\@\ÞÞ Ø@ || VV RURUTT LL wèwè^€^€RURUTQTQN¬NvO bcK„N LQ_V w ÛYNSKWR„V w\~RYTZ~pbcN•NvOZÞ¬u އV\_€Þ¬_ ^€Þ`OQ^ VÞ¬REއREÞ¬N XEÞ¬L O*އެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@@ ( (

(120)

(121) rErEÞÞ @\@\ÞÞ

(122) ï æ| RV RULET NPML O wèX ^€RU~ TQNNvM OCÞ¬wYÞ¬OœT އLQVYÞ¬KEއƒÍ Þ¬On^xއ† XÞ¬NPÞ¬OCއNTÞ¬u Þ`V OQÞ¬~ އV\Þ¬_€V\Þ¬ ^xއ† X Þ¬NPއO¯Þ¬Þ¬Þ‡Þ‡Þ¬Þ¬Þ¬Þ¬Þ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@@ ()(\Ú( rErEÞÞ ïØ ˆ| L]V V RUb T LX wèu¿^€T]RU^ VTQNvR OCbcwYN‡OœT T LQLQVYVYKEX ƒÍ R OnV ^x^ † L{X wá NPO _œNPM u އƒ NÞ¬_a_ Þ¬N‡Þ‡b X0Þ¬Þ`] NÞ¬ އެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@@ (\(Úr rErEÞÞ ïEïEÞÞ Ø@ ˆ| L]V V RUb T LX wèu¿^€T]RU^ VTQNvR OC u w V _ OQw\~ uTQV\^x_€† V\X  Nq^x† NSX T NPLO{w އ YV Þ¬REÞ`RENPÞ¬~pއNSRUÞ¬TtÞ¬u އV OQÞ¬~pއ^€† Þ¬X އNjÞ¬Þ¬Þ¬Þ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@@PÚY( 6Ú rEÞ

(123) rE| Þ V

(124) „RUÞ @ T L wè^€| RUTQV NvRUOCT Lw wèXE^€KERULPTQNPNvá OCOÁbcNPRrNvO T uƒtVYN M _aV\_ ^€L OQ^a^N‡V REbcNREN é XELw OŒX OQÞ`Onð“Þ¬ß އV REÞ¬REÞ¬NST އެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@P@PÚFÚ 6s rErEÞÞ

(125) „

(126) „ÞÞ ïØ å| ^aV RRUT bcL N¬wè^€ÛÍRU^€TQN‡NvOCbENPO OtXELZT LQ_ VYwX u OtV R R„V OœT^ L wèOqRUTQz N‡NM T u X V bcOn~NPO VYK„_aVYLEN M _^x^€† ~pX N.^aRWwèއ^ L Þ¬NvOpއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE@@r%s(@  

(127) . BcBcB ?F Ô¬ÓÐ  Ó @< ¯Ñ  ÁÒœÓ $  5 3q F Ux G‚c.! 4= ! = S G jB   G

(128) K 5 ] T m ë 6EÞ @ NvOCT L]V\X OtR V ^ L O KEL ^a~ V\L bc^xw X ç™Þ‡Þ¬Þ¬Þ‡Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@rF6 6EÞ @\Þ @ å VYL ~wÌT]^ V RrbENPOZˆ¯ßtê އެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@rF6 6EÞ @\Þ Ø | V RUT L wè^€RUTQNvO VY[ OQN L ÛÜwèTQ^ V RER„N _€_ NvO Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE@76YÙ 6EÞ Ø ì VYX Û\N _a_ NPOtu V RUT L wè^€RYT]NPOtO XELZ_ N/O K NPu¿T L N¬bcN¬~wYOQOQN އެއެއެެÞ`ެއެއެެއެއެÞ`ÞE7@ 6UØ 6EÞ ï | V R„O NvM † X NSR„uSNPOCu V OQ~ V\_€V\ ^€† X NvO އެެއެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞE7@ 6!( Te @PÙEށ]@  ë !* N  KEL]'KV\[E‚?_ÎxNPá S~ N‡ Gbc N K_ w Bâ wÌ)T] ^ Ná KL N‡!ì V  ^ L N އެÞ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`ÞET 7@ 5 6" s @P@Pللބބ@Y@YÞ„Þ Ø@ îj R„X bcN ^xu_ † NvXO NPV\OZ[ uPOQwèN R„L ÛÌbEwÌ^€T]bE^ wèV T]REO REâ N _ O`wèTQÞ¬^ Ná Þ¬L N‡Þ‡ì Þ¬V Þ`^ L Þ¬N¦Þ‡Þ¬Þ¬Þ¬Þ¬Þ‡Þ‡Þ¬Þ¬Þ‡Þ‡Þ¬Þ¬Þ‡Þ‡Þ¬Þ¬Þ¬Þ¬Þ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`ÞEÞE7@@76)6rs â @PÙEÞ Ø@P@PللîÞ„Þ ØE@Yâ Þބï@Aˆ¯OZˆñ b„L]R Vwè?R„[½_O V RbE_ NPNPOtuSO w\~ ƒ R„w Vbc_a^xb V bENáOZwÌ_ NvTbcOtN â NçÍwèTTQwÌL^ T]NáwÌ^ L ð“Ná N`bcL ^€N‡ì ~ì V NP^ VR„L ^NOQL ^ @NËV REއއREN Þ¬Þ¬_ O9ެެއއއެެެއއއެެެއއއެެެެެެÞ`Þ`Þ`ެެެއއއެެެއއއެެެެެެއއއެެެއއއެެެÞ`Þ`Þ`Þ}Þ}Þ}ØèØèØèÙ%ÙYÙ%Ù@@ @P@PللÞÞ ØEØEÞÞ ïØ îà RÍNPÛ\R„NPOQOn^yTQT ^ NM wèL TQN ^ _ V ^x†R„X OCN NSç Þ¬KtN MއL ^aÞ¬~pއNPRYÞ¬TÞ¬w _ NPއOËÞ¬Þ`Þ`ެެއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`Þ}Þ}ØèØèÙ!ÙYï( @PÙEÞ ï à@PلNM Þ TQï„Nvބu¿@ T]^ Vs R V\X„^€LR„uSbcN`^ L NSNvT u¿T]KEN L]V\K K w w L  wèwÌRUT]T]^ V ^ KER L]V TÞ¬V Þ¬R„O އ Þ¬w Þ`_ w\Þ¬u¿T]އ^€† Þ¬X NvÞ¬OhއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`Þ}Þ}ØèØèÙ!Ù!(( @P@PللÞÞ ï„ï„ÞÞ ïØ ää NvNvMM OO XEXE__ T]T]wèwèT]T]OtOtNPNPRrRrñqä sæ à އެެއއެެެެއއެެÞ`Þ`ެެއއެެެެއއެެއއެެއއެެެެÞ`Þ`ެެއއެެއއެެެެއއެެއއެެÞ`Þ`Þ}Þ}ØèØèÙÙss @PÙ„Þ ï„Þ

(129) êw _aVp\L]X ~pN _ N X çfNT NSçcu _aX On^ V R*Þ¬Þ`ެއެެއެއެއެެÞ`ެއެއެެއެއެÞ`Þ}ØèÙF6 B 89ÔqÔ Ó Z!Ó   $!D. 9%G z‚?G ‚cGG!  'E 'E4‚cE  &UT]l

(130)  ‚? B  'G~ ‚?

(131) G  :E }o)B%x SO€!B G! x  ! &UT 5 9‚?GG ‚? &?&%d.

(132) ÛU^€^€^.  

(133) .

(134)   

(135)    

(136)   

(137) 

(138)  . )-¯ÔF

(139) ÔBÍÓ  ¯Ô  ÓÔ<

(140) ÑœÓ  q^yT]NPO]OnN/bEN _ w _€X ~p^ N á L N  ? Ø @  6 Ù)6 ( t w@P@vÙ Ù

(141) 

(142)  `¬~rÝWÞ ÞOO

(143) CW | V R„OnT]wèRUT]N‡bEN/ˆ _ wèR„u || V R„R„OnOnT]T]wèwèRURUT]T]N‡N‡bEbEN/N/ßì VYN _ TOgST ~R wèR„R ? Ú@ Ú! ïsr t t@P@PÙ Ù

(144) a

(145) W:W‡~ÝWèÞ f Þ 

(146) a

(147) aW WÜÞ O

(148)  V h V  )-¯ÔF

(149) ÔBÍÓ ,Ó’ÐqÔÒ  Ó "  æ¯] NSRE~ N L]Kt N ^€M NL wÌT X„L N â w\O]OnN ë V R YX N X„L ]â NS~ K O w\O]OnN¬bcN/ˆ _ w\R„u ë V R YX N X„L bcN/ˆ _ wèR„u ] NS~ K ObcN/ˆ _ wèR„u.  ÓA<*Ñ

(150) Ô@. 4ÓÔUӵР,Ó  Ó " „Ò  EÒ ¯Ô  ]] NSNSRWRWOnOnNN XEXELL ~bcN NM Të L VY^x† L NPX RUN T:g ] NSN RW^€OnÛÌN wÌXETQL ^ bcRN/bcäZ^ ^€NSNv~u¿T]wèN R„g@R - à ML V L à N M L ^€ÛÌwÌTQ^ V Rbc^ L Nvu¿T]N ÎØ  à N M L ^€ÛÌwÌTQ^ V Ru V ÛÌw L ^xwèRUTQN W@ à N M L ^€ÛÌwÌTQ^ V Ru V ÛÌw L ^xwèRUTQN Ø . @ éé N ! @ Ú w@vÙ

(151) aW#"¬f Ý @ é N ! @ @PÚ t@PلW$ @ é N ! @{sSr t@PÙ

(152) &%   @ é N '

(153) aW @( 6s w@vÙ

(154) CW)`~ @ N '

(155) aW;Ú* Ú!( w@vÙ

(156) &+‡O ,.-0/1 23546, WW7676  Ø  @s t@PÙ

(157)    8 -0/ :92346 <; W76  (@  Ú%=@ t@PÙ

(158) >&+ ~ ?$-0/1@92346+ ;  (  Fï 6 w@v Ù

(159) A&¬O. FB CECEDD GK DCEL DHJC I NM<OQP UL UOQCXV WP @ U UR VM5S RTK S DL C C L ] ^_^ OQV DP  M5M<U UO1RTR V SZP L Y\C W [D D]. +  Ó " C cӵРÒ$` Ó " EÓµÔBEҜÓьӵԙÓ!  éj L w\bE^aNPRYT b  X R O]uSw _ w\^ L N j XX w\w\bb LL ^y^yðð“L]bcV ^€Û\T]wèN TQLQ^ V NSRER„R„uSNNq_ b b  X X RRÛ\Û\NvNPu¿uTQTQN N XEXEL L j X w\b L ^yð“bc^€Û\N LQ NSR„uSNqb  X RrTQNPR„OnN XEL. @}Ó+@¯Ða¬Ó. bcdCW C W D=efcgD W C hK DEcdCe K C cgD c CECW D DW iKjC Wc C Y[ C]<C c ] CE D k W

(160) >l D M5RM PQm CE] e F c C n C  k

(161) >l M5RM PQm e F n Y[ ]5C n ^aç.

(162) ç. 8 a Ó"  EÒ ¯Ô   Ó!.Ó!  @}Ó

(163) ÍÓ   æÁæÁOO K w\w\uuNN s ‚ u RUTQ^ w ‘ð“bcgPO]N u s ^^aTnbÍT]NðL ‚RUTQ^ ‘ð“bcN s ^yTQTQN æÁO KK w\uN s u ƒ„ƒ„hh w LL gPO]u ƒƒ ^ __ bÍð é w X OQOnð‘ß V RERENT L. . æÁæÁOO K w\w\uuNN æÁO KK w\uN.  .   .  . ssE‚ é ‚ œb œbs s ß. ) ¯ÔB¯ÓµÔBEÒ ¯Ô    Ò  ÓµÔ ÍÒ ¯Ô  bEbcNPwèOR„ì O KEV\LE_ NPNpXM uPO

(164) uSw w\RX O¬V\T]^X bEV O NPR„OqKEO

(165) _ Tb w\ƒtVuN N^€M Û\V\LQNPLV RU^€R„NPT OO N<

(166) X T NPMLO R XN N MN K„L _€wL_ Nv^x_ OnONPNv~wO¯á NP†

(167) RUX Tgbcw\bER„^€~pw\bR„NSRO R„VY_OQNX^ V O¯O R„ u OPOnV Þ±T R„NPáæOQ~p^€R*b NtNáuSbL NN  XL]† V R„X R„^y^T O NPuM _O V NqRWR„uPuwèw\N T O¯LXEREbEL NN N _€__T NPwrƒtOZN uM z3VYV  L R„^€NPOniT]O

(168) wèwÜRUÛYT] NPNu  bcbc N^€~piìNSN R„ h OQT^  V V R„R±@O  O XEK„KEì _V\NSM X~pO¯NSRRUVT]w\TQN^ L LQNPV OPR„Þ O¯O OœT NSM ~wÌT]^€† X NP~pNSRUT  _ NR V ~ [EL NZT V T]w _ bENqbc^€~pNSR„OQ^ V R„O O K wÌT]^€w _ NvO¯NST¯TQNP~ KWVYL N _a_ N- N_ wrTu V  R„OœT wèRUe TQN@ _ bcNCNR ì V ~ N h [ETL VNtR bcNZ bc^€K ~pN XNSR„T/OQw\^ V uPR„† O XCNO M KL ^ wÌLTQX^xw RE_ NPNOPÛÌÞ wà _ Nw\XER„L O _bcNv^ Og TN M ƒtL NSN M RUV\TQL N^€NPObcNpwqá bcuN ^€~p_€_ NpNSR„b OQV ^ VRER„R O NSM N O XEK„KELEKENvM _u NSMNvM ~pbcNSNP~pRYT~pwè^ NSL RUNvTvOS u, V\L]L NPwáO KWhV R„bcbE^€wè~RUNPTZR„w OQX ^ V uSR„wYO OCO †V XRUwYT b _ ^L NP^yM ð“NPbcO ^€~_ X NPRER„N OQ^ Vwá RE_RE w N X _ ÞT L ë N¬wpÛÍu ^xVw R„_ Onw T]w\L RYN _T]wÌN`T]^bEV N/R ì  N h T  V R W@6 4E^ , NT  _^ w

(169) ~  w\V±O]OQX á N‡ bEN/ ˆ !_ wè R„u@\ Þ à w\^ R„O _ N‡uPw\O

(170) e bc^a~pNPR„On^ V R„REN _  _ w L N _ wÌT]^ V R   g@T4, -0/   NvOœT [ ^€NSR ^ L NT LQVYX Û NSM NY^ Þ )-¯ÔB¯ÓµÔBEÒ ¯Ô   ¯Ð3Ñ  ¯Ô@ EÒ¯Ô  Ó "  WÒAtÐ Ó OK KEw ƒtL‡]µN M _ L wfVY^€†X u XTÁV NYw~ Þ XKWà _€V Vw\OQRR„w\O RYT]ubcNN¬NbcuPuw\NNqXOP~ç*_ wèw; RV ~ X^€OqO]NM u TQT L NPL ^y~^xTv† èKWX R N‡VYV\L XNPN OnO¯_aTZ_ Nw NSX„FRULQTQV ^ R„Ná LbONSX w~p›T]NPwèNSRYR„^ LT OQN N b XEw¬á NM L TQbcN ~NPL OÁ~pNSM O T ^€ RL ^€OnNP†M T N\XNPá U~NNSRNvFOCEKEDfOn_€T]X w̆ O T]X ^ bc^ V NRERER„Np_ w w\b ^ KL N M NPwK O

(171) L NPTQNSR„^€T N¬b w/á wè† R O X YNp~XE_bcNw\M N T ^ LL _^€N\wN  u; V VÍR„V\uL TQb ^ VV R„R±R ENSNSM N T L_wYw bcK„^€K w N_ N _a_ N ÍL]Þ V à R„O,w\R„; V OqR„T u¿V\T]X ^ V O`RruS~NPO‡NSM uST LwY^€OS† ½X R"&NY" VYÞ X O‡b NSM R V TQN LQV R„OuSNTQTQNpu V ~ K½V O]wèRUTQN 0 ¿›NPR T]w\RUT‡† X N.

(172)

(173)     

(174)      !# "  $&% ' " ( )$$ *V$  + "  !,. .

(175) - / 

(176)  ! .01/ 1   

(177) 1 .  576 /(81. !, 0 / ,

(178) ,1 #2 43 #243 * 9!,92:;'

(179) <

(180) >=?;@ " BA  #C)D% 

(181)   E2/1  ) ! 6 1#

(182) F$)HGHY. 5 I1:$ J$ F$ $KL

Références

Documents relatifs

Les antiprotons et les antideutérons (noyaux formés d’un antiproton et d’un antineutron) sont des sondes particu- lièrement adaptées à la recherche de trous noirs primor- diaux

On s'est ainsi rendu compte qu'une étoile de type géante, c'est à dire de densité faible et dont le rayon peut être de plusieurs centaines de milliers de kilomètres, tournant

Quatrièmement : Sans le savoir nous labourons la poussière des étoiles qui nous a été apportée par le vent et buvons l'univers dans une goutte d'eau de pluie. Car la molécule

Comme dans le cas des trous noirs en rotation de TMG [25], les conditions imposées aux paramètres (c &gt; 0 et 0 2 1) pour que l’espace-temps soit causalement régulier entrainent que

Dans le troisi`eme chapitre, nous construirons de nouvelles solutions trou noir en ro- tation de la th´eorie d’Einstein-Maxwell dilatonique pour une valeur particuli`ere de la

L’objectif de cette partie est d’estimer les effets Doppler classiques et relativistes sur la mesure de la fr´ equence de l’horloge du satellite dans le r´ ef´ erentiel li´ e au

– Afin de contourner les nombreuses difficultés liées aux théories de gravité massive et à leurs perturbations en présence de trous noirs, nous avons d’abord travaillé sur

Dans le quatri`eme chapitre, nous avons ´etudi´e la thermodynamique de trou noir de Schwarzschild en pr´esence d’un GUP `a tous les ordres de la longueur de Planck en cal- culant