NathalieineBRelativitllascGeneralkyHDeruelleo1Six LecturesCEA, January-February 20092CEA-D IRECTION DES S CIENCES DE LA M ATIÈREINSTITUT DE PHYSIQUE THÉORIQUEU N I T É D E R E C H E R C H E A S S O C I É E A U CNRSCOURS DE PHYSIQUE THÉORIQUE DE L'IPHT, ANNÉE 2008-2009Organisé en commun avec l'Ecole Doctorale de Physique de la Région Parisienne (ED 107)Nathalie DeruelleBlack Holes in General Relativity APC, Université Paris 7Les vendredis 9/1 , 16/1 ,23/1, 30/1, 6/2 et 13/2/2009. 1 – From Schwarzschild to Kerr: the development of a concept 2 – The geometry of black holes 3 – The energetics of black holes 4 – Black holes and astrophysics 5 – Hawking's radiation and black hole thermodynamics 6 – Hairy and higher-dimensional black holes John Archibald WheelerHoraires : les vendredis de 10h15 à 12h15. (1912-2008)Lieu : IPhT, CEA Saclay, Orme des Merisiers, Bât. 774, p.1A Salle C. Itzykson.Accès : Par lignes de bus publiques (269.02et 91.06) ou - navettes CREEAR: B Le Guichet vers CEA OrBmâet . 774, toutes les 15min de 8h30 à 9h45; - navette CEA: CEA BOâtr.m 7e7 4 vers RER B Le Guicheàt 12h36. who coined the wordRenseignements :ht tp://ipht.cea.fro u ipht-lectures@cea.fr–“Black Hole” in 1967romhildh:arzscerScenheimwOpptoF3Lecture Onethe DEVELOPMENT of a CONCEPTReferencesEinstein et la relativit´e g´en´erale, Jean Eisenstaedt, Cnrs-Eds, 2002English translation : Oxford and Princeton ...
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Six Lectures
CEA, January-February 2009
oaykRelativitBGeneralHincslelNathalieDeruelle2
CEA-DIRECTION DES SCIENCES DE LA MATIÈRE
INSTITUT DE PHYSIQUE THÉORIQUE
U N IT É D E R E C H E R C H E A S S O C I É E A U CNRS
COURS DE PHYSIQUE THÉORIQUE DE L'IPHT, ANNÉE 2008-2009
Organisé en commun avec l'Ecole Doctorale de Physique de la Région Parisienne (ED 107)
Nathalie DeruelleBlack Holes in General Relativity
APC, Université Paris 7
Les vendredis 9/1, 16/1, 23/1, 30/1, 6/2 et 13/2/2009.
1 – From Schwarzschild to Kerr: the development of a concept
2 – The geometry of black holes
3 – The energetics of black holes
4 – Black holes and astrophysics
5 – Hawking's radiation and black hole thermodynamics
6 – Hairy and higher-dimensional black holes
John Archibald Wheeler
Horaires : les vendredis de 10h15 à 12h15. (1912-2008)Lieu : IPhT, CEA Saclay, Orme des Merisiers, Bât. 774, p.1A Salle C. Itzykson.
Accès : Par lignes de bus publiques (269.02 et 91.06) ou
- navettes CEA: RER B Le Guichet vers CEA Orme Bât. 774, toutes les 15min de 8h30 à 9h45;
- navette CEA: CEA Orme Bât. 774 vers RER B Le Guichet à 12h36. who coined the word
Renseignements : http://ipht.cea.fr ou ipht-lectures@cea.fr
–
“Black Hole” in 19673
Lecture One
the DEVELOPMENT of a CONCEPT
References
Einstein et la relativit´e g´en´erale, Jean Eisenstaedt, Cnrs-Eds, 2002
English translation : Oxford and Princeton U-Press, 2006
Black holes and time warps, Kip Thorne, Norton Publ., 1994
Dark stars : the evolution of an idea, Werner Israel
in 300 years of Gravitation, CUP, 1987
OppScerromhildarzscenheimwtoh:F4
John Michell (1783), Pierre-Simon de Laplace (1796), Robert Blair (1786)
Laplace, 1749-1827Michell, 1724-1793 Blair, 1748-1828
see Jean Eisenstaedt, “Avant Einstein”, Seuil, 2005
Prehistory5
(box1.) Newtonian “Dark bodies”
GMF =m a , F =−m ∇U , U =− , m =min grav in gravr
22GM L L2 ˙hence r˙ = 2E + − , φ = (1)2 2r r r
2GM• escape velocity is c if r = (E = 0, L = 0 in (1))2c
(Michell, Laplace)
p• deviation of “light” : r = with velocity c at r =r :min1+ecosφ
2r cminΔφ = 2(φ −π/2) ; cosφ =−1/e ; 1+e =∞ ∞ GM
2GMif e 1 : Δφ≈ (Soldner, 1801)2c rmin
GM• “collapse” : L = 0, E = in (1) ; hence :r0
p p
r r r rπ0 0 0 0t = (η+sinη) ; r = (1+cosη) ; and : t = rcollapse 02 2GM 2 2 2GM6
All forgotten for 150 years
Revived by Oliver Lodge (1921) and Arthur Eddington (1924)
Lodge, 1851-1940 Eddington, 1882-1944
“M.T.W.” and Hawking-Ellis textbooks (1973); Gibbons/Schaffer (1979)
reason : Dark Bodies have nothing much to do with Black holes...7
Alain Riazuelo (2007) A Modern View of a Black Hole8
Early years of discoveries and debates
1915 : Einstein’s equations of General Relativity
1916 : Schwarzschild solution
1922 : Einstein at the Coll`ege de France
Input from Quantum Physics and Cosmology
1930 : Chandrasekhar’s maximum mass of white dwarfs
1932 : Lemaˆıtre’s insights
1939 : Oppenheimer-Snyder’s collapsing star
“Low-water mark” (1940-1955)
Renaissance
1960 : Kruskal diagram
1963 : Discovery of quasars
1963 : Kerr solution
y-oearsFiftofddstruggley9
: Einstein’s equations of General Relativity
November 1915 : Einstein and Hilbert’s “race” to G =κTμν μν
Albert Einstein (1879-1955) David Hilbert (1862-1943)
see, e.g., Todorov, arXiv:physics/0504179
YEarlyears10
(box2.) Einstein’s equations in a nutshell (beginning)
Special Relativity
2 i j 2 2~• Space and Time as M : ds =η dX dX =−dT +dX4 ij
α• (T,X ) represent a “clock” at rest and “position” in inertial frameS
i 0i i j 2 02 02 0 0~• X →X = Λ X such that ds =−dT +dX . T : time inSj
idXi i i• If U ≡ s.t. U U =−1, then τ is “proper time” along X (τ).idτ
idU• equation of motion of a free particle : = 0.dτ
i i i jSpecial Relativity in accelerated frames (X →x =x (X ))
k l∂X ∂X2 i j• ds =‘ dx dx with ‘ = ηij ij kli j∂x ∂x
direct correspondence between coordinates and clock/position is lost
i i˜Du du i j k˜• eom of a free particle : = 0 ⇐⇒ +Γ u u = 0jkdτ dτ
i∂x 1i j i ip˜where u ≡ U and Γ = ‘ (∂ ‘ +∂ ‘ −∂ ‘ )j kp k pj p jkj jk 2∂X
i˜inertial accelerations are “encoded” in the “Christoffel symbols” Γjk