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These lecture notes are intended to introduce the theory of rotating stars in general relativity.
H. Weyl : Zur Gravitationtheorie , Annalen der Physik 54
1917
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J. Lense & H. Thirring : Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie , Physikalische Zeitschrift 19
1918
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W. J. van Stockum : The gravitational field of a distribution of particles rotating around an axis of symmetry , Proc. Roy. Soc. Edinburgh 57
1937
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S. Chandrasekhar : An introduction to the study of stellar structure , University of Chicago Press, Chicago (1939)
1939
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A. Lichnerowicz : Sur un théorème d’hydrodynamique relativiste , Comptes Rendus des Séances de l’Académie des Sciences 211
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A. Lichnerowicz : Sur l’invariant intégral de l’hydrodynamique relativiste , Annales scientifiques de l’École Normale Supérieure 58
1941
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A. Komar : Covariant Conservation Laws in General Relativity , Phys. Rev. 113
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R. Arnowitt, S. Deser and C.W Misner : The Dynamics of General Relativity , in Gravitation: an introduction to current research
1962
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R. H. Boyer : Rotating fluid masses in general relativity , Mathematical Proceedings of the Cambridge Philosophical Society 61
1965
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J. B. Hartle & D. H. Sharp : Variational Principle for the Hydrostatic Equilibrium of a Relativistic, Rotating Fluid , Phys. Rev. Lett. 15
1965
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R. H. Boyer : Rotating fluid masses in general relativity. II , Mathematical Proceedings of the Cambridge Philosophical Society 62
1966
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R. H. Boyer & R. W. Lindquist : A variational principle for a rotating relativistic fluid , Phys. Lett. 20
1966
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W. Kundt & M. Trümper : Orthogonal Decomposition of Axi-symmetric Stationary Spacetimes , Zeitschrift für Physik 192
1966
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A. Papapetrou : Champs gravitationnels stationnaires à symétrie axiale , Ann. Inst. Henri Poincaré (A) Phys. théor. 4
1966
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J. B. Hartle : Slowly Rotating Relativistic Stars. I. Equations of Structure , Astrophys. J. 150
1967
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J. B. Hartle & D. H. Sharp : Variational Principle for the Equilibrium of a Relativistic, Rotating Star , Astrophys. J. 147
1967
Earlier work this paper cites.
A. Lichnerowicz : Relativistic hydrodynamics and magnetohydrodynamics , Benjamin, New York (1967)
1967
Earlier work this paper cites.
J. B. Hartle & K.S. Thorne: Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars , Astrophys. J. 153
1968
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J. P. Ostriker & J. W.-K. Mark : Rapidly rotating stars. I. The self-consistent-field method , Astrophys. J. 151
1968
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D. M. Sedrakian & E. V. Chubaryan : Stationary axially symmetric gravitational fields (in Russian), Astrofizika 4
1968
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B. Carter : Killing Horizons and Orthogonally Transitive Groups in Space-Time , J. Math. Phys. 10
1969
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J. M. Bardeen : Stability of Circular Orbits in Stationary, Axisymmetric Space-Times , Astrophys. J. 161
1970
Earlier work this paper cites.
J. M. Bardeen : A Variational Principle for Rotating Stars in General Relativity , Astrophys. J. 162
1970
Earlier work this paper cites.
B. Carter : The commutation property of a stationary, axisymmetric system , Commun. Math. Phys. 17
1970
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M. A. Abramowicz : The Relativistic von Zeipel’s Theorem , Acta Astron. 21
1971
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J. M. Bardeen & R. V. Wagoner : Relativistic Disks. I. Uniform Rotation , Astrophys. J. 167
1971
Earlier work this paper cites.
S. Bonazzola & G. Maschio : Models of Rotating Neutron Stars in General Relativity , in The Crab Nebula, Proceedings from IAU Symposium no. 46 , edited by R. D. Davies and F. Graham-Smith, Reidel, Dordrecht (1971), p. 346; http://adsabs.harvard.edu/abs/1971IAUS...46..346B
1971
Earlier work this paper cites.
J. R. Wilson : Models of Differentially Rotating Stars , Astrophys. J. 176
1972
Earlier work this paper cites.
S. Bonazzola : The virial theorem in general relativity , Astrophys. J. 182
1973
Earlier work this paper cites.
B. Carter : Black hole equilibrium states , in Black holes — Les Houches 1972 , Eds. C. DeWitt & B.S. DeWitt, Gordon and Breach, New York (1973), p. 57
1973
Earlier work this paper cites.
C.W. Misner, K.S. Thorne & J.A. Wheeler : Gravitation
1973
Earlier work this paper cites.
J. R. Wilson : Rapidly Rotating Neutron Stars , Phys. Rev. Lett. 30
1973
Earlier work this paper cites.
M. A. Abramowicz : Theory of Level Surfaces Inside Relativistic, Rotating Stars. II. , Acta Astron. 24
1974
Earlier work this paper cites.
S. Bonazzola & J. Schneider : An Exact Study of Rigidly and Rapidly Rotating Stars in General Relativity with Application to the Crab Pulsar , Astrophys. J. 191
1974
Earlier work this paper cites.
E. M. Butterworth & J. R. Ipser : Rapidly rotating fluid bodies in general relativity , Astrophys J. 200
1975
Earlier work this paper cites.
E. M. Butterworth : On the structure and stability of rapidly rotating fluid bodies in general relativity. II - The structure of uniformly rotating pseudopolytropes , Astrophys J. 204
1976
Cited alongside, same era.
E. M. Butterworth & J. R. Ipser : On the structure and stability of rapidly rotating fluid bodies in general relativity. I. The numerical method for computing structure and its application to uniformly rotating homogeneous bodies , Astrophys J. 204
1976
Cited alongside, same era.
L. Lindblom : Stationary stars are axisymmetric , Astrophys. J. 208
1976
Cited alongside, same era.
R. Beig : Arnowitt-Deser-Misner energy and g 00 g_{00} , Phys. Lett. 69A
1978
Cited alongside, same era.
A. Ashtekar and A. Magnon-Ashtekar : On conserved quantities in general relativity , J. Math. Phys. 20
1979
Cited alongside, same era.
J.-L. Tassoul : Stellar rotation , Cambridge University Press, Cambridge (2000)
2000
Later among the works it cites.
F. Douchin & P. Haensel : A unified equation of state of dense matter and neutron star structure , Astron. Astrophys. 380
2001
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P. Grandclément, S. Bonazzola, E. Gourgoulhon & J.-A. Marck : A multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources , J. Comput. Phys. 170
2001
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J.L. Zdunik & E. Gourgoulhon : Small strange stars and marginally stable orbit in Newtonian theory , Phys. Rev. D 63
2001
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J.L. Zdunik, P. Haensel & E. Gourgoulhon : The crust of rotating strange quark stars , Astron. Astrophys. 372
2001
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B. Carter : Perfect fluid and magnetic field conservations laws in the theory of black hole accretion rings , in Active Galactic Nuclei , Eds. C. Hazard & S. Mitton, Cambridge University Press, Cambridge (1979), p. 273
1979
Cited alongside, same era.
Y. Choquet-Bruhat and J.W. York : The Cauchy Problem , in General Relativity and Gravitation, one hundred Years after the Birth of Albert Einstein
1980
Cited alongside, same era.
K. S. Thorne & D. Macdonald : Electrodynamics in curved spacetime: 3+1 formulation , Mon. Not. R. Astron. Soc. 198
1982
Cited alongside, same era.
J. M. Bardeen & T. Piran : General relativistic axisymmetric rotating systems: coordinates and equations , Phys. Rep. 96
1983
Cited alongside, same era.
R. M. Wald : General Relativity , Univ. Chicago Press, Chicago (1984)
1984
Cited alongside, same era.
J.L. Friedman, J.R. Ipser & L. Parker: Rapidly rotating neutron star models , Astrophys. J. 304
1986
Cited alongside, same era.
J.L. Friedman, J.R. Ipser & L. Parker: Implications of a half-millisecond pulsar , Phys. Rev. Lett. 62
1989
Cited alongside, same era.
M. Ansorg, A. Kleinwaechter & R. Meinel : Highly accurate calculation of rotating neutron stars , Astron. Astrophys. 381
2002
Later among the works it cites.
J. L. Synge : Relativistic Hydrodynamics , Proceedings of the London Mathematical Society 43
2002
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J. B. Hartle : Gravity: An Introduction to Einstein’s General Relativity , Addison Wesley (Pearson Education), San Fransisco (2003)
2003
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H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers & E. Herlt : Exact Solutions of Einstein’s Field Equations (2nd edition), Cambridge University Press, Cambridge (2003)
2003
Later among the works it cites.
N. Stergioulas : Rotating Stars in Relativity , Living Rev. Relativity 6
2003
Later among the works it cites.
M. Ansorg, T. Fischer, A. Kleinwächter, R. Meinel, D. Petroff & K. Schöbel: Equilibrium configurations of homogeneous fluids in general relativity , Mon. Not. Roy. Astron. Soc. 355
2004
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N. Straumann : General Relavity, with Applications to Astrophysics , Springer-Verlag, Berlin (2004)
2004
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J.L. Zdunik, P. Haensel, E. Gourgoulhon & M. Bejger : Hyperon softening of the EOS of dense matter and the spin evolution of isolated neutron stars , Astron. Astrophys. 416
2004
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E. Gourgoulhon : An introduction to relativistic hydrodynamics
2006
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E. Gourgoulhon : 3+1 Formalism and Bases of Numerical Relativity
2006
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J. W. T. Hessels, S. M. Ransom, I. H. Stairs, P. C. C. Freire, V. M. Kaspi & F. S. Camilo : A Radio Pulsar Spinning at 716 Hz , Science 311
2006
Later among the works it cites.
L.-M. Lin & J. Novak : Rotating star initial data for a constrained scheme in numerical relativity , Class. Quantum Grav. 23
2006
Later among the works it cites.
R. Meinel : On the black hole limit of rotating fluid bodies in equilibrium , Class. Quantum Grav. 23
2006
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M. Rieutord : Modeling rapidly rotating stars , in Compte-rendus de la Semaine de l’Astrophysique Française 2006 , edited by D. Barret, F. Casoli, T. Contini, G. Lagache, A. Lecavelier & L. Pagani, http://proc.sf2a.asso.fr/2006/2006sf2a.conf..0501R.pdf
2006
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L. Villain : Instabilities of rotating compact stars: A brief overview , in Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars
2006
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N. Andersson & G. L. Comer : Relativistic Fluid Dynamics: Physics for Many Different Scales , Living Rev. Relativity 10
2007
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P. Haensel, A. Y. Potekhin & D. G. Yakovlev : Neutron stars 1: Equation of state and structure , Springer, New York (2007)
2007
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M. Alcubierre : Introduction to 3+1 Numerical Relativity , Oxford University Press, Oxford (2008)
2008
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A. Lichnerowicz : Théories relativistes de la gravitation et de l’électromagnétisme , Masson, Paris (1955); reprinted by Éditions Jacques Gabay, Paris (2008)
2008
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J. Martín, A. Molina & E. Ruiz : Can rigidly rotating polytropes be sources of the Kerr metric? , Class. Quantum Grav. 25
2008
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M. Rieutord : The dynamics of rotating fluids and binary stars , in Tidal Effects in Stars, Planets and Disks , edited by M.-J. Goupil & J.-P. Zahn, EAS Publications Series 29
2008
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J.L. Zdunik, M. Bejger, P. Haensel & E. Gourgoulhon : Strong first-order phase transition in a rotating neutron star core and the associated energy release , Astron. Astrophys. 479
2008
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M. Ansorg, D. Gondek-Rosińska & L. Villain : On the solution space of differentially rotating neutron stars in general relativity , Mon. Not. Roy. Astron. Soc. 396
2009
Later among the works it cites.
P. Grandclément & J. Novak : Spectral Methods for Numerical Relativity , Living Rev. Relat. 12
2009
Later among the works it cites.
P. Haensel, J.L. Zdunik, M. Bejger, J.M. Lattimer : Keplerian frequency of uniformly rotating neutron stars and quark stars , Astron. Astrophys. 502
2009
Later among the works it cites.
L. B. Szabados : Quasi-Local Energy-Momentum and Angular Momentum in General Relativity , Living Rev. Relativity 12
2009
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T. W. Baumgarte & S. L. Shapiro : Numerical Relativity. Solving Einstein’s Equations on the Computer , Cambridge University Press, Cambridge (2010)
2010
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J. A. Pons : Magnetic field structure and evolution in neutron stars , lectures at the Compstar 2010 School http://ipnweb.in2p3.fr/compstar2010/
2010
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R. Birkl, N. Stergioulas & E. Müller : Stationary, axisymmetric neutron stars with meridional circulation in general relativity , Phys. Rev. D 84
2011
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E. Gourgoulhon, C. Markakis, K. Uryu & Y. Eriguchi : Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach , Phys. Rev. D 83
2011
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J.L. Friedman & N. Stergioulas : Rotating Relativistic Stars , Cambridge University Press, Cambridge, to be published (2012)
2012
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