Abstract
In these notes we describe recent results concerning the inequality \(m\geq \sqrt{|J|}\) for axially symmetric black holes.
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References
D. Brill, On the positive definite mass of the Bondi-Weber-Wheeler time-symmetric gravitational waves. Ann. Phys. 7, 466–483 (1959)
Y. Choquet-Bruhat and J.E. Marsden, Solution of the local mass problem in general relativity. Commun. Math. Phys. 51(3), 283–296 (1976)
P.T. Chruściel, Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass. arXiv:0710.3680 [gr-qc] (2007)
P.T. Chruściel, Y. Li, and G. Weinstein, Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum. arXiv:0712.4064 [gr-qc] (2007)
S. Dain, Angular momentum-mass inequality for axisymmetric black holes. Phys. Rev. Lett. 96, 101101 (2006). gr-qc/0511101
S. Dain, Proof of the (local) angular momentum-mass inequality for axisymmetric black holes. Class. Quantum Gravity 23, 6845–6855 (2006). gr-qc/0511087
S. Dain, A variational principle for stationary, axisymmetric solutions of Einstein’s equations. Class. Quantum Gravity 23, 6857–6871 (2006). gr-qc/0508061
S. Dain, Axisymmetric evolution of Einstein equations and mass conservation. Class. Quantum Gravity 25, 145021 (2008). arXiv:0804.2679
S. Dain, The inequality between mass and angular momentum for axially symmetric black holes. Int. J. Mod. Phys. D 17(3–4), 519–523 (2008). arXiv:0707.3118 [gr-qc]
S. Dain, Proof of the angular momentum-mass inequality for axisymmetric black holes. J. Differ. Geom. 79(1), 33–67 (2008). gr-qc/0606105
R. Geroch, A method for generating solutions of Einstein’s equations. J. Math. Phys. 12(6), 918–924 (1971)
G.W. Gibbons and G. Holzegel, The positive mass and isoperimetric inequalities for axisymmetric black holes in four and five dimensions. Class. Quantum Gravity 23, 6459–6478 (2006). gr-qc/0606116
R. Penrose, Gravitational collapse: The role of general relativity. Riv. Nuovo Cimento 1, 252–276 (1969)
R. Wald, Final states of gravitational collapse. Phys. Rev. Lett. 26(26), 1653–1655 (1971)
R.M. Wald, General Relativity. The University of Chicago Press, Chicago (1984)
R. Wald, Gravitational collapse and cosmic censorship. In: Iyer, B.R., Bhawal, B. (eds.) Black Holes, Gravitational Radiation and the Universe. Fundamental Theories of Physics, vol. 100, pp. 69–85. Kluwer Academic, Dordrecht (1999). gr-qc/9710068
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Dain, S. (2009). Angular Momentum-Mass Inequality for Axisymmetric Black Holes. In: Sidoravičius, V. (eds) New Trends in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2810-5_12
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DOI: https://doi.org/10.1007/978-90-481-2810-5_12
Publisher Name: Springer, Dordrecht
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