Abstract
In order to formulate the equations for the metric, the first step is to consider an alternative definition of the energy–momentum tensor of particles and fields. In Chap. 2, we already learned the canonical definition of the energy and momentum conservations in classical mechanics and the energy–momentum tensor of particles and fields in special relativity. It happens that in general relativity, things somehow turn out to be simpler—here, we gain an alternative and in fact more economic, dynamical definition of the energy–momentum tensor.
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References
F. Jüttner, Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Ann. Phys. Bd 116, 145 (1911)
W. Pauli, Theory of Relativity (Dover, 1981)
S. Weinberg, Gravitation and Cosmology (Wiley, 1972)
S. Weinberg, The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)
P.J.E. Peebles, B. Ratra, The cosmological constant and dark energy. Rev. Mod. Phys. 75, 559 (2003). arXiv:astro-ph/0207347
T. Padmanabhan, Cosmological constant: the weight of the vacuum. Phys. Rep. 380, 235 (2003). arXiv:hep-th/0212290
D. Finkelstein, Past-future asymmetry of the gravitational field of a point particle. Phys. Rev. 110, 965 (1958)
M. Kruskal, Maximal extension of Schwarzschild metric. Phys. Rev. 119, 1743 (1960)
S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space–Time (Cambridge University Press, 1973)
C.W. Misner, K.S. Thorn, J.A. Wheeler, Gravitation (W.H. Freeman and C, San Francisco, 1973)
R. D’Inverno, Introducing Einstein’s Relativity (Oxford University Press, 1992–1998)
V.P. Frolov, I.D. Novikov, Black Hole Physics—Basic Concepts and New Developments (Kluwer Academic Publishers, 1989)
S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon Press, Oxford, 1998)
V.P. Frolov, A. Zelnikov, Introduction to Black Hole Physics (Oxford University Press, 2015)
D.F. Carneiro, E.A. Freitas, B. Gonçalves, A.G. de Lima, I.L. Shapiro, On useful conformal tranformations in general relativity. Gravit. Cosmol. 40, 305 (2004). arXiv:gr-qc/0412113
W. Siegel, Fields. arXiv:hep-th/9912205
L.D. Landau, E.M. Lifshits, The Classical Theory of Fields—Course of Theoretical Physics, vol. 2 (Butterworth-Heinemann, 1987)
I.L. Shapiro, G. de Berredo Peixoto, Lecture Notes on Newtonian Mechanics: Lessons from Modern Concepts (Springer, 2013)
B.P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016). arXiv:1602.03837
M. Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford University Press, 2007)
B.P. Abbott et al., Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. Lett. 848, L13 (2017)
K.S. Stelle, Renormalization of higher derivative quantum gravity. Phys. Rev. D 16, 953 (1977)
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Shapiro, I.L. (2019). Einstein Equations, Schwarzschild Solution, and Gravitational Waves. In: A Primer in Tensor Analysis and Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26895-4_15
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