## $$C^3$$ matching for asymptotically flat spacetimes.(English)Zbl 1477.83007

### MSC:

 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 83C30 Asymptotic procedures (radiation, news functions, $$\mathcal{H}$$-spaces, etc.) in general relativity and gravitational theory 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 76E20 Stability and instability of geophysical and astrophysical flows
Full Text:

### References:

 [1] Darmois G 1927 Les Équations de la Gravitation Einsteinienne (Paris: Gauthier-Villars) [2] Lake K 2017 Gen. Relativ. Gravit.49 134 · Zbl 1380.83022 [3] Israel W 1966 Il Nuovo Cimento B (1965-1970)44 1-14 [4] Stephani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E 2009 Exact Solutions of Einstein’s Field Equations (Cambridge: Cambridge University Press) [5] Quevedo H 2012 Matching conditions in relativistic astrophysics On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories. Proc., 12th Marcel Grossmann Meeting on General Relativity(Paris, France, 12-8 July 2009) ed T Damour et al [6] Luongo O and Quevedo H 2012 Toward an invariant definition of repulsive gravity On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories. Proc., 12th Marcel Grossmann Meeting on General Relativity(Paris, France, 12-8 July 2009) ed T Damour et al [7] Luongo O and Quevedo H 2014 Phys. Rev. D 90 084032 [8] Luongo O and Quevedo H 2018 Found. Phys.48 17-26 · Zbl 1387.83132 [9] Misner C W, Thorne K S and Wheeler J A 2017 Gravitation (Princeton, NJ: Princeton University Press) [10] Savvidou N and Anastopoulos C 2017 Singularity stars (arXiv:1704.07250 [gr-qc]) [11] Mannheim P D 1999 ASP Conf. Ser.182 413 [12] Mannheim P D 1998 Curvature and cosmic repulsion (arXiv:9803135) [13] Hayasaka H and Minami Y 1999 AIP Conf. Proc.458 1040 [14] Deser S and Ryzhov A V 2005 Class. Quantum Grav.22 3315 · Zbl 1076.83001 [15] Gasperini M 1998 Gen. Relativ. Gravit.30 1703 · Zbl 1047.83532 [16] Liu C-Y, Lee D S and Lin C Y 2017 Class. Quantum Grav.34 235008 · Zbl 1381.83071 [17] Novikov I D, Bisnovatyi-Kogan G S and Novikov D I 2018 Phys. Rev. D 98 063528 [18] Phillips P R 2015 Mon. Not. R. Astron. Soc.448 681 [19] Resca L 2018 Eur. J. Phys.39 035602 · Zbl 1393.83006 [20] Woszczyna A, Kutschera M, Kubis S, Czaja W, Plaszczyk P and Golda Z A 2016 Gen. Relativ. Gravit.48 5 · Zbl 1332.83030 [21] Pugliese D, Quevedo H and Ruffini R 2013 Phys. Rev. D 88 024042 [22] Burinskii A 2008 Grav. Cosm.14 109-22 · Zbl 1145.83333 [23] Pugliese D, Quevedo H and Ruffini R 2011 Phys. Rev. D 84 044030 [24] Pugliese D, Quevedo H and Ruffini R 2011 Phys. Rev. D 84 104052 [25] Binney J and Tremaine S 2011 Galactic Dynamics (Princeton, NJ: Princeton University Press) p 36 [26] Tolman R C 1939 Phys. Rev.55 364 · Zbl 0020.28407 [27] Raghoonundun A M and Hobill D W 2016 The geometrical structure of the Tolman VII solution (arXiv:1601.06337 [gr-qc]) [28] Ovalle J and Linares F 2013 Phys. Rev. D 88 104026 [29] MacFadden P 2006 A signature of higher dimensions at the cosmic singularity PhD Thesis
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.