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Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry. (English) Zbl 1111.83028

Summary: We study a set of static solutions of the Einstein equations in the presence of a massless scalar field and establish their connection to the Kantowski–Sachs cosmological solutions based on some kind of duality transformations. The physical properties of the limiting case of an empty hyperbolic space–time (pseudo-Schwarzschild geometry) are analyzed in some detail.

MSC:

83C57 Black holes
83F05 Relativistic cosmology
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
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References:

[1] DOI: 10.1017/CBO9780511535185 · doi:10.1017/CBO9780511535185
[2] Schwarzschild K., Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 189 pp 424–
[3] DOI: 10.1103/PhysRev.55.364 · Zbl 0020.28407 · doi:10.1103/PhysRev.55.364
[4] DOI: 10.1103/PhysRev.55.374 · Zbl 0020.28501 · doi:10.1103/PhysRev.55.374
[5] Fisher I. Z., ZhETF 18 pp 636–
[6] DOI: 10.1103/PhysRev.107.1157 · doi:10.1103/PhysRev.107.1157
[7] Buchdahl H. A., Phys. Rev. 111 pp 1417–
[8] DOI: 10.1103/PhysRevLett.20.878 · doi:10.1103/PhysRevLett.20.878
[9] DOI: 10.1103/PhysRev.186.1729 · doi:10.1103/PhysRev.186.1729
[10] DOI: 10.1103/PhysRevD.24.839 · doi:10.1103/PhysRevD.24.839
[11] DOI: 10.1103/PhysRevD.31.1280 · doi:10.1103/PhysRevD.31.1280
[12] DOI: 10.1103/PhysRevD.40.2564 · doi:10.1103/PhysRevD.40.2564
[13] DOI: 10.1063/1.1666161 · doi:10.1063/1.1666161
[14] Bronnikov K. A., Acta Physica Polonica B 4 pp 251–
[15] DOI: 10.1103/PhysRevD.65.104010 · doi:10.1103/PhysRevD.65.104010
[16] DOI: 10.1103/PhysRevD.65.064003 · doi:10.1103/PhysRevD.65.064003
[17] DOI: 10.1023/B:GERG.0000032159.46106.63 · Zbl 1058.83550 · doi:10.1023/B:GERG.0000032159.46106.63
[18] DOI: 10.1063/1.1704952 · doi:10.1063/1.1704952
[19] DOI: 10.1063/1.529717 · doi:10.1063/1.529717
[20] DOI: 10.1016/S0370-2693(98)01183-6 · doi:10.1016/S0370-2693(98)01183-6
[21] DOI: 10.1142/S0217732304013246 · doi:10.1142/S0217732304013246
[22] DOI: 10.1088/0305-4470/13/3/027 · doi:10.1088/0305-4470/13/3/027
[23] DOI: 10.1016/B978-0-08-025072-4.50012-5 · doi:10.1016/B978-0-08-025072-4.50012-5
[24] DOI: 10.1080/00018736300101283 · doi:10.1080/00018736300101283
[25] DOI: 10.1103/PhysRev.116.1285 · Zbl 0087.42501 · doi:10.1103/PhysRev.116.1285
[26] DOI: 10.1103/PhysRev.119.1743 · Zbl 0098.19001 · doi:10.1103/PhysRev.119.1743
[27] Adler R., Introduction to General Relativity (1975)
[28] Hawking S. W., The Large Scale Structure of Space–Time (1975)
[29] Chandrasekhar S., The Mathematical Theory of Black Holes (1983) · Zbl 0511.53076
[30] Weinberg S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (1972)
[31] DOI: 10.2307/2370192 · JFM 48.1040.02 · doi:10.2307/2370192
[32] DOI: 10.1080/00018737000101171 · doi:10.1080/00018737000101171
[33] DOI: 10.1080/00018738200101428 · doi:10.1080/00018738200101428
[34] DOI: 10.1088/0264-9381/20/9/201 · Zbl 1138.83306 · doi:10.1088/0264-9381/20/9/201
[35] DOI: 10.1103/PhysRev.48.73 · Zbl 0012.13401 · doi:10.1103/PhysRev.48.73
[36] DOI: 10.1103/RevModPhys.21.447 · Zbl 0041.56701 · doi:10.1103/RevModPhys.21.447
[37] DOI: 10.4310/ATMP.1998.v2.n2.a1 · Zbl 0914.53047 · doi:10.4310/ATMP.1998.v2.n2.a1
[38] DOI: 10.1016/S0550-3213(00)00463-6 · Zbl 1043.81680 · doi:10.1016/S0550-3213(00)00463-6
[39] DOI: 10.1103/PhysRevD.28.2960 · Zbl 1370.83118 · doi:10.1103/PhysRevD.28.2960
[40] DOI: 10.1142/S0217732386000129 · doi:10.1142/S0217732386000129
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