Some restrictions on algebraically general vacuum metrics

In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these solutions the authors missed some of the possible solutions discussed in this article. An exact solution is demonstrated, which is absent in the book by Landau and Lifshitz. It describes space-time with a gravitational wave of zero frequency. It is shown that there are no other solutions of this type than listed above and Minkowski’s metrics. The list of vacuum metrics that depend on one coordinate is not complete without solution provided in this paper.

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General vacuum solution for Brans-Dicke-Bianchi type V

General Relativity and Gravitation ◽

10.1007/bf00756863 ◽

1991 ◽

Vol 23 (9) ◽

pp. 1007-1010 ◽

Cited By ~ 3

Author(s):

Enrique Guzmán

Keyword(s):

Bianchi Type ◽

Vacuum Solution ◽

General Vacuum ◽

Type V ◽

Bianchi Type V

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Class of "Noncanonical" Vacuum Metrics with Two Commuting Killing Vectors

Physical Review Letters ◽

10.1103/physrevlett.42.416 ◽

1979 ◽

Vol 42 (7) ◽

pp. 416-417 ◽

Cited By ~ 3

Author(s):

P. Kundu

Keyword(s):

Killing Vectors ◽

Vacuum Metrics

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A Note on the Factor Structure of Some Non-Rational Vacuum Metrics

General Relativity and Gravitation ◽

10.1023/a:1001946402507 ◽

2000 ◽

Vol 32 (11) ◽

pp. 2131-2139

Author(s):

J. L. Hernández-Pastora ◽

V. S. Manko ◽

J. Martín ◽

E. Ruiz

Keyword(s):

Factor Structure ◽

Vacuum Metrics

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I. General vacuum science and engineering

Vacuum ◽

10.1016/0042-207x(66)90237-5 ◽

1966 ◽

Vol 16 (7) ◽

pp. 404

Keyword(s):

Science And Engineering ◽

General Vacuum

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OSCILLATING INSTANTONS AS HOMOGENEOUS TUNNELING CHANNELS

International Journal of Modern Physics A ◽

10.1142/s0217751x13500826 ◽

2013 ◽

Vol 28 (18) ◽

pp. 1350082 ◽

Cited By ~ 7

Author(s):

BUM-HOON LEE ◽

WONWOO LEE ◽

DONG-HAN YEOM

Keyword(s):

Scalar Field ◽

Local Minimum ◽

Local Maximum ◽

Einstein Gravity ◽

Scale Factor ◽

The Other ◽

Vacuum Decay ◽

General Vacuum

In this paper, we study Einstein gravity with a minimally coupled scalar field accompanied with a potential, assuming an O(4) symmetric metric ansatz. We call an Euclidean instanton is to be an oscillating instanton, if there exists a point where the derivative of the scale factor and the scalar field vanish at the same time. Then, we can prove that the oscillating instanton can be analytically continued, both as inhomogeneous and homogeneous tunneling channels. Here, we especially focus on the possibility of a homogeneous tunneling channel. For the existence of such an instanton, we have to assume three things: (1) there should be a local maximum and the curvature of the maximum should be sufficiently large, (2) there should be a local minimum and (3) the other side of the potential should have a sufficiently deeper vacuum. Then, we can show that there exists a number of oscillating instanton solutions and their probabilities are higher compared to the Hawking–Moss instantons. We also check the possibility when the oscillating instantons are comparable with the Coleman–de Luccia channels. Thus, for a general vacuum decay problem, we should not ignore the oscillating instanton channels.

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