ℋ -Space with a cosmological constant

1982 ◽  
Vol 380 (1778) ◽  
pp. 171-185 ◽  
Keyword(s):  
Cosmological Constant ◽  
Riemannian Metric ◽  
The Self ◽  
Einstein Equations ◽  
Conformal Metric ◽  
First Case ◽  
Space Construction ◽  
Real Analytic

It is demonstrated that a real-analytic 3-manifold with Riemannian conformal metric is naturally the conformal infinity of a germ-unique real-analytic 4-manifold with real-analytic Riemannian metric satisfying the self-dual Einstein equations with cosmological constant — 1. Moreover, this result holds if ‘Riemannian’ is replaced in the first case by ‘Lorentzian’ (i. e. signature + - - ) and in the second case by ‘pseudo-Riemannian with signature + + - - ’, or if ‘real-analytic’ is replaced by ‘complex-analytic’ and 'Riemannian’ is replaced by ‘holomorphic’. This provides a cosmological-constant analogue of Newman’s ℋ-space construction (Newman 1976, 1977).

WORMHOLE SOLUTIONS IN R1×S1×S2 TOPOLOGICAL SPACE

1992 ◽  
Vol 07 (27) ◽  
pp. 2463-2467 ◽  
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Scalar Field ◽  
Topological Space ◽  
Cosmological Constant ◽  
Symmetric Tensor ◽  
Einstein Equations ◽  
Second Step ◽  
Anisotropic Space ◽  
First Case ◽  
Frw Metric ◽  
Conformal Scalar Field

Wormhole solutions are discussed for two different physical situations in the background of a homogeneous anisotropic space-time. In the first case, the wormholes are solutions of the Euclidean Einstein equations with a cosmological constant and a two-index anti-symmetric tensor for monopole configuration on a space with three-surface of topology S1×S2. In the second step, conformal scalar field is coupled to gravity and wormhole are considered for both λ=0 and λ>0. These results are analogous to the wormhole solutions for FRW metric.

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

scholarly journals Vacuum solutions of Einstein equations that depend on one coordinate

2020 ◽  
pp. 10-11
Author(s):  
S. Parnovsky
Keyword(s):  
Exact Solution ◽  
General Theory ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Einstein Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Vacuum Metrics ◽  
Vacuum Solutions ◽  
Zero Frequency

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.

scholarly journals Brane cosmology and the self-tuning of the cosmological constant

2019 ◽  
Vol 2019 (10) ◽  
pp. 007-007 ◽  
Author(s):  
A. Amariti ◽  
C. Charmousis ◽  
D. Forcella ◽  
E. Kiritsis ◽  
F. Nitti
Keyword(s):  
Cosmological Constant ◽  
The Self ◽  
Brane Cosmology ◽  
Self Tuning

scholarly journals Cosmological model favored by the holographic principle

2016 ◽  
Vol 41 ◽  
pp. 1660127
Author(s):  
Irina Dymnikova ◽  
Anna Dobosz ◽  
Bożena Sołtysek
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Space Time ◽  
Holographic Principle ◽  
Einstein Equations ◽  
Energy Tensor ◽  
De Sitter ◽  
Quantum Evaporation ◽  
Stress Energy ◽  
De Sitter Vacua

We present a regular spherically symmetric cosmological model of the Lemaitre class distinguished by the holographic principle as the thermodynamically stable end-point of quantum evaporation of the cosmological horizon. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. Global structure of space-time is the same as for the de Sitter space-time. Cosmological evolution goes from a big initial value of the cosmological constant towards its presently observed value.

scholarly journals A TOY MODEL OF THE FIVE-DIMENSIONAL UNIVERSE WITH THE COSMOLOGICAL CONSTANT

2004 ◽  
Vol 19 (29) ◽  
pp. 5051-5084
Author(s):  
WOJCIECH TARKOWSKI
Keyword(s):  
Cosmological Constant ◽  
Zero Point ◽  
Einstein Equations ◽  
Vacuum Energy Density ◽  
Coupling Constant ◽  
Virtual Particles ◽  
A Value ◽  
Proposed Model ◽  
Intrinsic Angular Momentum ◽  
Energy Cutoff

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vanishing of the observed value of the cosmological constant is a consequence of the existence of an energy cutoff exactly at the Planck level. In turn, a model for both a virtual and a real particle–antiparticle pair is proposed which describes properly some energetic properties of both the vacuum fluctuations and created particles, as well as it allows one to calculate the discrete "bare" values of an elementary particle's mass, electric charge and intrinsic angular momentum (spin) at the energy cutoff. The relationships between the discussed model and some phenomena such as the Zitterbewegung and the Unruh–Davies effect are briefly analyzed, too. The proposed model also allows one to derive the Lorentz transformation and the Maxwell equations while considering the properties of the vacuum filled with the sea of virtual particles and their antiparticles. Finally, the existence of a finite value of the vacuum-energy density resulting from the toy model leads us to the formulation of dimensionless Einstein equations which may be derived from the Lagrangian with a dimensionless (naively renormalized) coupling constant.

scholarly journals The universality of vacuum Einstein equations with cosmological constant

1994 ◽  
Vol 11 (6) ◽  
pp. 1505-1517 ◽  
Author(s):  
Marco Ferraris ◽  
Mauro Francaviglia ◽  
Igor Volovich
Keyword(s):  
Cosmological Constant ◽  
Einstein Equations ◽  
Vacuum Einstein Equations
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