scholarly journals SCHWARZSCHILD–DE SITTER METRIC AND INERTIAL BELTRAMI COORDINATES

2013 ◽  
Vol 28 (29) ◽  
pp. 1350114 ◽  
Author(s):  
LI-FENG SUN ◽  
MU-LIN YAN ◽  
YA DENG ◽  
WEI HUANG ◽  
SEN HU
Keyword(s):  
Inertial Force ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Solar Mass ◽  
Vacuum Einstein Equation ◽  
Pure Gravity ◽  
Beltrami Coordinates ◽  
Coordinate Conditions ◽  
De Sitter Metric

Under consideration of coordinate conditions, we get the Schwarzschild–Beltrami–de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant Λ. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a Λ) is presented. The Beltrami metric Bμν provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild–de Sitter (S-dS) metric [Formula: see text] existed in literatures since 1918, we find that the existed S-dS metric [Formula: see text] describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" M in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric [Formula: see text]. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.

A static generalization of the Einstein universe

1958 ◽  
Vol 245 (1241) ◽  
pp. 202-212
Keyword(s):  
General Problem ◽  
Constant Density ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Einstein Universe

Solutions of the Einstein field equations are found for the problem of a sphere of constant density surrounded by matter of different constant density. The solutions are discussed and particular attention paid to the topology of the surrounding matter. The Schwarzschild, de Sitter, and Einstein solutions emerge as particular cases of the general problem.

scholarly journals GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

Anisotropic universe and generalized ghost dark energy in Brans–Dicke theory

2016 ◽  
Vol 94 (2) ◽  
pp. 201-208 ◽  
Author(s):  
V. Fayaz ◽  
H. Hossienkhani ◽  
A. Pasqua ◽  
Z. Zarei ◽  
M. Ganji
Keyword(s):  
Dark Energy ◽  
State Parameter ◽  
Anisotropic Universe ◽  
Type I ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ghost Dark Energy ◽  
The Stability ◽  
Generalized Ghost Dark Energy

In this paper, we consider the generalized ghost dark energy in a Bianchi type-I metric (which is a spatially homogeneous and anisotropic) in the framework of Brans–Dicke theory. For this purpose, we use the squared sound speed [Formula: see text] the sign of which determines the stability of the model. At first, we obtain the equation of state parameter, ωΛ = pΛ/ρΛ, the deceleration parameter q and the evolution equation of the generalized ghost dark energy. We find that, in this case, ωΛ cannot cross the phantom line (ωΛ > –1) and eventually the universe approaches a de-Sitter phase of expansion (ωΛ → –1). Then, we extend our study to the case of generalized ghost dark energy in a non-isotropic and Brans–Dicke framework and find out that the transition of ωΛ to the phantom regime can be more easily accounted for than when it is restored into the Einstein field equations. In conclusion, we find evidence that the generalized ghost dark energy in BD theory can lead to a stable universe favored by observations at the present time.

scholarly journals Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

2020 ◽  
pp. 1-14
Author(s):  
Yu-Ching, Chou
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Kerr Metric ◽  
Tensor Structure ◽  
De Sitter ◽  
Field Equations ◽  
Null Tetrad ◽  
Axisymmetric Solutions ◽  
Metric Function ◽  
De Sitter Metric

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r. Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations. Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

Cosmology

2019 ◽  
pp. 92-100
Author(s):  
Steven Carlip
Keyword(s):  
De Sitter Space ◽  
Red Shift ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Cosmological Solutions ◽  
Expansion Of The Universe ◽  
Topology Of The Universe ◽  
The Universe

Starting with the assumptions of homogeneity and isotropy, the cosmological solutions of the Einstein field equations—the Friedmann-Lemaitre-Robertson-Walker metrics—are derived. After a discussion of constant curvature metrics and the topology of the Universe, the chapter moves on to discuss observational implications: expansion of the Universe, cosmological red shift, primordial nucleosynthesis, the cosmic microwave background, and primordial perturbations. The chapter includes a brief discussion of de Sitter and anti-de Sitter space and an introduction to inflation.

scholarly journals TORSION CORRECTIONS IN BRANE WORLD GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 150-160 ◽  
Author(s):  
R. MAIER
Keyword(s):  
Cosmological Model ◽  
Extrinsic Curvature ◽  
Matter Content ◽  
Brane World ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Sitter Spacetime ◽  
World Theory

In the frame of brane world theory the effects of torsion fields are examined. Considering a five dimensional Non-Riemannian bulk with a noncompact extra dimension, we derive the modified Einstein field equations in a four dimensional (3-brane) arbitrary manifold embedded in this bulk. The necessary matching conditions are investigated assuming that the torsion in the bulk is continuous. In this context the extrinsic curvature is connected to the matter content restricted to the brane and the torsion components of the bulk. As a final result we observe that the corrections – due to torsion fields – in the modified field equations depend crucially on the embedding that is taken. Therefore, by considering a simple embedding, we develop a cosmological model that describes a flat FLRW embedded in a 5-dimensional de Sitter (or Anti de Sitter) spacetime, where a 5-dimensional cosmological constant emerges from the torsion components of the bulk.

scholarly journals $$\mathbf {O}(D,D)$$ completion of the Friedmann equations

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Stephen Angus ◽  
Kyoungho Cho ◽  
Guilherme Franzmann ◽  
Shinji Mukohyama ◽  
Jeong-Hyuck Park
Keyword(s):  
General Relativity ◽  
Momentum Tensor ◽  
Closed String ◽  
Matter Content ◽  
Positive Energy ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Generalized Continuity ◽  
Friedmann Equations

AbstractIn string theory the closed-string massless NS-NS sector forms a multiplet of $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry fixes the correct couplings to other matter fields and the Einstein field equations are enriched to comprise $$D^{2}+1$$ D 2 + 1 components, dubbed recently as the Einstein Double Field Equations. Here we explore the cosmological implications of this framework. We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the $$\mathbf {O}(D,D)$$ O ( D , D ) -covariant energy-momentum tensor. Crucially, the former admits space-filling magnetic H-flux. Substituting them into the Einstein Double Field Equations, we obtain the $$\mathbf {O}(D,D)$$ O ( D , D ) completion of the Friedmann equations along with a generalized continuity equation. We discuss how solutions in this framework may be characterized by two equation-of-state parameters, w and $$\lambda $$ λ , where the latter characterizes the relative intensities of scalar and tensor forces. When $$\lambda +3w=1$$ λ + 3 w = 1 , the dilaton remains constant throughout the cosmological evolution, and one recovers the standard Friedmann equations for generic matter content (i.e. for any w). We further point out that, in contrast to General Relativity, neither an $$\mathbf {O}(D,D)$$ O ( D , D ) -symmetric cosmological constant nor a scalar field with positive energy density gives rise to a de Sitter solution.

Sign in / Sign up

Export Citation Format

Share Document