Orthogonal transitivity, invertibility, and null geodesic separability in typeDelectrovac solutions of Einstein’s field equations with cosmological constant

1981 ◽  
Vol 22 (8) ◽  
pp. 1711-1726 ◽  
Author(s):  
R. Debever ◽  
R. G. McLenaghan
Keyword(s):  
Cosmological Constant ◽  
Null Geodesic ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

On fractional and fractal Einstein’s field equations

2021 ◽  
Vol 36 (05) ◽  
pp. 2150030
Author(s):  
Rami Ahmad El-Nabulsi ◽  
Alireza Khalili Golmankhaneh
Keyword(s):  
Cosmological Constant ◽  
Fractional Order ◽  
Order Parameter ◽  
Lorentz Invariance ◽  
Radio Interferometry ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Fractal Sets ◽  
Einstein's Field Equations ◽  
Fractal Calculus

In this study, Einstein’s field equations are derived based on two dissimilar frameworks: the first is based on the concepts of “fractional velocity” and “fractal action” motivated by Calcagni’s approach to fractional spacetime while the second is derived based on fractal calculus which is a generalization of ordinary calculus that include fractal sets and curves. The fractional theory displays a breakdown of Lorentz invariance. It was observed that a spatially dependent cosmological constant emerges in the fractional theory. A connection between the fractional order parameter and the dimensionless parameter [Formula: see text] arising in the parameterized post-Newtonian (PPN) formalism is observed. A confrontation with very long-baseline radio interferometry targeting quasars 3C273 and 3C279 is done which proves that the fractional order parameter is within the range [Formula: see text]. Moreover, emergence of quantum Hawking radiation is realized in the theory supporting Hawking’s best calculations that black holes are not black. Nevertheless, based on the fractal calculus approach, there is a conservation of the Lorentz invariance and absence of spatially-dependent cosmological constant. The theory depends on the fractal order [Formula: see text] and gives rise to a fractal Schwarzschild radius of the massive body greater than the conventional radius besides a fractal Hawking’s temperature less than the standard one. However, the confrontation with radio interferometry targeting quasars 3C273 and 3C279 gives [Formula: see text].

Expanding Universe with a Variable Cosmological Term

2015 ◽  
Vol 70 (11) ◽  
pp. 905-911 ◽  
Author(s):  
Carlos Blanco-Pérez ◽  
Antonio Fernández-Guerrero
Keyword(s):  
Cosmological Constant ◽  
Cosmological Term ◽  
Expanding Universe ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Variable Cosmological Term ◽  
Einstein's Field Equations ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Entropy Of The Universe

AbstractWe propose a model of expansion of the universe in which a minimal, ‘quantised’ rate is dependent upon the value of the cosmological constant Λ in Einstein’s field equations, itself not a constant but a function of the size and the entropy of the universe. From this perspective, we offer an expression which relates Hubble’s constant with the cosmological constant.

scholarly journals ON SIGNATURE TRANSITION IN ROBERTSON–WALKER COSMOLOGIES

2000 ◽  
Vol 15 (10) ◽  
pp. 1521-1531 ◽  
Author(s):  
K. GHAFOORI-TABRIZI ◽  
S. S. GOUSHEH ◽  
H. R. SEPANGI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Upper Bound ◽  
Classical Model ◽  
Space Time ◽  
Scale Factor ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Lorentzian Space ◽  
Einstein's Field Equations

We analyze a classical model of gravitation coupled to a self-interacting scalar field. We show that, within the context of this model for Robertson–Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian space–time. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be constant. Moreover we find that the signature changing solutions do not exist when the scalar field is massless.

scholarly journals Null hypersurfaces in de Sitter and anti-de Sitter cosmologies

2018 ◽  
Vol 27 (04) ◽  
pp. 1850045
Author(s):  
P. A. Hogan
Keyword(s):  
Cosmological Constant ◽  
Gravitational Waves ◽  
Constant Curvature ◽  
Focus Attention ◽  
De Sitter ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Null Hypersurfaces ◽  
Einstein's Field Equations ◽  
Line Elements

The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in spacetimes of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision spacetime is a solution of Einstein’s field equations with a cosmological constant, and the second originated in the generalization of plane fronted gravitational waves with parallel rays to include a cosmological constant.

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

scholarly journals A review of total energy–momenta in GR with a positive cosmological constant

2019 ◽  
Vol 28 (01) ◽  
pp. 1930003 ◽  
Author(s):  
László B. Szabados ◽  
Paul Tod
Keyword(s):  
Cosmological Constant ◽  
Total Energy ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Einstein's Field Equations ◽  
Main Ideas

A review is given of the various approaches to and expressions for total energy–momentum and mass in the presence of a positive cosmological constant in Einstein’s field equations, together with a discussion of the key conceptual questions, main ideas and techniques behind them.

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