scholarly journals On global properties of warped solutions in General Relativity with an electromagnetic field and a cosmological constant

2020 ◽  
Author(s):  
Mikhail Katanaev ◽  
Daniel Afanasev
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Global Properties

scholarly journals GRAVITATION, ELECTROMAGNETISM AND THE COSMOLOGICAL CONSTANT IN PURELY AFFINE GRAVITY

2009 ◽  
Vol 18 (05) ◽  
pp. 809-829 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Ricci Tensor ◽  
Einstein Equations ◽  
Metric Tensor ◽  
Affine Metric ◽  
Affine Gravity

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris–Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein–Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric–affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric–affine pictures, unless the electromagnetic field couples to the cosmological constant.

scholarly journals Plebański–Demiański solution of general relativity and its expressions quadratic and cubic in curvature: Analogies to electromagnetism

2015 ◽  
Vol 24 (10) ◽  
pp. 1550079 ◽  
Author(s):  
Jens Boos
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
General Type ◽  
Coordinate Systems ◽  
Irreducible Decomposition ◽  
Asymptotically Flat ◽  
Type D ◽  
Curvature Invariants ◽  
Free Parameters ◽  
First Time

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution — the exact seven parameter solution of Plebański–Demiański (PD) — to demonstrate these analogies for a physically meaningful spacetime. The two quadratic curvature invariants B2 - E2 and E⋅B are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel–Robinson tensor reads (B2 + E2)2 for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy–momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel–Robinson 3-form, from which the Bel–Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: In the original polynomial PD coordinates and in a modified Boyer–Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.

ON THE COSMOLOGICAL CONSTANT AS A CONSTANT OF INTEGRATION

1991 ◽  
Vol 06 (23) ◽  
pp. 2107-2111 ◽  
Author(s):  
A. N. PETROV
Keyword(s):  
General Relativity ◽  
Cosmological Constant

The possibilities to construct a modification of General Relativity (MGR), where the cosmological constant appears as a constant of integration are considered. A class of new constraints on the metric is found, such that their inclusion in the Hilbert–Einstein action before its variation leads to MGR.

scholarly journals The invalidity of “negative mass” description of the dark sector

2019 ◽  
Vol 34 (35) ◽  
pp. 1975002
Author(s):  
A. Stepanian
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Observational Data ◽  
Weak Field ◽  
Dark Sector ◽  
Negative Mass ◽  
Negative Cosmological Constant ◽  
Viable Model

It is shown that the concept of “negative mass” introduced by Farnes [Astron. Astrophys. 620, A92 (2018)] to describe the dark sector within a unifying theory with the negative cosmological constant contradicts both the essence of the General Relativity (GR) and the available observational data. A viable model with modified weak-field GR is mentioned.

scholarly journals Some Cosmological Solutions of a New Nonlocal Gravity Model

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 917
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Alexey S. Koshelev ◽  
Zoran Rakic ◽  
Jelena Stankovic
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Analytic Function ◽  
Cosmological Constant ◽  
Explicit Form ◽  
Gravity Model ◽  
Necessary Conditions ◽  
Equations Of Motion ◽  
Nonlocal Operator ◽  
Cosmological Solutions

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G ∫ [ R − 2 Λ + ( R − 4 Λ ) F ( □ ) ( R − 4 Λ ) ] − g d 4 x , where F ( □ ) = ∑ n = 1 + ∞ f n □ n is an analytic function of the d’Alembertian □. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ ≠ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e Λ 4 t 2 , that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one a ( t ) = A e Λ t 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F ( □ ) , which satisfies obtained necessary conditions.

scholarly journals General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 24
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Positive Cosmological Constant ◽  
Four Dimensions ◽  
Action Integral ◽  
Fields Equations

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

Sign in / Sign up

Export Citation Format

Share Document