scholarly journals Dark matter from non-relativistic embedding gravity

2021 ◽  
pp. 2150101
Author(s):  
S. A. Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Additional Contribution ◽  
Relativistic Limit ◽  
The Core ◽  
The Stability ◽  
Dimensional Surface

We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the [Formula: see text]CDM model.

scholarly journals Non-Relativistic Limit of Embedding Gravity as General Relativity with Dark Matter

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 163 ◽  
Author(s):  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Cold Dark Matter ◽  
Equations Of Motion ◽  
Dynamical Equations ◽  
Relativistic Limit ◽  
Change Of Variables ◽  
Modified Theory ◽  
Mimetic Gravity

Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle—our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular theory of mimetic gravity—the modification of gravity appears in both theories as a result of the change of variables in the action of General Relativity. Embedding gravity, as well as mimetic gravity, can be used in explaining the dark matter mystery since, in both cases, the modified theory can be presented as General Relativity with additional fictitious matter (embedding matter or mimetic matter). For the general case, we obtain the equations of motion of embedding matter in terms of embedding function as a set of first-order dynamical equations and constraints consistent with them. Then, we construct a non-relativistic limit of these equations, in which the motion of embedding matter turns out to be slow enough so that it can play the role of cold dark matter. The non-relativistic embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the Λ-Cold Dark Matter (ΛCDM) model.

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 Investigation of Faddeev variant of embedding theory

2021 ◽  
Vol 2103 (1) ◽  
pp. 012003
Author(s):  
S. S. Kuptsov ◽  
S. A. Paston
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original Form ◽  
Additional Contribution ◽  
Specific Class ◽  
Embedding Theory ◽  
Weak Gravitational Field ◽  
Independent Variable ◽  
Dimensional Surface ◽  
Embedding Function

Abstract Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional surface representing our spacetime. In Faddeev variant, the independent variable is a non-square vielbein, which is a derivative of embedding function in embedding theory. We study the possibility of the existence of extra solutions in Faddeev variant, which makes this theory non-equivalent to GR. To separate the degrees of freedom corresponding to extra matter, we propose a formulation of this theory as GR with an additional contribution to the action. We analyze the equations of motion for a specific class of solutions corresponding to a weak gravitational field. We construct a simple exact solution corresponding to arbitrary matter and nontrivial torsion, which is an extra solution in Faddeev variant in the absence of real matter.

scholarly journals BAROTROPIC THIN SHELLS WITH LINEAR EOS AS MODELS OF STARS AND CIRCUMSTELLAR SHELLS IN GENERAL RELATIVITY

1999 ◽  
Vol 08 (04) ◽  
pp. 549-555 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Equilibrium Configurations ◽  
Barotropic Fluids ◽  
Circumstellar Shells ◽  
Relativistic Models ◽  
The Stability

The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.

scholarly journals DARK ENERGY AND DARK MATTER IN GENERAL RELATIVITY WITH LOCAL SCALE INVARIANCE

2009 ◽  
Vol 24 (20) ◽  
pp. 1583-1595 ◽  
Author(s):  
PAVAN KUMAR ALURI ◽  
PANKAJ JAIN ◽  
NAVEEN K. SINGH
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Scale Invariance ◽  
Equations Of Motion ◽  
Local Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Λcdm Model ◽  
Frw Metric

We consider a generalization of Einstein's general theory of relativity such that it respects local scale invariance. This requires the introduction of a scalar and a vector field in the action. We show that the theory naturally displays both dark energy and dark matter. We solve the resulting equations of motion assuming an FRW metric. The solutions are found to be almost identical to those corresponding to the standard ΛCDM model.

scholarly journals DE SITTER STABILITY IN QUADRATIC GRAVITY

2007 ◽  
Vol 16 (06) ◽  
pp. 1075-1085 ◽  
Author(s):  
A. V. TOPORENSKY ◽  
P. V. TRETYAKOV
Keyword(s):  
General Relativity ◽  
Simple Form ◽  
Equations Of Motion ◽  
Cosmological Solution ◽  
Stability Conditions ◽  
De Sitter ◽  
Bianchi I ◽  
Quadratic Gravity ◽  
The Stability ◽  
Hilbert Action

Quadratic curvature corrections to the Einstein–Hilbert action lead in general to higher-order equations of motion, which can induce instability of some unperturbed solutions of General Relativity. We study the conditions for the stability of the de Sitter cosmological solution. We argue that the simple form of this condition known for the FRW background in (3+1) dimensions changes seriously if at least one of these two assumptions is violated. In the present paper, the stability conditions for the de Sitter solution are found for the multidimensional FRW background and for Bianchi I metrics in (3 + 1) dimensions.

Vibrations of an Elastically Mounted Spinning Rotor Partially Filled With Liquid

1982 ◽  
Vol 104 (2) ◽  
pp. 389-396 ◽  
Author(s):  
G. Lichtenberg
Keyword(s):  
Equations Of Motion ◽  
Constant Angular Velocity ◽  
Two Dimensional ◽  
Field Equations ◽  
Stability Boundaries ◽  
Inviscid Incompressible Fluid ◽  
Wide Range ◽  
The Stability ◽  
Elastically Supported ◽  
Dimensional Surface

The stability of a rotor with a cylindrical cavity, spinning with constant angular velocity and partially filled with an inviscid, incompressible fluid is studied. The rotor is elastically supported on a vertically mounted massless shaft in overhung position. A set of coupled linearized spatial equations of motion of the rotor and field equations, as well as boundary conditions of the liquid, is established and solved, leading to a characteristic equation. First numerical results predict a wide range of rotor speeds, where the system performs unstable motions caused by a two-dimensional surface wave of the liquid. The stability boundaries are calculated for a flat rotor in dependence on the mass of the contained liquid and agree extremely well with experimental data.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

scholarly journals On the formation and stability of fermionic dark matter halos in a cosmological framework

2020 ◽  
Author(s):  
Carlos R Argüelles ◽  
Manuel I Díaz ◽  
Andreas Krut ◽  
Rafael Yunis
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Space Distribution ◽  
Coarse Grained ◽  
Dark Matter Halos ◽  
The Core ◽  
The Galaxy ◽  
Gravitating Systems ◽  
The Given ◽  
First Time

Abstract The formation and stability of collisionless self-gravitating systems is a long standing problem, which dates back to the work of D. Lynden-Bell on violent relaxation, and extends to the issue of virialization of dark matter (DM) halos. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi-Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is able to explain the galaxy rotation curves while the DM core can mimic the central black hole. A yet open problem is whether this kind of astrophysical core-halo configurations can form at all, and if they remain stable within cosmological timescales. We assess these issues by performing a thermodynamic stability analysis in the microcanonical ensemble for solutions with given particle number at halo virialization in a cosmological framework. For the first time we demonstrate that the above core-halo DM profiles are stable (i.e. maxima of entropy) and extremely long lived. We find the existence of a critical point at the onset of instability of the core-halo solutions, where the fermion-core collapses towards a supermassive black hole. For particle masses in the keV range, the core-collapse can only occur for Mvir ≳ E9M⊙ starting at zvir ≈ 10 in the given cosmological framework. Our results prove that DM halos with a core-halo morphology are a very plausible outcome within nonlinear stages of structure formation.

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