scholarly journals The Effective Equation of Motion on the Brane World Gravity

2006 ◽  
Vol 38 (1) ◽  
pp. 1-20
Author(s):  
F. P. Zen ◽  
Arianto ◽  
B. E. Gunara ◽  
H. Zainuddin
Keyword(s):  
Equation Of Motion ◽  
Brane World ◽  
Effective Equation

scholarly journals A TOPOLOGICAL EXTENSION OF GENERAL RELATIVITY TO EXPLORE THE NATURE OF QUANTUM SPACETIME, DARK ENERGY AND INFLATION

2013 ◽  
Vol 22 (10) ◽  
pp. 1330022
Author(s):  
M. SPAANS
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Discrete Time ◽  
Thought Experiment ◽  
Planck Scale ◽  
Equation Of Motion ◽  
Effective Equation ◽  
Dark Energy Density ◽  
Topological Quantum ◽  
Quantum Spacetime

General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BHs)/wormholes. Paths are fundamental and prime three-manifolds like T3, S1 × S2 and S3 are used to construct quantum spacetime. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum spacetime. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic BHs in the universe and is time-dependent in a manner consistent with current astrophysical observations, having an effective equation of state w ≈ -1.1 for redshifts smaller than unity. Inflation driven by mini BHs proceeds over n ≈ 55 e-foldings, without strong inhomogeneity. A discrete time effect visible in the cosmic microwave background is suggested.

MOMENTS OF THE SPIN-DEPENDENT PROTON STRUCTURE FUNCTION

1990 ◽  
Vol 05 (14) ◽  
pp. 1125-1130
Author(s):  
D. INDUMATHI ◽  
M. V. N. MURTHY ◽  
V. RAVINDRAN
Keyword(s):  
Structure Function ◽  
Operator Product Expansion ◽  
Equation Of Motion ◽  
Proton Structure Function ◽  
Operator Product ◽  
Effective Equation ◽  
The Third ◽  
Proton Structure ◽  
First Moment ◽  
Third Moment

We discuss the moments of the recently measured spin-dependent structure function, [Formula: see text], of the proton. Using the operator product expansion and an effective equation of motion, we show that the third moment can be related to the first moment.

scholarly journals Application of the method of asymptotic homogenization to an acoustic metafluid

2011 ◽  
Vol 467 (2135) ◽  
pp. 3318-3331 ◽  
Author(s):  
John D. Smith
Keyword(s):  
Material Properties ◽  
Effective Properties ◽  
Low Frequency ◽  
Equation Of Motion ◽  
Effective Equation ◽  
Asymptotic Homogenization ◽  
Effective Wave ◽  
Dynamic Effective Properties ◽  
Anisotropic Stiffness ◽  
Natural Way

The method of asymptotic homogenization is used to find the dynamic effective properties of a metamaterial consisting of two alternating layers of fluid, repeating periodically. As well as the effective wave equation, the method gives the effective equation of motion and constitutive relation in a natural way. When the material properties are such that resonant effects can be present in one of the layers, it is found that the metamaterial changes dynamically from a metafluid with anisotropic density and isotropic stiffness at low frequency to one with anisotropic stiffness when the frequency is near to one of the local resonances. In this region of frequency, the resulting metamaterial is not a pentamode material and thus does not belong to the class of metafluids that can be transformed to an isotropic fluid by a coordinate transformation.

Scalar field thin shell collapse in the Brane-world geometry

2020 ◽  
Vol 35 (06) ◽  
pp. 2050028
Author(s):  
G. Abbas ◽  
M. R. Shahzad
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Effective Potential ◽  
Thin Shell ◽  
Quadratic Function ◽  
Equation Of Motion ◽  
Brane World ◽  
Massive Scalar ◽  
Dynamical Equations ◽  
Massive Scalar Field

In this paper, we studied the dynamics of thin shell in the perfect fluid composed of scalar field. To formulate the equation of motion of the shell, we used the Israel thin-shell formalism for the Brane-world black hole in the two surrounding vacuum regions (interior and exterior). In this study, we considered the potential function as a quadratic function of scalar field. The resulting dynamical equations have been analyzed numerically for both the cases, massless and massive scalar field through the effective potential and radius of the shell by considering different settings of the parameters involved. We found that there are three possibilities in this geometry, thin shell in the scalar field can expand, collapse or attain equilibrium for a while, however, in most of the cases for large value of radius, thin shell collapses to zero size. The effects of the parameters [Formula: see text] and [Formula: see text] (involved due to the Brane-world geometry) on the expansion and collapsing rates have been analyzed and the obtained results compared with the Schwarzschild case ([Formula: see text], [Formula: see text]).

scholarly journals Warm constant-roll inflation in brane-world cosmology

2021 ◽  
Author(s):  
M. R. Setare ◽  
A. Ravanpak ◽  
K. Bahari ◽  
G. F. Fadakar
Keyword(s):  
Scalar Field ◽  
Analytical Solution ◽  
Friedmann Equation ◽  
Equation Of Motion ◽  
Brane World ◽  
Inflationary Model ◽  
Warm Inflation ◽  
Scalar Spectral Index ◽  
Good Consistency ◽  
Numerical Approaches

In this paper, we study a constant-roll inflationary model in the context of brane-world cosmology caused by a quintessence scalar field for warm inflation with a constant dissipative parameter [Formula: see text]. We determine the analytical solution for the Friedmann equation coupled to the equation of motion of the scalar field. The evolution of the primordial scalar and tensor perturbations is also studied using the modified Langevin equation. To check the viability of the model, we use numerical approaches and plot some figures. Our results for the scalar spectral index and the tensor-to-scalar ratio show good consistency with observations.

scholarly journals Perturbation analysis of the effective equation for two coupled periodically driven oscillators

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Andrzej Okniński ◽  
Jan Kyzioł
Keyword(s):  
Dynamical System ◽  
Perturbation Analysis ◽  
Approximate Equation ◽  
Equation Of Motion ◽  
Internal Motion ◽  
Effective Equation ◽  
Periodically Driven

Dynamics of two coupled periodically driven oscillators is analyzed via approximate effective equation of motion. The internal motion is separated off exactly and then approximate equation of motion is derived. Perturbation analysis of the effective equation is used to study the dynamics of the initial dynamical system.

scholarly journals On causal structure of 4D-Einstein–Gauss–Bonnet black hole

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Naresh Dadhich
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Causal Structure ◽  
Equation Of Motion ◽  
Cauchy Horizon ◽  
Coupling Constant ◽  
Schwarzschild Black Hole ◽  
Effective Equation ◽  
Central Singularity ◽  
Static Black Hole

AbstractThe recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in $$D\ge 5$$ D ≥ 5 , the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.

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