scholarly journals Stability of oscillating gaseous masses in massive Brans–Dicke gravity

2017 ◽  
Vol 27 (01) ◽  
pp. 1750172
Author(s):  
M. Sharif ◽  
Rubab Manzoor
Keyword(s):  
General Relativity ◽  
Equation Of Motion ◽  
Marginal Stability ◽  
Radial Perturbation ◽  
Wide Range ◽  
Perturbed Equation ◽  
Schwarzschild Radius

This paper explores the instability of gaseous masses for the radial oscillations in post-Newtonian correction of massive Brans–Dicke (BD) gravity. For this purpose, we derive linearized perturbed equation of motion through Lagrangian radial perturbation which leads to the condition of marginal stability. We discuss radius of instability of different polytropic structures in terms of the Schwarzschild radius. It is concluded that our results provide a wide range of difference with those in general relativity and BD gravity.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

scholarly journals Vibration Based Damage Detection of Rotating Beams

2018 ◽  
Vol 148 ◽  
pp. 14008 ◽  
Author(s):  
Stanislav Stoykov ◽  
Emil Manoach ◽  
Maosen Cao
Keyword(s):  
Damage Detection ◽  
Selection Criteria ◽  
Excitation Frequency ◽  
Real Life ◽  
Equation Of Motion ◽  
Damage Localization ◽  
Rotating Beam ◽  
Free Boundary Conditions ◽  
Wide Range ◽  
Detection And Localization

The early detection and localization of damages is essential for operation, maintenance and cost of the structures. Because the frequency of vibration cannot be controlled in real-life structures, the methods for damage detection should work for wide range of frequencies. In the current work, the equation of motion of rotating beam is derived and presented and the damage is modelled by reduced thickness. Vibration based methods which use Poincaré maps are implemented for damage localization. It is shown that for clamped-free boundary conditions these methods are not always reliable and their success depends on the excitation frequency. The shapes of vibration of damaged and undamaged beams are shown and it is concluded that appropriate selection criteria should be defined for successful detection and localization of damages.

scholarly journals Dark matter in logarithmic F(R) gravity

2019 ◽  
Vol 28 (12) ◽  
pp. 1950157 ◽  
Author(s):  
Tomohiro Inagaki ◽  
Yamato Matsuo ◽  
Hiroki Sakamoto
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Modified Gravity ◽  
Field Method ◽  
Quantum Corrections ◽  
Prototype Model ◽  
Wide Range ◽  
Modified Gravity Theories ◽  
Primordial Inflation ◽  
Cmb Fluctuations

The logarithmic [Formula: see text]-corrected [Formula: see text] gravity is investigated as a prototype model of modified gravity theories with quantum corrections. By using the auxiliary field method, the model is described by the general relativity with a scalaron field. The scalaron field can be identified as an inflaton at the primordial inflation era. It is also one of the dark matter candidates in the dark energy (DE) era. It is found that a wide range of the parameters is consistent with the current observations of CMB fluctuations, DE and dark matter.

scholarly journals Secular evolution of close-in planets: the effects of general relativity

2020 ◽  
Vol 493 (1) ◽  
pp. 427-436
Author(s):  
F Marzari ◽  
M Nagasawa
Keyword(s):  
General Relativity ◽  
Numerical Integration ◽  
Time Scales ◽  
Initial Conditions ◽  
Outer Planet ◽  
Secular Perturbations ◽  
Secular Evolution ◽  
Eccentric Orbits ◽  
Wide Range ◽  
Comparable Time

ABSTRACT Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet–planet scattering, Kozai, or secular migration. In this scenario, general relativity and secular perturbations have comparable time-scales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which typically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two-planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.

scholarly journals Stability Criterion for the Centrifugal Instability of Surface Intensified Anticyclones

2019 ◽  
Vol 49 (3) ◽  
pp. 827-849 ◽  
Author(s):  
Eunok Yim ◽  
Alexandre Stegner ◽  
Paul Billant
Keyword(s):  
Turbulent Viscosity ◽  
Maximum Velocity ◽  
Stability Limit ◽  
Velocity Profiles ◽  
Instability Criterion ◽  
Marginal Stability ◽  
Vertical Wavelength ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Anticyclonic Eddies

AbstractWe investigate the linear stability of intense baroclinic anticyclones, with a particular focus on the centrifugal (inertial) instability. Various vertical and radial velocity profiles are studied. The vertical profiles are such that the velocity is maximum at the surface. These profiles correspond to oceanic eddies such as submesoscale mixed-layer eddies or intense mesoscale eddies in the upper thermocline. The results show that the main characteristics of the centrifugal instability (growth rate, vertical wavelength) depend weakly on the baroclinic structure of the anticyclone. The dominant azimuthal wavenumber is for small Burger number (Bu) and for higher Bu, where Bu is the square root of the ratio of the deformation radius over the characteristic eddy radius where the velocity is maximum. The marginal stability limits of the centrifugal instability for the different velocity profiles collapse approximately on a single curve in the parameter space (Ro, Bu), where is the Rossby number, with being the maximum velocity. By means of an asymptotic analysis for short vertical wavelength, an explicit prediction for the marginal stability limit is derived for a wide range of velocity profiles. We then suggest to use, for most of oceanic anticyclones, the instability criterion valid for a Gaussian eddy: where is the Ekman number, H is the eddy depth, and ν is the turbulent viscosity at the ocean surface. Some baroclinic anticyclones can remain stable even if they have a core region of negative absolute vorticity provided that they are small enough. This formula explains the few observations of intense anticyclonic eddies having a negative core vorticity around .

Entwicklung einer physikalischen Geometrie der Raum-Zeit zum Zwecke der Interpretation der allgemeinen Relativitätstheorie

1964 ◽  
Vol 19 (6) ◽  
pp. 665-675 ◽  
Author(s):  
Ernst Schmutzer
Keyword(s):  
General Relativity ◽  
Physical Meaning ◽  
Physical Space ◽  
Equation Of Motion ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Einstein's Equation ◽  
Physical Geometry ◽  
Fixed System ◽  
Physical Components

Up to date the interpretation of the theory of general relativity is discussed. One cause for this situation is the use of mathematical coordinates without physical meaning. In continuation of thoughts of MØLLER and CATTANEO here physical coordinates are used and on this basis a 4-dimensional physical geometry of space-time is developed by projection the mathematical tensor components into physical components. For studying the curvature of the 3-dimensional physical space and for other purposes new socalled projective partial and projective covariant derivations are introduced. On this foundation EINSTEIN’S equation of motion is investigated. Definitions for the CORIOLIS acceleration and the centrifugal-gravitational acceleration for a fixed system of reference are given. The problem of energy conservation is analysed.

scholarly journals Inflation without a trace of lambda

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
John D. Barrow ◽  
Spiros Cotsakis
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Conformal Transformation ◽  
Vacuum Energy ◽  
Einstein Equations ◽  
Scale Invariant ◽  
Field Source ◽  
Scale Theory ◽  
Wide Range

AbstractWe generalise Einstein’s formulation of the traceless Einstein equations to f(R) gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally homogeneous (‘no-scale’) theory in the conformal frame with a scalar field source that has an exponential potential. We then formulate the traceless version of f(R) gravity, and we find that a conformal transformation leads to a no-scale theory conformally equivalent to general relativity and a scalar field $$\phi $$ ϕ with a potential given by the scale-invariant form: $$V(\phi )=\frac{D-2}{4D}Re^{-\phi }$$ V ( ϕ ) = D - 2 4 D R e - ϕ , where $$\phi =[2/(D-2)]\ln f^{\prime }(R)$$ ϕ = [ 2 / ( D - 2 ) ] ln f ′ ( R ) . In this theory, the cosmological constant is a mere integration constant, statistically distributed in a multiverse of independent causal domains, the vacuum energy is another unrelated arbitrary constant, and the same is true of the height of the inflationary plateau present in a huge variety of potentials. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we are led to a novel interpretation of the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of no-scale theories. Fine-tunings required in traceless general relativity or standard non-traceless f(R) theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data concerning the primordial tilt and the tensor-to-scalar ratio.

Sign in / Sign up

Export Citation Format

Share Document