ENERGY DENSITY, PRESSURE, AND PARTICLES PRODUCED BY A SPHERICAL, STATIC GRAVITATIONAL FIELD

1995 ◽  
Vol 10 (12) ◽  
pp. 1821-1844
Author(s):  
CHRISTOPHE M. MASSACAND
Keyword(s):  
Gravitational Field ◽  
Scalar Field ◽  
Energy Density ◽  
Gravitational Potential ◽  
Extrinsic Curvature ◽  
Spherical Body ◽  
The Body ◽  
Initial State ◽  
Gauge Invariant ◽  
Finite Step

We compute the energy density and pressures due to the quantum production of particles of a scalar field. This scalar field propagates in the external gravitational field of a (3+1)-dimensional, spherically symmetric, static geometry with flat spatial sections. We assume that the gravitational potential is weak, and we work to the first order in the strength of this potential. We consider only the l=0 sector of the scalar field. Our method for computing the energy density is based on the gauge-invariant definition of particles and normal ordering with respect to the energy measurable on a hypersurface with no extrinsic curvature. The initial state of the quantum field is the gauge-invariant vacuum on one of these hypersurfaces. Our computations are finite step by step. For the pressures we use the covariant conservation of Tμν and its four-dimensional trace. We apply our results to the gravitational potential of a homogeneous spherical body. At late times, i.e. when all switch-on effects are far away from the body, the result is that a static, gravitational vacuum polarization cloud of energy and pressure is formed inside and outside the body.

On the cosmological constant problem and brane-world geometry

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abraão Capistrano ◽  
Pedro Odon
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Extrinsic Curvature ◽  
Brane World ◽  
Vacuum Energy Density ◽  
Cosmological Constant Problem ◽  
Riemannian Geometries

AbstractThe cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.

scholarly journals Figures of Pluto and Charon and their relative motion

2021 ◽  
Vol 8 (3) ◽  
pp. 533-546
Author(s):  
Konstantin V. Kholshevnikov ◽  
◽  
Denis V. Mikryukov ◽  
Mohammad S. Jazmati ◽  
◽  
...  
Keyword(s):  
Gravitational Field ◽  
Gravitational Potential ◽  
Relative Motion ◽  
Tidal Effect ◽  
The Body ◽  
Surface Shape ◽  
The Sun ◽  
Comparative Effect ◽  
Translatory Motion ◽  
Two Factors

The comparative effect of two factors on the translatory motion of the centres of mass of the Pluto-Charon system is investigated. The first important factor is the non-sphericity of the shape and gravitational field of the bodies in the system. The second is the gravitation of the Sun. As a measure of the influence of both factors we use the ratio of the corresponding perturbing acceleration to the main one. The main acceleration is caused by the mutual Newtonian attraction of Pluto and Charon. It has been established that for the first factor this measure is of the order of 10^−6, while for the second factor it is two orders of magnitude smaller. This explains why the Lidov-Kozai effect (despite a large mutual slope of 96 between the planes of the satellite’s orbit around the planet, and the barycentre of the system around the Sun) does not appear. The situation is similar to the case with the satellites of Uranus. As a result, the Pluto-Charon system remains stable at least on a timescale of millions of years. The tidal effect of the Sun on the surface shape of the bodies under study is also estimated. The ratio of the tidal potential of the Sun at a point on the surface of the body to the gravitational potential of the body itself at this point is taken as a measure of impact. It turned out to be of the order of 3 · 10^−12, which is more than six orders less than the influence of rotation and mutual attraction of Pluto and Charon. In fact, the Sun does not affect the figures of the bodies of the system.

THREE DIMENSIONAL INTERPRETATION OF GRAVITATIONAL ANOMALIES

Geophysics ◽  
1952 ◽  
Vol 17 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Fraser S. Grant
Keyword(s):  
Gravitational Field ◽  
Mass Distribution ◽  
Three Dimensional ◽  
Relaxation Method ◽  
The Body ◽  
Multipole Moments ◽  
Size And Shape ◽  
Surface Field ◽  
Derivatives Of

A method is developed for determining the approximate size and shape of the three‐dimensional mass distribution that is required to produce a given gravitational field. The first few reduced multipole moments of the distribution are calculated from the derivatives of the surface field, and the approximative structure is determined from the values of these moments and a knowledge of the density contrast between the body and its surroundings. A system of classification of problems by symmetry is introduced and its practical usage discussed. A relaxation method is described which may be used to adjust the initial solution systematically to give agreement over the whole field. A descriptive discussion is appended.

Contact force analysis on two-fingered robot grasping

2020 ◽  
pp. 146441932096402
Author(s):  
Jiun-Ru Chen ◽  
Wei-En Chen ◽  
CH Liu ◽  
Yin-Tien Wang ◽  
CB Lin ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Contact Force ◽  
Numerical Procedure ◽  
Spherical Body ◽  
Solution Procedure ◽  
The Body ◽  
Contact Forces ◽  
Grasping Forces ◽  
Robot Grasping ◽  
Force Displacement

A procedure for inverse kinetic analysis on two hard fingers grasping a hard sphere is proposed in this study. Contact forces may be found for given linear and angular accelerations of a spherical body. Elastic force-displacement relations predicted by Hertz contact theory are used to remove the indeterminancy produced by rigid body modelling. Two types of inverse kinetic analysis may be dealt with. Firstly, as the fingers impose a given tightening displacement on the body, and carry it to move with known accelerations, corresponding grasping forces may be determined by a numerical procedure. In this procedure one contact force may be chosen as the principal unknown, and all other contact forces are expressed in terms of this force. The numerical procedure is hence very efficient since it deals with a problem with only one unknown. The solution procedure eliminates slipping thus only nonslip solutions, if they exist, are found. Secondly, when the body is moving with known accelerations, if the grasping direction of the two fingers is also known, then the minimum tightening displacement required for non-sliding grasping may be obtained in closed form. In short, the proposed technique deals with a grasping system that has accelerations, and in this study the authors show that indeterminancy may be used to reduce the complexity of the problem.

On the Energy Density in a Gravitational Field

1950 ◽  
Vol 18 (4) ◽  
pp. 237-237
Author(s):  
Julius Sumner Miller
Keyword(s):  
Gravitational Field ◽  
Energy Density

scholarly journals Einstein-aether theory in Weyl integrable geometry

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
John D. Barrow
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Scalar Field ◽  
Field Model ◽  
Affine Connection ◽  
Dynamical Evolution ◽  
Field Equations ◽  
Gravitational Field Equation ◽  
Gravitational Field Equations ◽  
Geometric Origin

AbstractWe study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.

Interlaced Attitude Estimation for Spacecraft Using Vector Observations

2021 ◽  
Vol 01 (03) ◽  
Author(s):  
Lubin Chang
Keyword(s):  
Prior Information ◽  
State Of The Art ◽  
Estimation Method ◽  
Attitude Estimation ◽  
The Body ◽  
Body Frame ◽  
Initial Value ◽  
Initial State ◽  
Initial Errors ◽  
Initial Attitude

This paper proposes an interlaced attitude estimation method for spacecraft using vector observations, which can simultaneously estimate the constant attitude at the very start and the attitude of the body frame relative to its initial state. The arbitrary initial attitude, described by constant attitude at the very start, is determined using quaternion estimator which requires no prior information. The multiplicative extended Kalman filter (EKF) is competent for estimating the attitude of the body frame relative to its initial state since the initial value of this attitude is exactly known. The simulation results show that the proposed algorithms could achieve better performance compared with the state-of-the-art algorithms even with extreme large initial errors. Meanwhile, the computational burden is also much less than that of the advanced nonlinear attitude estimators.

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

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