Parametrized-post-Newtonian limit of the scalar-tetradic theory A

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

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The Equation of State and the Temperature, Pressure, and Shear Dependence of Viscosity for a Highly Viscous Reference Liquid, Dipentaerythritol Hexaisononanoate

Journal of Tribology ◽

10.1115/1.4033050 ◽

2016 ◽

Vol 139 (1) ◽

Cited By ~ 7

Author(s):

Scott Bair ◽

Tsuyoshi Yamaguchi

Keyword(s):

Molecular Weight ◽

Shear Stress ◽

Equation Of State ◽

High Molecular Weight ◽

Free Volume ◽

Newtonian Limit ◽

Scaling Models ◽

The Difference ◽

Better Than ◽

Low Shear

Measurements are reported for dipentaerythritol hexaisononanoate (DiPEiC9) of pressure–volume–temperature (pVT) response to pressures to 400 MPa and temperatures to 100 °C, and of viscosity at pressures to 700 MPa and temperatures to 90 °C and shear stress to 18 MPa. These data complement the low-shear viscosities published by Harris to pressures to 200 MPa and the compressions by Fandiño et al. to 70 MPa. The improved Yasutomi correlation reproduces all viscosity measurements with accuracy better than the Doolittle free volume and the Bair and Casalini thermodynamic scaling models which require an equation of state (EoS). The interaction parameter for thermodynamic scaling, γ = 3.6, is less than that reported by Harris (γ = 4.2) and the difference is primarily in the choice of EoS. The shear stress at the Newtonian limit, about 6 MPa, is exceptionally large given the high molecular weight of DiPEiC9. The large Newtonian limit is also seen in the oscillatory shear response.

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NUMERICAL STUDY OF THE INTERACTION BETWEEN POSITIVE AND NEGATIVE MASS OBJECTS IN GENERAL RELATIVITY

International Journal of Modern Physics D ◽

10.1142/s0218271812500617 ◽

2012 ◽

Vol 21 (07) ◽

pp. 1250061 ◽

Cited By ~ 2

Author(s):

ZHOUJIAN CAO

Keyword(s):

Boundary Condition ◽

General Relativity ◽

Numerical Study ◽

Naked Singularity ◽

Newtonian Limit ◽

Computational Domain ◽

Positive Mass ◽

Negative Mass ◽

Mass Particle ◽

Causal Property

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

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