Addendum: Conformally Invariant Generalization of Einstein Equations and the Causality Principle

2002 ◽  
Vol 34 (7) ◽  
pp. 1131-1133 ◽  
Author(s):  
M. V. Gorbatenko ◽  
A. V. Pushkin
Keyword(s):  
Einstein Equations ◽  
Causality Principle ◽  
Conformally Invariant

scholarly journals A VACUUM-LIKE CONFIGURATION IN GENERAL RELATIVITY AS A MANIFESTATION OF A LORENTZ-INVARIANT MODE OF FIVE-DIMENSIONAL GRAVITY

2007 ◽  
Vol 16 (04) ◽  
pp. 711-736
Author(s):  
VALENTIN D. GLADUSH
Keyword(s):  
General Relativity ◽  
Dimensional Space ◽  
Flat Space ◽  
Mass Function ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Integral Of Motion ◽  
Birkhoff Theorem ◽  
Conformally Invariant ◽  
Dimensional Gravity

A Lorentz-invariant cosmological model is constructed within the framework of five-dimensional gravity. The five-dimensional theorem which is analogical to the generalized Birkhoff theorem is proved, that corresponds to the Kaluza's "cylinder condition." The five-dimensional vacuum Einstein equations have an integral of motion corresponding to this symmetry, the integral of motion is similar to the mass function in general relativity (GR). Space closure with respect to the extra dimensionality follows from the requirement of the absence of a conical singularity. Thus, the Kaluza–Klein (KK) model is realized dynamically as a Lorentz-invariant mode of five-dimensional general relativity. After the dimensional reduction and conformal mapping the model is reduced to the GR configuration. It contains a scalar field with a vanishing conformally invariant energy–momentum tensor on the flat space–time background. This zero mode can be interpreted as a vacuum configuration in GR. As a result the vacuum-like configuration in GR can be considered as a manifestation of the Lorentz-invariant empty five-dimensional space.

Einstein equations for a Finsler-Larange space with canonical N-linear connections

2020 ◽  
Vol 4 (1) ◽  
pp. 240-247
Author(s):  
Roopa M. K ◽  
◽  
Narasimhamurthy S. K ◽  
Keyword(s):  
Einstein Equations ◽  
Linear Connections

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals The Influence of Temperature and Viscosity of Polyethylene Glycol on the Rate of Microwave-Induced In Situ Amorphization of Celecoxib

Molecules ◽  
2020 ◽  
Vol 26 (1) ◽  
pp. 110
Author(s):  
Nele-Johanna Hempel ◽  
Tra Dao ◽  
Matthias M. Knopp ◽  
Ragna Berthelsen ◽  
Korbinian Löbmann
Keyword(s):  
Polyethylene Glycol ◽  
Microwave Radiation ◽  
Magnesium Stearate ◽  
Einstein Equations ◽  
Dissolution Process ◽  
Target Temperature ◽  
Peg 4000 ◽  
Lower Viscosity ◽  
Model Drug

Microwaved-induced in situ amorphization of a drug in a polymer has been suggested to follow a dissolution process, with the drug dissolving into the mobile polymer at temperatures above the glass transition temperature (Tg) of the polymer. Thus, based on the Noyes–Whitney and the Stoke–Einstein equations, the temperature and the viscosity are expected to directly impact the rate and degree of drug amorphization. By investigating two different viscosity grades of polyethylene glycol (PEG), i.e., PEG 3000 and PEG 4000, and controlling the temperature of the microwave oven, it was possible to study the influence of both, temperature and viscosity, on the in situ amorphization of the model drug celecoxib (CCX) during exposure to microwave radiation. In this study, compacts containing 30 wt% CCX, 69 wt% PEG 3000 or PEG 4000 and 1 wt% lubricant (magnesium stearate) were exposed to microwave radiation at (i) a target temperature, or (ii) a target viscosity. It was found that at the target temperature, compacts containing PEG 3000 displayed a faster rate of amorphization as compared to compacts containing PEG 4000, due to the lower viscosity of PEG 3000 compared to PEG 4000. Furthermore, at the target viscosity, which was achieved by setting different temperatures for compacts containing PEG 3000 and PEG 4000, respectively, the compacts containing PEG 3000 displayed a slower rate of amorphization, due to a lower target temperature, than compacts containing PEG 4000. In conclusion, with lower viscosity of the polymer, at temperatures above its Tg, and with higher temperatures, both increasing the diffusion coefficient of the drug into the polymer, the rate of amorphization was increased allowing a faster in situ amorphization during exposure to microwave radiation. Hereby, the theory that the microwave-induced in situ amorphization process can be described as a dissolution process of the drug into the polymer, at temperatures above the Tg, is further strengthened.

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