Equivalence of the Regge and Einstein equations for almost flat simplicial space-times

1989 ◽  
Vol 21 (6) ◽  
pp. 565-583 ◽  
Author(s):  
Leo Brewin
Keyword(s):  
Einstein Equations ◽  
Simplicial 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.

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.

Einstein Equations and Alternative Lagrangians

1995 ◽  
Vol 32 (2) ◽  
pp. 185-190 ◽  
Author(s):  
R. de Ritis ◽  
C Rubano ◽  
P Scudellaro
Keyword(s):  
Einstein Equations

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2762-2762
Author(s):  
E. GOURGOULHON ◽  
J. NOVAK
Keyword(s):  
Numerical Simulations ◽  
Extrinsic Curvature ◽  
Einstein Equations ◽  
Numerical Implementation ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Tensor Density ◽  
Dirac Gauge ◽  
Ill Posed ◽  
Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

4D Einstein equations in a general gauge Kaluza–Klein space

2015 ◽  
Vol 12 (03) ◽  
pp. 1550036
Author(s):  
Aurel Bejancu ◽  
Constantin Călin
Keyword(s):  
Einstein Equations ◽  
Tensor Fields ◽  
New Approach ◽  
Higher Dimensional ◽  
High Level ◽  
General Gauge ◽  
Kaluza Klein

Using the new approach on higher-dimensional Kaluza–Klein theories developed by the first author, we obtain the 4D Einstein equations on a (4 + n)D relativistic gauge Kaluza–Klein space. Adapted frame and coframe fields, adapted tensor fields, and the Riemannian adapted connection, have a fundamental role in the study. The high level of generality of the study, enables us to recover several results from earlier papers on this matter.

Sign in / Sign up

Export Citation Format

Share Document