The Energy-Momentum Tensor in .NET framework

Generation QR Code in .NET framework The Energy-Momentum Tensor

The Energy-Momentum Tensor
Read QR-Code In .NET
Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET applications.
Generate QR-Code In .NET Framework
Using Barcode maker for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications.
In the local frame, the components of the stress-energy tensor are simply given by (7.6), and so we have T a b = diag ( , p, p, p). Now with nonzero cosmological constant, the Einstein equation can be written as (using units with c = G = 1) G ab gab = 8 Tab (7.14)
Decode Denso QR Bar Code In .NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Making Barcode In Visual Studio .NET
Using Barcode printer for VS .NET Control to generate, create barcode image in VS .NET applications.
In the local frame, the way we have written the line element, we have a b = diag ( 1, 1, 1, 1). We use this to lower the indices of the stress-energy tensor
Bar Code Reader In VS .NET
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
QR Code Printer In Visual C#.NET
Using Barcode maker for VS .NET Control to generate, create QR Code 2d barcode image in VS .NET applications.
Tab = a bd T cd c
Printing QR Code In .NET Framework
Using Barcode generation for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
QR Code JIS X 0510 Maker In VB.NET
Using Barcode generation for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications.
(7.15)
Barcode Encoder In .NET
Using Barcode encoder for Visual Studio .NET Control to generate, create bar code image in .NET framework applications.
Making Barcode In Visual Studio .NET
Using Barcode generation for Visual Studio .NET Control to generate, create bar code image in VS .NET applications.
In this case, this is easy since everything is diagonal, and it turns out any minus signs cancel. But you should be aware that in general you need to be careful about raising and lowering the indices. Anyway, we obtain Tab = diag ( , P, P, P) Putting this together with (7.14) and (7), we have G t t t t = 8 Tt t = 8 (7.17) (7.16)
Code39 Maker In VS .NET
Using Barcode drawer for VS .NET Control to generate, create Code 39 Extended image in VS .NET applications.
Paint USD - 8 In VS .NET
Using Barcode generator for Visual Studio .NET Control to generate, create Code11 image in VS .NET applications.
3 k + a2 + a2
Code 128A Encoder In .NET
Using Barcode creation for Reporting Service Control to generate, create Code 128 image in Reporting Service applications.
Barcode Encoder In Visual Studio .NET
Using Barcode generation for Reporting Service Control to generate, create bar code image in Reporting Service applications.
Since G r r = G = G and all of the spatial components of the stress-energy tensor are also identical, we need consider only one case. We nd that G r r r r = 8 Tr r = 8 P (7.18)
Universal Product Code Version A Printer In VB.NET
Using Barcode generation for VS .NET Control to generate, create UPC-A Supplement 2 image in Visual Studio .NET applications.
Decode ECC200 In Java
Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications.
1 a 2 + 2 k + a2 + a a
UPC-A Generation In Visual C#.NET
Using Barcode encoder for VS .NET Control to generate, create UPC-A image in .NET framework applications.
Creating ANSI/AIM Code 128 In Visual Basic .NET
Using Barcode creation for VS .NET Control to generate, create Code-128 image in .NET framework applications.
Equations (7.17) and (7.18) are the Friedmann equations.
Code-39 Generator In Java
Using Barcode encoder for Android Control to generate, create Code 39 Full ASCII image in Android applications.
Make Bar Code In None
Using Barcode generator for Office Word Control to generate, create bar code image in Word applications.
The Energy-Momentum Tensor
Relativistic Effects on Number Density
We now take a slight digression to investigate the effects of motion on the density of particles within the context of special relativity. Consider a rectangular volume V containing a set of particles. We can de ne a number density of particles which is simply the number of particles per unit volume. If we call the total number of particles in the volume N , then the number density is given by n= N V
In relativity, this is true only if we are in a frame that is at rest with respect to the volume. If we are not, then length contraction effects will change the number density that the observer sees. Suppose that we have two frames F and F in the standard con guration, with F moving at velocity v along the x-axis. The number of particles in the volume is a scalar, and so this does not change when viewed from a different frame. However, length contraction along the direction of motion means that the volume will change. In Fig. 7-2, we show motion along the x-axis. Lengths along the y and z axes are unchanged under a Lorentz transformation under these conditions. If the volume of the box in a co-moving rest frame is V, then the volume of the box as seen by a stationary observer is V = 1 v2V = 1 V
Therefore, the number density in a volume moving at speed v as seen by a stationary observer is given by n = N = n V
EXAMPLE 7-3 Consider a box of particles. In the rest frame of the box, the volume V = 1 m3 and the total number of particles is N = 2.5 1025 . Compare the number density of particles in the rest frame of the box and in a rest frame where the box has velocity v = 0.9. The box moves in the x-direction with respect to the stationary observer.
The Energy-Momentum Tensor
F' y'
x x' z z'
Fig. 7-2. A volume V, which we take in this example to be a rectangular box, is shortened along the direction of motion by the length contraction effect. This will change the number density of particles contained in V.
SOLUTION 7-3 In the rest frame of the box, the number density n = 2.5 1025 particles per cubic meter. Now 1 = = 1 v2 1 1 (0.9)
2.29
A stationary observer who sees the box moving at velocity v sees the number density of particles in the box as n = n = (2.3) 2.5 1025 = 5.75 1025 particles per cubic meter. Along the x-direction, the length of the box is x= 1 1 x = m 0.43 m 2.3
Copyright © OnBarcode.com . All rights reserved.