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Copyright 2006 by The McGrawHill Companies, Inc. Click here for terms of use. in .NET framework
Copyright 2006 by The McGrawHill Companies, Inc. Click here for terms of use. QR Code JIS X 0510 Reader In VS .NET Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET framework applications. Denso QR Bar Code Maker In .NET Framework Using Barcode generation for .NET Control to generate, create QR Code ISO/IEC18004 image in .NET applications. The Schwarzschild Solution
Decode QRCode In VS .NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications. Encode Bar Code In Visual Studio .NET Using Barcode encoder for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. The solution we will obtain is known as the Schwarzschild solution. It was found in 1916 by the German physicist Karl Schwarzschild while he was serving on the Russian front during the First World War. He died from an illness soon after mailing his solution to Einstein, who was surprised that such a simple solution to his equations could be obtained. Reading Bar Code In .NET Framework Using Barcode recognizer for .NET Control to read, scan read, scan image in VS .NET applications. Making QRCode In Visual C# Using Barcode maker for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in VS .NET applications. The Vacuum Equations
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Bar Code Generator In Java Using Barcode creation for Android Control to generate, create barcode image in Android applications. Generating Code 128 Code Set C In Visual Basic .NET Using Barcode maker for .NET Control to generate, create Code128 image in Visual Studio .NET applications. Our next task is to think about how spherical symmetry affects the form of a metric. A spherically symmetric metric is one that has no preferred angular direction in space, meaning that we should be able to change d d and d d without changing the form of the metric. In the same way that time independence eliminated mixed terms involving dt from consideration, we cannot have mixed terms such as dr d , dr d , d d that would be affected by the changes d d and d d . So we have arrived at a metric that must have an entirely diagonal form. We have already eliminated any explicit time dependence from the terms of the metric. Since we are imposing radially symmetry, each term in the metric can be multiplied by a coef cient function that depends only on r . Using (10.2) as a guide, we can write this metric as ds 2 = A (r )dt 2 B (r ) dr 2 C (r ) r 2 d 2 D (r ) r 2 sin2 d 2 (10.3) Printing Linear 1D Barcode In Java Using Barcode generation for Java Control to generate, create Linear Barcode image in Java applications. GS1  12 Creator In None Using Barcode maker for Software Control to generate, create UPC Symbol image in Software applications. Spherical symmetry requires that the angular terms assume the normal form of d 2 that we are used to, and so we take C = D and write this as ds 2 = A (r ) dt 2 B (r ) dr 2 C (r ) r 2 d 2 + r 2 sin2 d 2 (10.4) Now we can simplify matters even further by a change of radial coordinate to eliminate C. For the moment we will call the new radial coordinate and de ne it using = C (r ) r . Then we have 2 = Cr 2 and the angular part of the metric assumes the familiar form C (r ) r 2 d 2 + r 2 sin2 d 2 = Cr 2 d 2 + Cr 2 sin2 d 2 = 2 d 2 + 2 sin2 d 2 From the de nition = C (r ) r , we see that we can write 1 d = dC r + C dr 2 C = = 1 dC r + C dr 2 C dr C r dC r + 1 dr 2C dr 1 n

