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qr code reader c# .net Frame Dragging in VS .NET
Frame Dragging Quick Response Code Scanner In VS .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications. Encode QR Code In .NET Framework Using Barcode encoder for Visual Studio .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications. The rotational nature of the Kerr solution leads to an interesting effect known as frame dragging. We imagine dropping a particle in from in nity with zero angular momentum. This particle will acquire an angular velocity in the direction in which the source is rotating. An easy way to describe this phenomenon is to Scanning QR Code In Visual Studio .NET Using Barcode scanner for VS .NET Control to read, scan read, scan image in .NET applications. Make Barcode In Visual Studio .NET Using Barcode printer for .NET framework Control to generate, create barcode image in .NET framework applications. Black Holes
Scanning Barcode In .NET Framework Using Barcode scanner for .NET Control to read, scan read, scan image in VS .NET applications. Create QR In Visual C# Using Barcode creation for VS .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications. consider the momentum four vector and the components of the metric tensor. Looking at the inverse components of the metric (11.13) consider the ratio 2mar g t = = tt g (r 2 + a 2 )2 a 2 sin2 (11.17) Creating QR In VS .NET Using Barcode printer for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications. QR Code JIS X 0510 Printer In Visual Basic .NET Using Barcode generation for Visual Studio .NET Control to generate, create QRCode image in .NET framework applications. Now imagine a massive particle dropped in with zero angular momentum. The angular velocity is given by d /d p d = = t dt dt/d p With p = 0, we have p t = g tt pt and p = g t pt and so this expression becomes, using (11.17), g t 2mar p = tt = = t 2 + a 2 )2 a 2 sin2 p g (r Note that the angular velocity is proportional to terms that make up the metric, and so think of it as being due to the gravitational eld. Therefore, we see that if we drop a particle in from in nity with zero angular momentum, it will pick up an angular velocity from the gravitational eld. This effect is called frame dragging and it causes a gyroscopic precession effect known as the LenseThirring effect. In the equatorial plane we have = 0 and so sin2 = (1/2) (1 cos 2 ) = 0, giving a simpli ed expression for the angular velocity given by = 2mar (r 2 + a 2 )2 Code 128 Maker In .NET Framework Using Barcode creation for .NET Control to generate, create Code 128 Code Set B image in Visual Studio .NET applications. Encode Linear 1D Barcode In VS .NET Using Barcode printer for Visual Studio .NET Control to generate, create Linear Barcode image in Visual Studio .NET applications. Let s consider what happens to light near a Kerr black hole. More speci cally, we consider light that initially moves on a tangential path (so we set dr = 0). Recall that for a null ray ds 2 = 0, and so con ning ourselves to the equatorial plane using (11.14) we nd the following relation for light: a 2 2ma 2 2 2 4ma r d dtd 1 + 2 + 3 r r r Make Bar Code In VS .NET Using Barcode encoder for VS .NET Control to generate, create barcode image in VS .NET applications. Intelligent Mail Printer In Visual Studio .NET Using Barcode creator for .NET Control to generate, create 4State Customer Barcode image in .NET framework applications. 0= 1 Painting UPCA Supplement 2 In Java Using Barcode creation for Android Control to generate, create UPC A image in Android applications. Bar Code Printer In Java Using Barcode generator for Java Control to generate, create bar code image in Java applications. 2m r
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To simplify notation, we follow Taylor and Wheeler (2000) and introduce the reduced circumference R2 = r 2 + m2 + 2m 3 r (11.19) Then (11.18) can be written in the more compact form 0= 1 2m r dt 2 + 4ma dt d R 2 d 2 r (11.20) Dividing through (11.20) by dt 2 and then by R 2 gives us the following quadratic equation for d /dt: d dt 1 2m 4ma d 2 1 2 dt rR R r
(11.21) We wish to consider an important special case, the static limit where r = rs = 2m. In this case notice that the last term in (11.21) vanishes: 1 2m 2m =1 =1 1=0 r 2m Meanwhile, at the static limit R 2 = 6m 2 and the middle coef cient in (11.21) becomes 4ma 4ma 4ma a = = = 2 2 3 rR (2m)6m 12m 3m 2 Putting these results together, at the static limit (11.21) can be written as d dt a d =0 3m 2 dt
(11.22) There are two solutions to this equation, given by a d = dt 3m 2 and d =0 dt (11.23) a The rst solution, d = 3m 2 , represents light that is emitted in the same direction dt in which the black hole is spinning. This is a very interesting result indeed; note Black Holes
that the motion of the light is constrained by the angular momentum a of the black hole! The second solution, however, represents an even more astonishing result. If the light is emitted in the direction opposite to that of the black hole s rotation, then d = 0; that is, the light is completely stationary! Since no material particle dt can attain a velocity that is faster than that of light, it is absolutely impossible to move in a direction opposite to that of the black hole s rotation. No rocket ship, probe, or elementary particle can do it.

