(This is not homework. I am reading MTW on my own.) I have worked on this and worked on this and cannot see how to solve it. It is Exercise #2.6, on page 65 of MTW. I quote verbatim:(adsbygoogle = window.adsbygoogle || []).push({});

"To each event Q inside the sun one attributes a temperature T(Q), the temperature measured by a thermometer at rest in the hot sun there. Then T(Q) is a function; no coordinates are required for its definition and discussion. A cosmic ray from outer space flies through the sun with 4-velocityu. Show that, as measured by the cosmic ray's clock, the time derivative in its vicinity is

[tex]\frac{dT}{d\tau} = \partial_u T = <dT,u>[/tex].

In a local Lorentz frame inside the sun, this question can be written

[tex]\frac{dT}{d\tau} = u^\alpha \frac{\partial T}{\partial x^\alpha} = \frac{1}{\sqrt(1 - v^2)} \frac{\partial T}{\partial t} + \frac{v^j}{\sqrt(1 - v^2)} \frac{\partial T}{\partial x^j}[/tex].

Why is this result reasonable?"

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The temperature gradient inside the sun would be [tex]\frac{dT}{dt}[/tex]. But wrt the cosmic ray, the temperature gradient is [tex]\frac{dT}{d\tau}[/tex], which is the above equation. No? I guess I am askingwhatam I supposed to show?

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# GRAVITAION, by MTW, Exer. 2.6

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