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*A First Course in General Relativity*, and my solution to a particular problem has got me wondering if I'm being careful enough in my approach. The problem states:

Show that, in the rest frame ##\mathcal{O}## of a star of constant luminosity ##L## (total energy radiated per second), the stress-energy tensor of the radiation from the star at the event ##(t,x,0,0)## has components ##T^{00}=T^{0x}=T^{x0}=T^{xx}=L/(4\pi x^2)##. The star sits at the origin.

Starting with the ##T^{0x}## term, I know that it is the flux of 0-momentum (energy) across a surface of constant ##x##. Since the luminosity is the total power output of the star and the photons all move radially away from the source, I need simply divide ##L## by the surface area of a sphere of radius ##x##, and I obtain the desired quantity. And because ##T## is symmetric, I get ##T^{x0}## as well for free. For the ##T^{xx}## term, I know that the momentum of a photon is ##h\nu## (assuming units such that ##c=1##) which is the same as the photon's energy, so the momentum flux should be identical to the energy flux. Finally, for the ##T^{00}## term (energy flux across a surface of constant ##t##, i.e. energy density), I use the fact that for a photon, ##\Delta t=\Delta x##. So rather than dividing the total energy by some volume ##\Delta x\Delta y\Delta z##, I can use ##\Delta t\Delta y\Delta z## and I again obtain luminosity over the area of a sphere.

So, although I got the correct result, I wonder if I've been too "hand-wavey" about it. It's been a few years since I finished my undergrad, and I've lost some confidence in my ability to heuristically solve problems. Any comments?