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yotta

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**Main Question or Discussion Point**

Is red-shifted light brighter than what its black-body emission would be at the same temperature?

As a figurative example, a star, neutron star, or other astronomical body has a temperature of 6,000 K, and is so close to its Schwarzschild radius that its light is red-shifted by a factor of 3, meaning that it appears to an observer outside the gravity well to have a temperature of 2,000 K, and a measure of the equivalent black-body temperature of its light confirms this. Atomic spectral emission lines are red-shifted by a factor of 3. (Is red-shifting stated this way?) Doppler red-shifting, such as from the expansion of the universe, would be the same.

Photon energy and flux are decreased by the amount of red-shift. However, luminosity increases by the fourth power of temperature. Photon energy is directly proportional, flux varies by the third power, so the end result varies by the fourth power.

In red-shifting from 6,000 K to 2,000 K, the photon wavelength increases by 3, so the energy decreases by 3, and the flux decreases by 3 due to time dilation inside the gravity well. Cumulatively, these are decreases by the inverse square, or 9.

There still remains the square of photon flux that is not red-shifted. Therefore, outside of the gravity well, the star's light would be observed to be at the color temperature of 2,000 K, but shining 9 times brighter than what its black-body emission would be at that temperature.

The equivalent black-body temperature for the same energy of luminosity is 2,000 K(√3), or 3,464 K. Assuming it is far enough out to not be red-shifted itself, a planet with a semimajor axis where it would receive 1.0 Earth's received energy flux from the Sun, but at 3,464 K, will receive that same energy from the star's light at 2,000 K, but 9 times brighter.

Momentarily ignoring the impossibility of a star to be so dense, do I have the correct assessment of this situation? If not, why not? If yes, it seems to me highly unlikely that I'd be the first to see it, so I assume red-shifting is already being considered with the "un-red-shifted square?"

I don't think I'm putting forth any new theory, just pointing out something fairly easily seen, but seldom discussed. I just don't see any way that, if red-shifting and either gravitational time dilation or the slowing of arriving Doppler-shifted photons are both inversely proportional, and together they result in the energy of the light spectrum varying by the inverse square, and the black-body emitted light energy varies by the fourth power of temperature, there's any way to avoid having an "un-red-shifted square."

I'll refrain from discussion of the implications of this, until I have firmer ground to stand on. I don't want to be premature.

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