3. All three solutions in 2.b correspond to de Sitter spacetime (or a portion of it), with different choices of coordinates. One way to define 4D de Sitter spacetime is via an embedding in 5D Minkoswki spacetime, 4 ds² = -(dxº)² + dx³ dx², i=1 a) Consider the coordinates with constraint l² = − (xº)² + Σx²¹x². a = V 2 – R? sinh(T/), x¹ = √²-R² cosh(T/l), 4 r = {sinh(t/l), x² = y¹l cosh(t/l). What is the constraint in terms of the coordinates y? Determine the induced line element on de Sitter spacetime. You should recover one of the cases in question 2. b) With the coordinates where j = 2, 3, 4, the analogous exercise (Assignment 4) gives -1 i=1 ds² (1 - R²³) ar² + (1 - 1²) dR² + R²³d$²₂) · 12 x³ = R₂³, These are known as static coordinates. The cosmological horizon is located at R = l. How long does it take for an observer at rest at R = 0 to receive a radially directed light ray emitted at R= Rel?

I need help with A and B for this problem. I want to see the detailed steps.

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Have you ever chewed on a wintergreen mint in front of a mirror in the dark? If you have, you may have noticed some sparks of light coming out of your mouth as you chewed on the candy; and, without knowing it, you have experienced a physical phenomenon called triboluminescence. In this problem you will analyze some of the key elements of triboluminescence in wintergreen candies. Part C Image that the radiation emitted by the nitrogen at a frequency of 8.88×1014 Hz is absorbed by an electron in a molecule of methyl salicylate. As a result, the electron in the wintergreen oil molecule jumps to an excited state. Before returning to its ground state, the electron drops an intermediate energy level, releasing two-thirds of the energy previously absorbed and emitting a photon. What is the wavelength Xw of the photon emitted by the wintergreen oil molecule? Express your answer in nanometers to three significant figures. ► View Available Hint(s) Aw= Submit [-] ΑΣΦ ? nm