(1.) Consider a spacetime in which only photons (i.e., electromagnetic waves) are present. (a.) What must be the value of the curvature (Ricci) scalar R in such a spacetime? (b.) How does your result change if you now add a perfect fluid of massless particles, not necessarily photons? (c.) Find a condition on the sign of the Ricci (curvature) scalar for a spacetime filled with some arbitrary perfect fluid. (1.) Consider a spacetime in which only photons (i.e., electromagnetic waves) are present. (a.) What must be the value of the curvature (Ricci) scalar R in such a spacetime? (b.) How does your result change if you now add a perfect fluid of massless particles, not necessarily photons? (c.) Find a condition on the sign of the Ricci (curvature) scalar for a spacetime filled with some arbitrary perfect fluid