General Relativity Assignment #3

** (1) ** Download the GRTensor Package for MAPLE and use it to calculate all of the geometrical objects that you calculated by hand in the previous assignment in problem # 7. Hand in all of the input and output data from MAPLE.

** (2)** Show that adjusting the pressure in a perfect fluid solution of the Einstein Equations by a constant amount is equivalent to introducing the cosmological constant into the field equations when a perfect fluid is present.

** (3)** Calculate the equations that are analogous to the equation of continuity and the Navier-Stokes equations of motion for the full General Relativity case when a perfect fluid is present.

** (4)** Show explicitly that the 4

** (5)**
Explicitly verify all of the details that were left out in the calculation of the isotropic coordinate line element from identification with the Schwarzschild line element.

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** (6)** Transform the Schwarzschild line element using the transformations

Find the coefficient of . .

** (7)** What is the character of the coordinates of

(a) in the line element

(b) in the line element