Homework Statement
Problem in question is problem 5.6 in Dodelson's Modern Cosmology (https://www.amazon.com/dp/0122191412/?tag=pfamazon01-20)
Take the Newtonian limit of Einstein's equations. Combine the time-time equation (5.27) with the time-space equations of exercise 5 to obtain the...
I've been working on a problem that I can't seem to get started on. Here is how it is posted:
Metric of a space is:
ds^2 = (1+2\phi^2)dt^2 - (1-2\phi)(dx^2+dy^2+dz^2), where |\phi | << 1 everywhere. Given a point (t_0 , x_0 , y_0, z_0) find a coordinate transformation to a locally...
Homework Statement
Problem as stated: Consider a vector A^a. Is the four-component object \left( \frac{1}{A^0},\frac{1}{A^1},\frac{1}{A^2},\frac{1}{A^3}\right) a tensor?
Homework Equations
Roman indices run from 0 to 3. Einstein summation convention is used.
Tensors of rank 1 (vectors)...
Homework Statement
Question as stated: In special relativity consider the following coordinate transformation between inertial frames: first make a velocity boost v_x in the x-direction, then make a velocity boost v_y in the y-direction. 1) Is this a Lorentz transformation? 2) Find the matrix...