Thursday, July 11, 2019

general relativity - How to get space component of weak field (linearized) metric?


For Minkowski space with a weak gravitational field the metric takes the form ds2=(1+2ϕ)dt2(12ϕ)(dx2+dy2+dz2),

where ϕ is the Newtonian gravitational potential.


You can get the (1+2ϕ) factor in front of the dt2 by starting with the geodesic equation and going to the "Newtonian limit" of slow speeds and a slowly changing field.


But is there a way to get the (12ϕ) factor for the spatial part of the metric by a similar procedure? What about some clever thought experiment?




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...