- #1

The Wanderer

- 12

- 0

## Homework Statement

I have been trying to understand the actual applications and mathematics behind Einstein's Field Equations. I have watched a two hour long lecture on how they were derived and have pretty much understood it, however I still don't know how to actually "use" Einstein's Field Equations. I ran into Schwarzschild's Metric and I believe the first thing you do is you solve for metric tensor so for simplicity sake I am going to chose his metric. Now say if I wanted to calculate the time it takes for the Earth to orbit the sun, how would I go about this? I know you have to somehow use geodesics, but I'm not entirely sure how. If you don't want to go through all the work that is fine as long as you point me to something to read. Also I noticed that the Schwarzschild's metric equation looks a lot like the arc length formula. Is this correct? Can it somehow be rearranged to express it as an integral, then? Also, could you help me by telling me what mathematics I need to understand to further grasp this topic. I haven't been formally taught Calculus, but these are the topics that I understand/know.

- derivatives
- what a definite and indefinite integral is
- how to solve an indefinite integral
- don't know how to solve a definite integral rigorously, but know how to with a calculator as an aide
- understand what a differential equation is, but not how to solve for one. (I think you use a differential field or something, seen them and I could guess how you generate one)
- partial derivatives
- gradients

## Homework Equations

Schwarzschild's Metric

[itex]ds^{2} = (1 - \frac{r_s}{r})^{-1}dr^{2} + r^{2}(dθ^{2} + sin^{2}θd\varphi^{2})-c^{2}(1 - \frac{r_s}{r})dt^{2}[/itex]

## The Attempt at a Solution

Not exactly sure if I can show an attempt at a solution, but I do not need to be "spoonfed", just point me in the right direction and tell me what I need to learn and what to read. I do, however, learn from examples the best as I am a visual learner, but it isn't required. Thank you so much for the help.