This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
---|---|---|---|---|---|---|---|---|
2 | change two variables in expr |
|
|
|
valid |
8946383937:
4275004561: dimensions are consistent |
8946383937:
4275004561: N/A |
|
4 | divide both sides by |
|
|
|
valid |
2883079365:
dimensions are consistent 6800170830: |
2883079365:
N/A 6800170830: |
|
1 | raise both sides to power |
|
|
|
no check is performed |
5404822208:
8946383937: |
5404822208:
8946383937: |
|
3 | multiply both sides by |
|
|
|
valid |
4275004561:
dimensions are consistent 2883079365: dimensions are consistent |
4275004561:
N/A 2883079365: N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
---|---|---|---|---|---|---|---|---|---|
4567 | constant |
c
\(c\) |
['real'] |
|
speed of light in vacuum |
299792458 meters/second |
32 | ||
2530 | variable |
r
\(r\) |
['real'] |
|
radius | 34 | |||
6277 | constant |
G
\(G\) |
real |
|
gravitational constant |
6.67430*10^{-11} m^3 * kg^-1 * s^-2 |
46 | ||
4518 | variable |
r_{\rm Schwarzschild}
\(r_{\rm Schwarzschild}\) |
real |
|
Schwarzschild radius; event horizon | 5 | |||
8656 | variable |
v_{\rm escape}
\(v_{\rm escape}\) |
real |
|
escape velocity | 12 | |||
5156 | variable |
m
\(m\) |
['real'] |
|
mass |
|
57 |