Wednesday, 14 July 2010

gravity - gravitational time dilation multiple sources

I wondered how time would be dilated for an object in the middle of 2 black holes, however
https://en.wikipedia.org/wiki/Gravitational_time_dilation only provides a formula for one source of gravity



i tried approximating it by multiplying the time dilation factors, however when i used 1 single source with twice the mass the results differed from 2 objects with half the mass quite drastically



the examples:
mass 1,00E+036kg distance 3000000000m
time:0,7105905766



mass 2,00E+036kg distance 3000000000m
time:0,099387802



approximation: 0,71059057660,7105905766=0,5049389676
which is off by a factor of 5 and would be even more off the closer the distance gets to the schwarzschild radius



so how can the time dilation of multiple objects be approximated ?

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