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- TL;DR Summary
- If we could solve the EFE's for a given stress-energy configuration, the LHS of the equation would represent the whole history of the system

Please help me confirm that I understand this correctly.

Imagine a system comprised of two black holes orbiting each other, which will eventually merge. At any point in time we describe the stress-energy tensor of the system. Assume that we

It is my understanding that this is not really possible, so we have to do the following: we take ##T_{\alpha\beta}(t_0)## and solve numerically for ##G_{\alpha\beta}(t_0)##. Then we compute how ##T_{\alpha\beta}## changes in a short period Δt, in which the configuration of mass and energy follow whatever geodesics are there, obtaining ##T_{\alpha\beta}(t_0+\Delta t)##. Now we do it again, giving us ##G_{\alpha\beta}(t_0+\Delta t)##

Is this how numerical methods work, in essence?

Imagine a system comprised of two black holes orbiting each other, which will eventually merge. At any point in time we describe the stress-energy tensor of the system. Assume that we

*could*solve the EFE's for every point (t,x,y,z). This solution would contain the whole future (and past) evolution of the system, including the merge.It is my understanding that this is not really possible, so we have to do the following: we take ##T_{\alpha\beta}(t_0)## and solve numerically for ##G_{\alpha\beta}(t_0)##. Then we compute how ##T_{\alpha\beta}## changes in a short period Δt, in which the configuration of mass and energy follow whatever geodesics are there, obtaining ##T_{\alpha\beta}(t_0+\Delta t)##. Now we do it again, giving us ##G_{\alpha\beta}(t_0+\Delta t)##

Is this how numerical methods work, in essence?