At the risk of being directed to some trivial exercise in Misner, Thorne and Wheeler: is it obvious your monsters represent solutions to the Einstein equations? I just wonder if the distortion of space going on is entirely consistent with the way you're distributing matter.
You've complained we don't comment on your physics, so ...
I didn't complain... I was just being realistic. I'd like to have the guy who complained that I hate physics read the paper, though :-)
Our goal is to count the number of distinct initial conigurations with fixed ADM mass M. The configurations satisfy the Einstein constraints, so they make good initial data for any choice of density profile \rho (r) (note we impose a "moment in time" symmetry on the configuration). The form of both g_tt and g_rr can be deduced explicitly for our ansatze. Although the future evolution is not known analytically, we argue in the paper they will form black holes using a kind of "mean field" argument.
Hope that helps!
Gee, people can have interests in fundamental physics *and* financial markets! ;-)
Could you give me a reference for the computations for this type of isotropic initial condition? Even if it isn't in MTW, is there an old chestnut paper somewhere that works out the Ricci and stress-energy tensors for metrics of this general form?
I find this stuff entertaining, but don't have the hours to apply to warming up my brain on these calculations. I'd rather have somebody explain them to me ;)
STS, I was thinking about your request and I think a textbook is actually the place to find what you are asking for (perhaps I misunderstand). In our references the paper by Pavelle has some analytical results for solutions with spherical symmetry, but it's not very pedagogical. The paper by Sorkin et al. is nicely written and discusses the "moment in time" symmetry in more detail.
Perhaps you could email me if I'm not getting at your specific request :-)
At the risk of being directed to some trivial exercise in Misner, Thorne and Wheeler: is it obvious your monsters represent solutions to the Einstein equations? I just wonder if the distortion of space going on is entirely consistent with the way you're distributing matter.
ReplyDeleteYou've complained we don't comment on your physics, so ...
I didn't complain... I was just being realistic. I'd like to have the guy who complained that I hate physics read the paper, though :-)
ReplyDeleteOur goal is to count the number of distinct initial conigurations with fixed ADM mass M. The configurations satisfy the Einstein constraints, so they make good initial data for any choice of density profile \rho (r) (note we impose a "moment in time" symmetry on the configuration). The form of both g_tt and g_rr can be deduced explicitly for our ansatze. Although the future evolution is not known analytically, we argue in the paper they will form black holes using a kind of "mean field" argument.
Hope that helps!
Gee, people can have interests in fundamental physics *and* financial markets! ;-)
Could you give me a reference for the computations for this type of isotropic initial condition? Even if it isn't in MTW, is there an old chestnut paper somewhere that works out the Ricci and stress-energy tensors for metrics of this general form?
ReplyDeleteI find this stuff entertaining, but don't have the hours to apply to warming up my brain on these calculations. I'd rather have somebody explain them to me ;)
STS, I was thinking about your request and I think a textbook is actually the place to find what you are asking for (perhaps I misunderstand). In our references the paper by Pavelle has some analytical results for solutions with spherical symmetry, but it's not very pedagogical. The paper by Sorkin et al. is nicely written and discusses the "moment in time" symmetry in more detail.
ReplyDeletePerhaps you could email me if I'm not getting at your specific request :-)