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Thanks so much for the references! > > black hole solutions assume a perfect vacuum > Not quite You're right, I should have been more precise here. I was mer

Thanks so much for the references! > > black hole solutions assume a perfect vacuum > Not quite You're right, I should have been more precise here. I was merely trying to say: The spacetimes in the vicinity of celestial bodies can be modeled sufficiently well by vacuum black hole solutions (obviously as long as we don't get too close and don't need to consider accretion disks, radiation and what not).

raattgift 4y ago
... or actual surfaces, which we are allowed in Kerr (or more properly perturbations thereof) or Hartle-Thorne spacetimes where the central body is non-compact, for example. Where modelling an astrophysical body this way tends to fall down is that as far as we can tell the central mass evolves and is in general not uniform in the sense that it has long-lasting multipole moments (that would quickly bald away for a black hole), frustrating the hopes of matching the object's interior with the exterior solution. In comparison, outer space is practically always empty enough of stress-energy that the non-physicality of the vacuum or lambdavac region is rarely the issue (and can be dealt with perturbatively, for example). The other major problem is that binary (and triple) systems are surprisingly commonplace, and the N-body problem will drive one towards approximations of GR for tractability. This is the essence of this thread's cautions on the difficulties in superposing solutions to the EFEs. Worse, the two problems above can feed into one another, like when binary stars raise long-lived bumps on each other. This reminds me to re-read the invigorating <https://link.springer.com/article/10.1007/s00190-016-0927-4 https://link.springer.com/article/10.1007/s00190-016-0927-4> which compares the gravitation of Earth and its messy multibody neighbourhood with several exact vacuum solutions and a couple of formalisms. The first author is the redoubtable Michael Soffel <https://www.iau.org/administration/membership/individual/7332/ https://www.iau.org/administration/membership/individual/733...> A PDF of the paper can also be found at s c y h o b. The kicker is the two paragraphs before section 3.

raattgift 4y ago

... or actual surfaces, which we are allowed in Kerr (or more properly perturbations thereof) or Hartle-Thorne spacetimes where the central body is non-compact, for example. Where modelling an astrophysical body this way tends to fall down is that as far as we can tell the central mass evolves and is in general not uniform in the sense that it has long-lasting multipole moments (that would quickly bald away for a black hole), frustrating the hopes of matching the object's interior with the exterior solution. In comparison, outer space is practically always empty enough of stress-energy that the non-physicality of the vacuum or lambdavac region is rarely the issue (and can be dealt with perturbatively, for example). The other major problem is that binary (and triple) systems are surprisingly commonplace, and the N-body problem will drive one towards approximations of GR for tractability. This is the essence of this thread's cautions on the difficulties in superposing solutions to the EFEs. Worse, the two problems above can feed into one another, like when binary stars raise long-lived bumps on each other. This reminds me to re-read the invigorating <https://link.springer.com/article/10.1007/s00190-016-0927-4 https://link.springer.com/article/10.1007/s00190-016-0927-4> which compares the gravitation of Earth and its messy multibody neighbourhood with several exact vacuum solutions and a couple of formalisms. The first author is the redoubtable Michael Soffel <https://www.iau.org/administration/membership/individual/7332/ https://www.iau.org/administration/membership/individual/733...> A PDF of the paper can also be found at s c y h o b. The kicker is the two paragraphs before section 3.