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> While I'm not a cosmologist The people behind the above prove and similar works do research relatively far away from cosmology, in a field usually called mat

> While I'm not a cosmologist The people behind the above prove and similar works do research relatively far away from cosmology, in a field usually called mathematical General Relativity. In particular, they are usually mathematicians by training, not physicists. Sad side note: Most physicists (even many of those doing research in General Relativity) have never heard of mathematical GR.

ziddoap 4y ago
My understanding is that GR forms the basis of the discipline of cosmology, but your comment implies it doesn't. Could you expand on that a bit? What differentiates GR and 'mathematical GR'? Why is the formation/stability of blackholes not considered to be a part of cosmology, when the understanding of black holes is central to understanding how to universe formed? e.g. "General Relativity forms the basis for the disciplines of cosmology (the structure and origin of the Universe on the largest scales) and relativistic astrophysics (the study of galaxies, quasars, neutron stars, etc.)" from https://uwaterloo.ca/applied-mathematics/future-undergraduates/what-you-can-learn-applied-mathematics/relativity-and-cosmology https://uwaterloo.ca/applied-mathematics/future-undergraduat...
- layer8 4y ago
  A forming the basis of B doesn’t imply that everyone working on A will be considered a B-ologist.
  - ziddoap 4y ago
    Sure, I get that, but parent said: >relatively far away from cosmology and that surprised me, because it doesn't seem that far away in my eyes. Which is why I was genuinely asking for clarification. They might not be cosmologists, but this paper seems pretty close to cosmology, not 'far away' from it. If it's not, I'm happy to be wrong, but I'd like to be corrected rather than just told I'm wrong.
- codethief 4y ago
  As the sibling said, even if you consider cosmology a subfield of GR (which it is only to a small degree), not all relativists will be cosmologists. But you wanted me to expand on this a bit, so here you go: Cosmology is concerned with the cosmos as whole, i.e. the largest scales of the universe. GR looks at large scales, but not necessarily the largest ones. (A typical black hole is much smaller than a galaxy.) But this is not the only difference between the fields: General Relativity is just one tool inside a cosmologist's toolbox. Most of them also need quantum field theory, statistics and image processing in their daily work. The reason is that, while Relativity by itself is usually only concerned with theory, and mathematical GR even more so, cosmologists have to match their theories to actual observations. They are interested in the history of the universe and in the large-scale (average) behavior of what you can see on the sky. Meanwhile, mathematical GR is mostly a mathematical endeavor. People in that field tend to be mathematicians, with a background either in analysis / PDE theory or in geometry or both (geometric analysis). They are interested in physics-inspired questions but not exclusively so.
- curt15 4y ago
  >What differentiates GR and 'mathematical GR'? Mathematical GR seeks to rigorously derive mathematical properties of the equations underlying GR, such as the existence, stability, and long-range asymptotics of their solutions. It's largely a subfield of branch of math called "nonlinear wave equations".
raattgift 4y ago
> relatively far away from cosmology The preprint is in math.AP (Analysis of PDEs) alone. Most of the preprints by the three authors are found in math.AP, give or take some in math.CA (classical analysis & ODEs) and math.DG (diffgeo), with significant crossposting into math-ph and gr-qc. There is only a minority of <https://arxiv.org/list/gr-qc/new https://arxiv.org/list/gr-qc/new> that is crossposted into math.AP, but even fewer <https://arxiv.org/list/math.AP/recent https://arxiv.org/list/math.AP/recent> find themselves also in gr-qc. > Sad side note Amusingly, Alan Coley's [open problems in] "Mathematical General Relativity" <https://arxiv.org/abs/1807.08628 https://arxiv.org/abs/1807.08628> is only in gr-qc (§2.4 is relevant to the whole discussion here) and although he posts almost all his papers there, he is very much a mathematician <https://www.dal.ca/faculty/science/math-stats/faculty-staff/our-faculty/mathematics/alan-coley.html https://www.dal.ca/faculty/science/math-stats/faculty-staff/...>. (The earlier Chruściel, Galloway, Pollack "Mathematical general relativity: a sampler", citation [9] in Coley, <https://arxiv.org/abs/1004.1016 https://arxiv.org/abs/1004.1016> is in gr-qc, math.AP, and math.DG.) > (even many of those doing research in General Relativity) have never heard of mathematical GR Postdoc research? How did they avoid contact with mathematical GR? Hyper-hyper-specialization into an area where one diagonalizes almost as often as one breathes or spends all one's time in Cactus? If their shelves are surprisingly barren, they are liable to get thrown a copy of Wald, John M. Stewart (CUP 1991), and/or any of Choquet-Bruhat's books (esp. OUP 2008), and then Wald again.
- codethief 4y ago
  > Postdoc research? I obviously can't speak for everyone but, yes, at least it's been my impression that mathematical GR as a research field in mathematics is quite disconnected from physics and its existence, to some, completely unknown. Only very few people like Chruściel manage to bridge the gap and talk to and collaborate with people on both sides. To give a few data points: If you mostly do research on e.g. gravitational waves (think LIGO) you're usually far away from the typical geometric-analytical questions surrounding the foundations of GR and much more concerned with e.g. numeric simulations, elimination and modeling of noise and systematic errors, machine learning and such. Years ago, I talked to a professor in theoretical high-energy physics (mostly string theory / supergravity) and asked him for career advice because I wanted to do research on gravity and especially black holes. He told me that "GR as a research field is dead" and that, if I wanted to study black holes, there was "no way around string theory". Sure, he was probably biased and clearly living in a bubble relatively far away from "classic GR" but it still says a lot I would say. I mean even the people working on the Event Horizon Telescope don't know too much about mathematical/foundational questions in GR. They are much more interested in modeling and solving their specific problems, in this case: radioastronomical problems, problems in relativistic plasma physics etc. (Source: I have spoken to two leading scientists at the EHT about mathematical questions surrounding GR.)

ziddoap 4y ago

My understanding is that GR forms the basis of the discipline of cosmology, but your comment implies it doesn't. Could you expand on that a bit? What differentiates GR and 'mathematical GR'? Why is the formation/stability of blackholes not considered to be a part of cosmology, when the understanding of black holes is central to understanding how to universe formed? e.g. "General Relativity forms the basis for the disciplines of cosmology (the structure and origin of the Universe on the largest scales) and relativistic astrophysics (the study of galaxies, quasars, neutron stars, etc.)" from https://uwaterloo.ca/applied-mathematics/future-undergraduates/what-you-can-learn-applied-mathematics/relativity-and-cosmology https://uwaterloo.ca/applied-mathematics/future-undergraduat...

layer8 4y ago
A forming the basis of B doesn’t imply that everyone working on A will be considered a B-ologist.
- ziddoap 4y ago
  Sure, I get that, but parent said: >relatively far away from cosmology and that surprised me, because it doesn't seem that far away in my eyes. Which is why I was genuinely asking for clarification. They might not be cosmologists, but this paper seems pretty close to cosmology, not 'far away' from it. If it's not, I'm happy to be wrong, but I'd like to be corrected rather than just told I'm wrong.
codethief 4y ago
As the sibling said, even if you consider cosmology a subfield of GR (which it is only to a small degree), not all relativists will be cosmologists. But you wanted me to expand on this a bit, so here you go: Cosmology is concerned with the cosmos as whole, i.e. the largest scales of the universe. GR looks at large scales, but not necessarily the largest ones. (A typical black hole is much smaller than a galaxy.) But this is not the only difference between the fields: General Relativity is just one tool inside a cosmologist's toolbox. Most of them also need quantum field theory, statistics and image processing in their daily work. The reason is that, while Relativity by itself is usually only concerned with theory, and mathematical GR even more so, cosmologists have to match their theories to actual observations. They are interested in the history of the universe and in the large-scale (average) behavior of what you can see on the sky. Meanwhile, mathematical GR is mostly a mathematical endeavor. People in that field tend to be mathematicians, with a background either in analysis / PDE theory or in geometry or both (geometric analysis). They are interested in physics-inspired questions but not exclusively so.
curt15 4y ago
>What differentiates GR and 'mathematical GR'? Mathematical GR seeks to rigorously derive mathematical properties of the equations underlying GR, such as the existence, stability, and long-range asymptotics of their solutions. It's largely a subfield of branch of math called "nonlinear wave equations".

raattgift 4y ago

> relatively far away from cosmology The preprint is in math.AP (Analysis of PDEs) alone. Most of the preprints by the three authors are found in math.AP, give or take some in math.CA (classical analysis & ODEs) and math.DG (diffgeo), with significant crossposting into math-ph and gr-qc. There is only a minority of <https://arxiv.org/list/gr-qc/new https://arxiv.org/list/gr-qc/new> that is crossposted into math.AP, but even fewer <https://arxiv.org/list/math.AP/recent https://arxiv.org/list/math.AP/recent> find themselves also in gr-qc. > Sad side note Amusingly, Alan Coley's [open problems in] "Mathematical General Relativity" <https://arxiv.org/abs/1807.08628 https://arxiv.org/abs/1807.08628> is only in gr-qc (§2.4 is relevant to the whole discussion here) and although he posts almost all his papers there, he is very much a mathematician <https://www.dal.ca/faculty/science/math-stats/faculty-staff/our-faculty/mathematics/alan-coley.html https://www.dal.ca/faculty/science/math-stats/faculty-staff/...>. (The earlier Chruściel, Galloway, Pollack "Mathematical general relativity: a sampler", citation [9] in Coley, <https://arxiv.org/abs/1004.1016 https://arxiv.org/abs/1004.1016> is in gr-qc, math.AP, and math.DG.) > (even many of those doing research in General Relativity) have never heard of mathematical GR Postdoc research? How did they avoid contact with mathematical GR? Hyper-hyper-specialization into an area where one diagonalizes almost as often as one breathes or spends all one's time in Cactus? If their shelves are surprisingly barren, they are liable to get thrown a copy of Wald, John M. Stewart (CUP 1991), and/or any of Choquet-Bruhat's books (esp. OUP 2008), and then Wald again.

codethief 4y ago
> Postdoc research? I obviously can't speak for everyone but, yes, at least it's been my impression that mathematical GR as a research field in mathematics is quite disconnected from physics and its existence, to some, completely unknown. Only very few people like Chruściel manage to bridge the gap and talk to and collaborate with people on both sides. To give a few data points: If you mostly do research on e.g. gravitational waves (think LIGO) you're usually far away from the typical geometric-analytical questions surrounding the foundations of GR and much more concerned with e.g. numeric simulations, elimination and modeling of noise and systematic errors, machine learning and such. Years ago, I talked to a professor in theoretical high-energy physics (mostly string theory / supergravity) and asked him for career advice because I wanted to do research on gravity and especially black holes. He told me that "GR as a research field is dead" and that, if I wanted to study black holes, there was "no way around string theory". Sure, he was probably biased and clearly living in a bubble relatively far away from "classic GR" but it still says a lot I would say. I mean even the people working on the Event Horizon Telescope don't know too much about mathematical/foundational questions in GR. They are much more interested in modeling and solving their specific problems, in this case: radioastronomical problems, problems in relativistic plasma physics etc. (Source: I have spoken to two leading scientists at the EHT about mathematical questions surrounding GR.)