A naive question:
Are these subjects, i.e. classical GR and QFT in curved spacetime, being worked upon much anymore?
Who is researching this and what are the problems within these fields? Any sources are greatly appreciated.
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Sign up to join this communityA naive question:
Are these subjects, i.e. classical GR and QFT in curved spacetime, being worked upon much anymore?
Who is researching this and what are the problems within these fields? Any sources are greatly appreciated.
There are tons of research going on in the classical general relativity. One particularly active subarea is the so-called "numerical relativity", in which the evolution of the spacetime is simulated in computers.
Another smaller subarea, which I mention here because I'm personally interested in it, is the "fluid-gravity correspondence" which is the study of the hydrodynamic behavior of the spacetime close to the black holes. For example, the Navier-Stokes equation arises naturally as a certain limit of the Einstein equation.
From a very biased point of view of a mathematician, there are lots of open problems in classical general relativity. I enumerated some at this post at Math.Stackexchange. Note that some of those are considered "solved" by (members of) the physics community (the "No-hair theorem", for example, on the uniqueness of Kerr-Newman black holes); but mathematicians sometimes like to poke holes in arguments.
For the state of the art of research in general relativity, have a look at this site:
For research of QFT in curved spacetime there are actually two quite different approaches, Lagrangian QFT and axiomatic QFT. I don't know much about the former, I only skimmed this recently published texbook:
So at least two people are still active in that area :-)
People in axiomatic QFT have been busy to generalize the Haag-Kastler axioms to curved spacetimes. There are several concepts that obviously have to be generalized, like the spectral condition that uses the Poincare group. This has been accomplished several years ago and now people are generalizing theorems and concepts.
A good place to start is this textbook:
which includes a derivation of Hawking radiation and the Unruh effect.
Recently published review papers are:
A few topics comes to mind on QFT on curved spacetime are:
Quantum inequality, which addresses bounds on quantum violation of energy conditions. Just type in Larry Ford, Tom Roman or Chris Fewster for recent development.
DeSitter instabilities, which addresses whether DeSitter invariant vacua exist for interacting field theory. Perhaps a good starting point is a following paper by Polyakov.
http://arxiv.org/abs/0912.5503
and a paper by Higuchi, Marolf and Morrison.
http://arxiv.org/abs/1107.2712
There are several interesting approaches to dark matter in classical gravity. For explaining rotation curves in spiral galaxies without appealing to dark matter check out Cooperstock
http://lanl.arxiv.org/abs/astro-ph/0507619
and subsequent papers (which I am less familiar with).
Also, there is an interesting idea generically called "exotic smoothness", which (among other things) might reproduce lensing experiments that imply the existence of dark matter. A good introduction by Carl Brans can be found here:
http://lanl.arxiv.org/abs/gr-qc/9212003
He also coauthored a textbook on the subject with Torsten Asselmeyer-Maluga, Exotic Smoothness and Physics: Differential Topology and Spacetime Models published by World Scientific.
One field which uses part of the formalism is relativistic quantum information. You might want to check out http://www.isrqi.org/
Some of the problems being researched are: 1. Quantum information on curved backgrounds arXiv 1108.3896
Vacuum entanglement arXiv 1105.1192
Closed time like curves arXiv 1003.1987
Entanglement and quantum information for accelerating observes quant-ph/0410172
There is a 2003 review on the subject but it does not include too much about QFT on a curved ST.