But where are the wormholes?
August 20, 2022
My work has been on wormholes for about nearly a year now, and this was a question I kept asking myself — if wormholes are mathematically reasonable, where are they?
And they are, mathematically reasonable — that’s what you get from solving the field equations in general relativity, you get solutions that describe different physical phenomena with different topologies. But wormholes are special, since they contain exotic matter — saying which might make me sound like a dork, but this is simply the kind of matter to violate the strong energy condition, which says that two particles at most will get attracted to each other, but never repel. This was also characterised by Ellis in terms of a scalar field he called “phantom”. This is inconsistent with general relativity, and wormholes have been seen as evil since then.
But as is the case for most of physics (which fortunately for me gets me to work), this can be changed by curvature based corrections, using what are called as modified theories of gravity. These are theories obtained by perturbing the usual approach to general relativity, which for the geeks out there would make sense in terms of corrections based on the action and/or curvature Lagrangians. For others, here’s a way to get this: instead of letting one particular curvature term in the first order define the idea of gravitation (GR), we can extend it to arbitrary functions including higher orders, which allow us to understand phenomena in astrophysics differently, and hopefully, better. This was the case for describing the acceleration of cosmological expansion in terms of a modified theory of gravity in the fourth order [1] by Carroll et al in 2003. Wormholes can also be described similarly using a curvature sector theory, where we use the approach described above. This has been my research too, a paper here [2]. But then, where are the wormholes?
We are currently far from actually getting the total idea of whether or not all sorts of wormholes are possible. Black holes were different altogether — from the No hair theorem, the only parameters describing black holes (that are mass, electric charge and angular momentum) imply that there are only four sorts of black holes, since mass is a constant feature in all of them. Black holes are described only by these parameters, which is to say that they don’t have “hair”. Which is why today’s sponsor is Hair fall loss Control, get up to 40% off on the first 400 registrations by using the code “no hair”. Worst joke in the world, please don’t smack me.
Wormholes on the other hand have different sorts based on the topology, such as Morris-Thorne, Ellis, exponential, NUT wormholes (honestly, I will admit I giggled a little here the first time I heard it). Therefore, a must clearer understanding is yet to come up, and this would tell us whether or not there can be an observation of wormholes. But this is surely an interesting field to work on, and the only problem here is that for different topologies, the preservation of the energy conditions is sometimes on in certain regions of the wormhole, and therefore further corrections are required. But this is just like the Beauty and the Beast, only here the Beauty is the Beast.
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And they are, mathematically reasonable — that’s what you get from solving the field equations in general relativity, you get solutions that describe different physical phenomena with different topologies. But wormholes are special, since they contain exotic matter — saying which might make me sound like a dork, but this is simply the kind of matter to violate the strong energy condition, which says that two particles at most will get attracted to each other, but never repel. This was also characterised by Ellis in terms of a scalar field he called “phantom”. This is inconsistent with general relativity, and wormholes have been seen as evil since then.
But as is the case for most of physics (which fortunately for me gets me to work), this can be changed by curvature based corrections, using what are called as modified theories of gravity. These are theories obtained by perturbing the usual approach to general relativity, which for the geeks out there would make sense in terms of corrections based on the action and/or curvature Lagrangians. For others, here’s a way to get this: instead of letting one particular curvature term in the first order define the idea of gravitation (GR), we can extend it to arbitrary functions including higher orders, which allow us to understand phenomena in astrophysics differently, and hopefully, better. This was the case for describing the acceleration of cosmological expansion in terms of a modified theory of gravity in the fourth order [1] by Carroll et al in 2003. Wormholes can also be described similarly using a curvature sector theory, where we use the approach described above. This has been my research too, a paper here [2]. But then, where are the wormholes?
We are currently far from actually getting the total idea of whether or not all sorts of wormholes are possible. Black holes were different altogether — from the No hair theorem, the only parameters describing black holes (that are mass, electric charge and angular momentum) imply that there are only four sorts of black holes, since mass is a constant feature in all of them. Black holes are described only by these parameters, which is to say that they don’t have “hair”. Which is why today’s sponsor is Hair fall loss Control, get up to 40% off on the first 400 registrations by using the code “no hair”. Worst joke in the world, please don’t smack me.
Wormholes on the other hand have different sorts based on the topology, such as Morris-Thorne, Ellis, exponential, NUT wormholes (honestly, I will admit I giggled a little here the first time I heard it). Therefore, a must clearer understanding is yet to come up, and this would tell us whether or not there can be an observation of wormholes. But this is surely an interesting field to work on, and the only problem here is that for different topologies, the preservation of the energy conditions is sometimes on in certain regions of the wormhole, and therefore further corrections are required. But this is just like the Beauty and the Beast, only here the Beauty is the Beast.
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References
[1] S. Carroll et al, Phys. Rev. D 70, 043528 (2004)
[2] V. Kalvakota, web.ma.utexas.edu/mp_arc/c/22/22-38 (2022)
[2] V. Kalvakota, web.ma.utexas.edu/mp_arc/c/22/22-38 (2022)
