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| bio | website | jacobi.luc.edu |
|---|---|---|
| location | Chicago, IL | |
| age | ||
| visits | member for | 2 years, 4 months |
| seen | 11 hours ago | |
| stats | profile views | 110 |
I'm an assistant professor of physics at a university in Chicago.
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Apr 21 |
answered | Supergravity calculation using computer algebra system in early days |
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Mar 31 |
comment |
Space-like Killing vector of Robertson-Walker metric? Both of you are writing metrics on a portion of the full de Sitter spacetime. Four-dimensional de Sitter has topology $R^1 \times S^3$ and is conveniently realized as a hyperboloid in $R^5$. Various combinations of the coordinates on the hyperboloid give the metrics above, but will only cover part of the hyperboloid. There may be timelike Killing vectors on the patches associated with those metrics, but there is no global timelike Killing vector. |
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Feb 24 |
awarded | Supporter |
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Feb 4 |
comment |
Treatment of boundary terms when applying the variational principle The solution -- which goes back to the Regge and Teitelboim paper I mentioned -- is to add additional surface terms to the action until you have a functional that doesn't require $\delta g$ to fall off faster than whatever the appropriate asymptotics are. As long as the new surface terms are intrinsic to the boundary you can still impose Dirichlet boundary conditions. In AAdS spacetimes, the surface terms are the famous "boundary counterterms". The fundamental motivation for them is establishing a good variational formulation of the theory; finiteness of the action is a consequence of that. |
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Feb 4 |
comment |
Treatment of boundary terms when applying the variational principle The problem isn't with GHY. It's the claim that adding GHY to the EH action leads to a "well-defined variational problem". Take the EH action and add the GHY term. The Schwarzschild solution should be a stationary point of this action, right? Now consider the change in the action due to a small variation of the metric. You will find that the surface terms in the first-order change in the action only vanish if $\delta g$ falls off faster than 1/r. You have an 'action' that allows Dirichlet boundary conditions, but it can't tell between Schwarzschild and other metrics with 1/r asymptotics. |
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Feb 4 |
comment |
Treatment of boundary terms when applying the variational principle I'll let you know next time I head down, which will hopefully be soon. |
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Feb 4 |
answered | Treatment of boundary terms when applying the variational principle |
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Feb 2 |
comment |
Normalizable and non normalizable modes of gauge fields in AdS/CFT Sorry -- I don't remember a reference off the top of my head. You can work this result out by first linearizing the Einstein equation (i.e., write the metric as $g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}$, where $\bar{g}_{\mu\nu}$ is the AdS metric and $h_{\mu\nu}$ is the graviton) and then solving for the leading z dependence of the graviton. Like I said before, this will be easier if you pick a convenient gauge for $h_{\mu\nu}$. |
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Feb 2 |
awarded | Teacher |
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Feb 2 |
comment |
Normalizable and non normalizable modes of gauge fields in AdS/CFT What I said above goes for the graviton, but you'll need to linearize the Einstein equation to get the equation of motion for the field. Choosing the right gauge will help simplify the intermediate steps of this calculation. You will eventually find that the equation of motion for the spin-2 graviton on the AdS background reduces to that of a massless scalar. |
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Feb 2 |
answered | Normalizable and non normalizable modes of gauge fields in AdS/CFT |
