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Results tagged with general-relativity
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user 289490
A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
2
votes
0
answers
105
views
Brown-Henneaux central charge in Chern-Simons formulation
In the article of Pérez, Tempo and Troncoso, in the Chern-Simons formulation for three-dimensional general relativity, they compute the canonical generator of charges
\begin{align}
Q\left[\varepsilon\ …
- 378
2
votes
0
answers
577
views
Symmetries of Dual Riemann tensor
In four dimensions, the dual of the Riemann tensor is defined as
\begin{align}
^*R^{\mu}{}_{\nu}{}^{\gamma\delta}=\frac{1}{2}\epsilon^{\alpha\beta\gamma\delta}R^{\mu}{}_{\nu\alpha\beta}\,.
\end{align …
- 378
2
votes
1
answer
131
views
Hamiltonian equations of General Relativity
It is known that the Hamiltonian action principle for general relativity (with cosmological constant) is
\begin{align}
I_H\left[\gamma_{ij},\pi^{ij}\right]=\frac{1}{16\pi G}\int dt\;\int d^{n-1}x\;\le …
- 378
1
vote
0
answers
62
views
Closure of Lie brackets associated to Brown-Henneaux boundary conditions
When we impose Brown-Henneaux boundary conditions to the metric field on AdS$_3$,
\begin{align}
\begin{split}
g_{tt}&=-\frac{r^2}{\ell^2}+\mathcal{O}(r^0)\,,\\
g_{t\phi}&=\mathcal{O}\left(r^0\r …
- 378
2
votes
0
answers
88
views
BTZ partition function
I am unable to obtain the internal energy of the BTZ black hole. Recall its metric, which is given by
\begin{align}
ds^2=-N^2(r)dt^2+\frac{dr^2}{N^2(r)}+r^2\left(d\phi+N^\phi(r)dt\right)^2\,,
\end{al …
- 378
4
votes
2
answers
608
views
Confusion on metric determinant derivative
Maybe it is a stupid confusion. I need to compute the derivative of the metric determinant with respect to the metric itself, i.e., $\partial g/\partial g_{\mu\nu}$, but I have an indices confusion in …
- 378