All Questions
Tagged with adm-formalism general-relativity
62
questions
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ADM Formalism for the Effective String Theory
We will consider the following effective action of string theory in leading order of $\alpha'$:
$$S=\frac{1}{2\kappa^2_0}\int d^{D}X\sqrt{-G}e^{-2\Phi}\left[R-2\Lambda-\frac{1}{12}H_{\mu\nu\lambda}H^{\...
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Do the Komar/ADM mass equations also hold in 2+1D?
All definitions I have come across for the ADM mass require asymptotic flatness, which always is defined for 4 dimensional spacetimes. I was wondering if these formulae in 3+1D hold in 2+1D aswell?
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What is the determinant of the Wheeler-DeWitt metric tensor constructed from spatial metrics in ADM formalism?
The Hamiltonian constraint of General relativity has the following form
\begin{align}
\frac{(2\kappa)}{\sqrt{h}}\left(h_{ac} h_{bd} - \frac{1}{D-1} h_{ab} h_{cd} \right)p^{ab} p^{cd} - \frac{\sqrt{h}}{...
- 682
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Solving the Hamiltonian constraint equation in General Relativity
The constraint equation of general relativity reads as follows
\begin{align}
\frac{(2\kappa)}{\sqrt{h}}\left(h_{ac} h_{bd} - \frac{1}{D-1} h_{ab} h_{cd} \right)p^{ab} p^{cd} - \frac{\sqrt{h}}{(2\...
- 682
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ADM mass calculation for the BTZ black hole
Considering a non-rotating and non-charged 2+1 dimensional black hole, known as the BTZ black hole which obtained by adding a negative cosmological constant $\Lambda=-\frac{1}{l^2},l\ne0$ to the ...
2
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35
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Partial integration of the Gibbons-Hawking-York boundary term
In https://arxiv.org/abs/1402.6334 on page 16 in their Eq. (5.21), they go from the equation
$$S_G+S_\chi\approx\int d^2x\sqrt{-g}XR+\int dt\sqrt{-\gamma}XK$$
to the equation
$$=\int d^2x \sqrt{-g}\...
- 109
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Is the mass of curved space, additional mass?
According to Einstein, mass, say in the form of matter, curves space. It is the curvature of space that gives rise to gravity. Now I have heard there is an energy associated with the curvature of ...
- 131
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67
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Relation between the Wheeler–DeWitt equation and string theory
Can we derive the Wheeler–DeWitt equations from string theory? Since they are both quantum gravity theory.
A simple way seems to be the following logic:
The Wheeler–DeWitt equation is the canonically ...
- 547
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97
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Extrinsic curvature, Gauss equation and Christoffel symbol contribution
This question is in the context of geometry of hypersurfaces and ADM formalism. In a $4$-dimensional manifold, we define a $3$-hypersurface with space-like tangent basis $e_a$, $a=1,2,3$, and a normal ...
- 175
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55
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Lapse and shift choice meaning in asymptotic Minkowski space in ADM formalism
In A Relativist's toolkit by Poisson the defining of the ADM mass starts by introducing an asymptotic Lorenztian frame and in the asymptotic portion of the hypersurface the flow vector becomes:
$t^{\...
- 167
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151
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Star Radius in the Oppenheimer-Snyder metric using ADM formalism
I'm working with gravitational collapse models, in particular with the Oppenheimer-Snyder model.
Short list of the assumptions for those unfamiliar with the model, you have a spherical symmetric ...
- 1,611
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44
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How to extract mass from the tt component of the metric
Given an asymptotically flat metric, what is the general recipe in order to obtain the mass from the $tt$ component? In the case of the Schwarzschild metric it is obvious but is there a recipe that ...
- 31
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44
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Scalar curvature in ADM Formalism (coordinate to coordinate-free transition)
I am attempting to express the scalar curvature in a coordinate-independent manner. Following the works of Bojowald, Thiemann, we have:
$$ {}^{(4)}R= {}^{(3)}R+K_{a b}K^{a b}- (K_a^a)^2 - 2\nabla_a v^...
- 403
5
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1
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199
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BRST structure functions in gravity?
In the classical Hamiltonian BRST formalism, there arise structure functions $\Omega^{\beta_1...\beta_n}_{\alpha_1...\alpha_{n+1}}$ ($n\geq0$) --- see https://inspirehep.net/literature/221897 for ...
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ADM decomposition incompatible with black hole?
In establishing ADM or 3+1 decomposition, one starts with choosing a foliation $\Sigma_t$ where t is a scalar function and $\Sigma_t$ is demanded to be a spacelike slice, i.e. with time-like normal ...
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