Questions tagged [adm-formalism]
This tag contains questions relating to ADM formalism i.e., Arnowitt-Deser-Misner formalism which is a Hamiltonian formulation of General Relativity that plays an important role in canonical quantum gravity and numerical relativity.
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ADM mass of a black hole and mass of the associated matter
The ADM formalism gives a definition for the energy (Hamiltonian) of a static, asymptotically flat spacetime. This energy can be equated to the mass of the matter (for example, a black hole) which ...
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Hamiltonian formalism of General Relativity Textbook
I've been reading Wald's book on General Relativity and in appendix $E_{2}$ it discusses the Hamiltonian formalism of General Relativity.I would like to understand it more, can you recommend me a ...
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How to derive gravitational path integral from the Hamiltonian operator formalism?
How does one derive the gravitational path integral $\int [dg]\exp(iS_{\text{EH}}/\hbar)$ from the Hamiltonian operator formalism?
The connection between the Hamiltonian operator formalism and the ...
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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 ...
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Uniqueness or multiplicity of ADM masses for spacetime manifolds with more than one "end"?
The question is:
What is the mathematical and/or physical basis for saying that a
(static) spacetime manifold with more than one asymptotically flat
region at infinity ("end") has a distinct ...
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Static Spacetime = no cosmological constant?
I stumbled over a strange result, which cannot be true: In the (3+1)-formulation of general relativity, one considers a metric of the type
$$g_{\mu\nu}\mathrm{d}x^{\mu}\mathrm{d}x^{\nu}=(-\alpha^{2}+\...
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Basis vector as "Array" choice in tensor calculus / GR, and 3+1 decomposition
In differential geometry and general relativity, once we have chosen a basis on our spacetime, say $ \{t,r,\theta, \phi \} $, we can represent every tensor as an "array" of numbers, so a &...
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Setting $N=1$ and $N^a=0$ in the Einstein-Hilbert action
In the ADM formalism of general relativity, one obtains a $3+1$ split of spacetime by setting $$\mathrm d s^2=(-N^2+N_a N^a) \,\mathrm d t^2 + 2N_a\,\mathrm d t\,\mathrm d x^a + q_{ab} \,\mathrm d x^a\...
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