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Adiabatic Solutions in General Relativity and Boundary Symmetries
High Energy Physics - Theory · Submitted 21 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Moreover using the Hodge-Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value.
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The abstract, sentence by sentence
We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described as a slow motion on the space of vacua-static solutions that minimize the energy -- is a good approximate solution. To apply this to the case of general relativity we first bring it to the natural form by splitting space and time and choosing Gaussian normal coordinates, where a spacetime is described by the metric on its spatial slices. Then following Manton we propose slow solutions such that each slice is a slowly changing diffeomorphism of a reference slice, and thus each solution is described by a vector field on the spatial slice. These solutions will have the property that the action will become a functional of the vector fields on the boundaries of the spatial slices. Moreover using the Hodge-Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value. Then we comment on the structure of the space of vacua which we show to be a (pseudo)-Riemannian homogeneous space. We illustrate our procedure for a specific reference slice we choose: the 3d Euclidean round ball.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. | contribution 1.00 | 0.89 | 0.07 | asserted 0.89 |
| s1 | This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described as a slow motion on the space of vacua-static solutions that minimize the energy -- is a good approximate solution. | background 0.86 | 0.10 | 0.09 | asserted 0.89 |
| s2 | To apply this to the case of general relativity we first bring it to the natural form by splitting space and time and choosing Gaussian normal coordinates, where a spacetime is described by the metric on its spatial slices. | method 1.00 | 0.68 | 0.03 | asserted 0.99 |
| s3 | Then following Manton we propose slow solutions such that each slice is a slowly changing diffeomorphism of a reference slice, and thus each solution is described by a vector field on the spatial slice. | method 0.88 | 0.82 | 0.08 | asserted 0.58 |
| s4 | These solutions will have the property that the action will become a functional of the vector fields on the boundaries of the spatial slices. | result 0.92 | 0.67 | 0.14 | asserted 0.80 |
| s5 | Moreover using the Hodge-Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value. | result 0.87 | 0.88 | 0.25 | asserted 1.00 |
| s6 | Then we comment on the structure of the space of vacua which we show to be a (pseudo)-Riemannian homogeneous space. | result 0.94 | 0.91 | 0.17 | asserted 1.00 |
| s7 | We illustrate our procedure for a specific reference slice we choose: the 3d Euclidean round ball. | method 0.55 | 0.89 | 0.04 | asserted 0.95 |
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Original abstract
We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described as a slow motion on the space of vacua-static solutions that minimize the energy -- is a good approximate solution. To apply this to the case of general relativity we first bring it to the natural form by splitting space and time and choosing Gaussian normal coordinates, where a spacetime is described by the metric on its spatial slices. Then following Manton we propose slow solutions such that each slice is a slowly changing diffeomorphism of a reference slice, and thus each solution is described by a vector field on the spatial slice. These solutions will have the property that the action will become a functional of the vector fields on the boundaries of the spatial slices. Moreover using the Hodge-Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value. Then we comment on the structure of the space of vacua which we show to be a (pseudo)-Riemannian homogeneous space. We illustrate our procedure for a specific reference slice we choose: the 3d Euclidean round ball.
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What it cites · 36 sentences without a confident label
Uses the method or tool of 1 paper
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We apply the Manton approximation [ref] to general relativity to derive solutions that are slow in timeBut we never use slowness actually!!.
Magnetic Monopole Dynamics, Supersymmetry, and Duality · Introduction · 0.82
Cites as background 8 papers
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Splitting of spacetime into space and time was famously performed by Arnowitt-Deser-Misner [ref] , and became a standard treatment in many of general relativity books, see e.g. [ref] and also [ref] , a nice review for the purposes of numerical relativity.
The Dynamics of General Relativity · Manton Approximation for Yang Mills · 0.97
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Splitting of spacetime into space and time was famously performed by Arnowitt-Deser-Misner [ref] , and became a standard treatment in many of general relativity books, see e.g. [ref] and also [ref] , a nice review for the purposes of numerical relativity.
3+1 Formalism and Bases of Numerical Relativity · Manton Approximation for Yang Mills · 0.97
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One can define different types of asymptotic symmetries: asymptotic symmetries of spacetimes that are asymptotically flat at spatial infinity is a different group known as the Spi group [ref] , whereas definitions of asymptotic symmetries of the spacetimes that are asymptotically de Sitter were also made [ref] .
Asymptotic Symmetries and Charges in De Sitter Space · Asymptotic Symmetries and Soft Theorems · 0.94
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