Asymptotic analysis of Einstein-Æther theory and its memory effects: the linearized case
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| Format: | Preprint |
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2023
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| author | Hou, Shaoqi Wang, Anzhong Zhu, Zong-Hong |
| author_facet | Hou, Shaoqi Wang, Anzhong Zhu, Zong-Hong |
| contents | This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-æther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various multipolar moments. The suitable coordinate transformations are then determined, and the so-called pseudo-Newman-Unti coordinate systems are constructed for all radiative modes. In these coordinates, it is easy to identify the asymptotic symmetries. It turns out that all three kinds of modes possess the familiar Bondi-Metzner-Sachs symmetries or the extensions as in general relativity. Moreover, there also exist the \emph{subleading} asymptotic symmetries parameterized by a time-independent vector field on a unit 2-sphere. The memory effects are also identified. The tensor gravitational wave also excites similar displacement, spin, and center-of-mass memories to those in general relativity. New memory effects due to the vector and scalar modes exist. The subleading asymptotic symmetry is related to the (leading) vector displacement memory effect, which can be viewed as a linear combination of the electric-type and magnetic-type memory effects. However, the scalar memory effect seems to have nothing to do with the asymptotic symmetries at least in the linearized theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_01165 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis of Einstein-Æther theory and its memory effects: the linearized case Hou, Shaoqi Wang, Anzhong Zhu, Zong-Hong General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-æther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various multipolar moments. The suitable coordinate transformations are then determined, and the so-called pseudo-Newman-Unti coordinate systems are constructed for all radiative modes. In these coordinates, it is easy to identify the asymptotic symmetries. It turns out that all three kinds of modes possess the familiar Bondi-Metzner-Sachs symmetries or the extensions as in general relativity. Moreover, there also exist the \emph{subleading} asymptotic symmetries parameterized by a time-independent vector field on a unit 2-sphere. The memory effects are also identified. The tensor gravitational wave also excites similar displacement, spin, and center-of-mass memories to those in general relativity. New memory effects due to the vector and scalar modes exist. The subleading asymptotic symmetry is related to the (leading) vector displacement memory effect, which can be viewed as a linear combination of the electric-type and magnetic-type memory effects. However, the scalar memory effect seems to have nothing to do with the asymptotic symmetries at least in the linearized theory. |
| title | Asymptotic analysis of Einstein-Æther theory and its memory effects: the linearized case |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.01165 |