Non-stationary Energy of Perfect Fluid Sources in General Relativity
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arXiv
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| Format: | Preprint |
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2023
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| author | Altas, Emel Tekin, Bayram |
| author_facet | Altas, Emel Tekin, Bayram |
| contents | The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a geometric invariant of the spatial hypersurface of the spacetime and is expressed as an integral on the boundary of the hypersurface. For non-stationary spacetimes, there is a refinement of the ADM energy, the so-called Dain's invariant that measures the non-stationary part, the gravitational radiation component, of the total energy. Dain's invariant uses the metric and the extrinsic curvature of the spatial hypersurface together with the so-called approximate Killing initial data and vanishes for stationary spacetimes. In our earlier work [Phys.Rev.D 101 (2020)2, 024035], we gave a reformulation of the non-stationary energy for vacuum spacetimes in the Hamiltonian form of General Relativity written succinctly in the Fischer-Marsden form. That formulation is relevant for merging black holes or other compact sources. Here we extend this formulation to non-vacuum spacetimes with a perfect fluid source. This is expected to be relevant for spacetimes that have a compact star, say a neutron star colliding with a black hole or another non-vacuum object. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02822 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-stationary Energy of Perfect Fluid Sources in General Relativity Altas, Emel Tekin, Bayram General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a geometric invariant of the spatial hypersurface of the spacetime and is expressed as an integral on the boundary of the hypersurface. For non-stationary spacetimes, there is a refinement of the ADM energy, the so-called Dain's invariant that measures the non-stationary part, the gravitational radiation component, of the total energy. Dain's invariant uses the metric and the extrinsic curvature of the spatial hypersurface together with the so-called approximate Killing initial data and vanishes for stationary spacetimes. In our earlier work [Phys.Rev.D 101 (2020)2, 024035], we gave a reformulation of the non-stationary energy for vacuum spacetimes in the Hamiltonian form of General Relativity written succinctly in the Fischer-Marsden form. That formulation is relevant for merging black holes or other compact sources. Here we extend this formulation to non-vacuum spacetimes with a perfect fluid source. This is expected to be relevant for spacetimes that have a compact star, say a neutron star colliding with a black hole or another non-vacuum object. |
| title | Non-stationary Energy of Perfect Fluid Sources in General Relativity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2312.02822 |