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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.14076 |
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| _version_ | 1866910636113395712 |
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| author | Nguyen, Hoang Ky Chauvineau, Bertrand |
| author_facet | Nguyen, Hoang Ky Chauvineau, Bertrand |
| contents | We present an exact static spherisymmetric solution for the Brans-Dicke action sourced by a self-gravitating massless Klein-Gordon helicity-0 field. In contrast to the Maxwell electromagnetic field, a Klein-Gordon field possesses an energy-momentum tensor with $\textit{non-vanishing trace}$. Upon a Weyl mapping into the Einstein frame, the transformed Brans-Dicke scalar field takes on the role of a "dilaton" coupled with the Klein-Gordon field. Despite this dilatonic coupling, the field equations of the resulting Einstein-Klein-Gordon-dilaton action are fully soluble when employing the harmonic radial coordinate. The exact solution derived herein can serve as a prototype for future Brans-Dicke gravity studies involving trace-carrying matter fields. Notably, in the limit of infinite $ω$, the Brans-Dicke scalar field exhibits an anomalous behavior of ${\cal O}\,(1/\sqrtω)$ as opposed to ${\cal O}\,(1/ω)$. As a consequence, the solution converges to a spacetime configuration of General Relativity sourced by the original Klein-Gordon field and a free scalar field, the latter of which is the ${\cal O}\,(1/\sqrtω)$ "remnant" of the Brans-Dicke scalar field. Furthermore, we provide a formal mathematical proof substantiating these two conclusions. Although the ${\cal O}\,(1/\sqrtω)$ anomaly has been previously discovered for Brans-Dicke vacuum and Brans-Dicke-Maxwell electrovacuum, our findings establish its prevalence in Brans-Dicke gravity $\textit{regardless}$ of the trace of the energy-momentum tensor of the source. Taken together, the ${\cal O}\,(1/\sqrtω)$ anomaly challenges the conventional belief in the ${\cal O}\,(1/ω)$ signature commonly associated with Brans-Dicke gravity. In particular, it may have implications in improving the relativistic corrections to Newtonian gravity beyond the weak-field parametrized post-Newtonian formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New exact solution and $\mathcal{O}\,(1/\sqrtω)$ anomaly in Brans-Dicke gravity with trace-carrying matter Nguyen, Hoang Ky Chauvineau, Bertrand General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We present an exact static spherisymmetric solution for the Brans-Dicke action sourced by a self-gravitating massless Klein-Gordon helicity-0 field. In contrast to the Maxwell electromagnetic field, a Klein-Gordon field possesses an energy-momentum tensor with $\textit{non-vanishing trace}$. Upon a Weyl mapping into the Einstein frame, the transformed Brans-Dicke scalar field takes on the role of a "dilaton" coupled with the Klein-Gordon field. Despite this dilatonic coupling, the field equations of the resulting Einstein-Klein-Gordon-dilaton action are fully soluble when employing the harmonic radial coordinate. The exact solution derived herein can serve as a prototype for future Brans-Dicke gravity studies involving trace-carrying matter fields. Notably, in the limit of infinite $ω$, the Brans-Dicke scalar field exhibits an anomalous behavior of ${\cal O}\,(1/\sqrtω)$ as opposed to ${\cal O}\,(1/ω)$. As a consequence, the solution converges to a spacetime configuration of General Relativity sourced by the original Klein-Gordon field and a free scalar field, the latter of which is the ${\cal O}\,(1/\sqrtω)$ "remnant" of the Brans-Dicke scalar field. Furthermore, we provide a formal mathematical proof substantiating these two conclusions. Although the ${\cal O}\,(1/\sqrtω)$ anomaly has been previously discovered for Brans-Dicke vacuum and Brans-Dicke-Maxwell electrovacuum, our findings establish its prevalence in Brans-Dicke gravity $\textit{regardless}$ of the trace of the energy-momentum tensor of the source. Taken together, the ${\cal O}\,(1/\sqrtω)$ anomaly challenges the conventional belief in the ${\cal O}\,(1/ω)$ signature commonly associated with Brans-Dicke gravity. In particular, it may have implications in improving the relativistic corrections to Newtonian gravity beyond the weak-field parametrized post-Newtonian formalism. |
| title | New exact solution and $\mathcal{O}\,(1/\sqrtω)$ anomaly in Brans-Dicke gravity with trace-carrying matter |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2402.14076 |