Journal
PHYSICAL REVIEW D
Volume 106, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.106.064027
Keywords
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Funding
- FONDECYT post -doctoral Grant [3190873]
- FONDECYT post- doctoral Grant [3200884]
- National Agency for Research and Development ANID - PAI [77190078]
- FONDECYT [1181047]
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In this study, analytical solutions describing black holes and black strings in the Einstein SU(N)-nonlinear sigma model were constructed using the embedding ansatz and parametrization methods. These configurations not only satisfy the model equations but also demonstrate the impact of the flavor number on the geometry and thermodynamics.
We construct analytical solutions describing black holes and black strings in the Einstein SU(N)- nonlinear sigma model in (3 + 1) dimensions. This construction is carried out using the maximal embedding ansatz of SU(2) together with the Euler parametrization of the SU(N) group, in such a way that the nonlinear sigma model equations are automatically satisfied for arbitrary values of the flavor number N while the Einstein equations can be solved analytically. In particular, we construct black holes with spherical and flat horizons as well as black strings that present the geometry of a three-dimensional charged Banados-Teitelboim-Zanelli black hole on the transverse section of the string. These configurations are not trivial embeddings of SU(2) into SU(N), which allow us to explicitly show the role that the flavor number plays on the geometry and thermodynamics of the black holes and black strings. Finally, we perform a thermal comparison between these configurations.
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