A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes
We introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by t...
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2025-06-01
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| author | Mario Imbrogno Rita Megale Luca Del Zanna Sergio Servidio |
| author_facet | Mario Imbrogno Rita Megale Luca Del Zanna Sergio Servidio |
| author_sort | Mario Imbrogno |
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| description | We introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by the “1 + log” slicing condition and Gamma-driver shift conditions, which have been shown to improve numerical stability in spacetime evolution. A key innovation of our work is the logarithmic transformation applied to critical variables such as rest-mass density, energy density, and pressure, thus preserving physical positivity and mitigating numerical issues associated with extreme variations. Our formulation is fully compatible with advanced numerical techniques, including spectral methods and Fourier-based algorithms, and it is particularly suited for simulating highly nonlinear regimes in which gravitational fields play a significant role. This approach aims to provide a solid foundation for future numerical implementations and investigations of relativistic hydrodynamics, offering promising new perspectives for modeling complex astrophysical phenomena in strong gravitational fields, including matter evolution around compact objects like neutron stars and black holes, turbulent flows in the early universe, and the nonlinear evolution of cosmic structures. |
| format | Article |
| id | doaj-art-c5cc3f3dde2f4386933442aa11261297 |
| institution | Kabale University |
| issn | 2218-1997 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Universe |
| spelling | doaj-art-c5cc3f3dde2f4386933442aa112612972025-08-20T03:26:56ZengMDPI AGUniverse2218-19972025-06-0111619410.3390/universe11060194A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical SpacetimesMario Imbrogno0Rita Megale1Luca Del Zanna2Sergio Servidio3Dipartimento di Fisica, Università della Calabria, Via Pietro Bucci, Arcavacata, 87036 Cosenza, ItalyDipartimento di Fisica, Università della Calabria, Via Pietro Bucci, Arcavacata, 87036 Cosenza, ItalyDipartimento di Fisica e Astronomia, Università Degli Studi di Firenze e INFN-Sezione di Firenze, Via G. Sansone 1, Sesto Fiorentino, 50019 Firenze, ItalyDipartimento di Fisica, Università della Calabria, Via Pietro Bucci, Arcavacata, 87036 Cosenza, ItalyWe introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by the “1 + log” slicing condition and Gamma-driver shift conditions, which have been shown to improve numerical stability in spacetime evolution. A key innovation of our work is the logarithmic transformation applied to critical variables such as rest-mass density, energy density, and pressure, thus preserving physical positivity and mitigating numerical issues associated with extreme variations. Our formulation is fully compatible with advanced numerical techniques, including spectral methods and Fourier-based algorithms, and it is particularly suited for simulating highly nonlinear regimes in which gravitational fields play a significant role. This approach aims to provide a solid foundation for future numerical implementations and investigations of relativistic hydrodynamics, offering promising new perspectives for modeling complex astrophysical phenomena in strong gravitational fields, including matter evolution around compact objects like neutron stars and black holes, turbulent flows in the early universe, and the nonlinear evolution of cosmic structures.https://www.mdpi.com/2218-1997/11/6/194general relativityrelativistic hydrodynamicsnumerical relativity |
| spellingShingle | Mario Imbrogno Rita Megale Luca Del Zanna Sergio Servidio A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes Universe general relativity relativistic hydrodynamics numerical relativity |
| title | A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes |
| title_full | A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes |
| title_fullStr | A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes |
| title_full_unstemmed | A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes |
| title_short | A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes |
| title_sort | novel logarithmic approach to general relativistic hydrodynamics in dynamical spacetimes |
| topic | general relativity relativistic hydrodynamics numerical relativity |
| url | https://www.mdpi.com/2218-1997/11/6/194 |
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