New Insights into Relativistic Hydrodynamic Theories

Recent research has established a connection between various formulations of relativistic hydrodynamic theories, focusing on the necessity for stability and causality. The paper titled "Frame transformation and stable-causal hydrodynamic theory" by Sayantani Bhattacharyya, Sukanya Mitra, and Shuvayu Roy discusses two primary approaches to ensure these properties in hydrodynamic theories:

1. Non-fluid Variables: The first approach suggests that additional variables, which are not typically considered fluid variables, need to be introduced as new degrees of freedom. This inclusion is essential for maintaining stability and causality in the hydrodynamic framework.
2. Generalized Hydrodynamic Frames: The second approach indicates that the theory must be expressed in a generalized hydrodynamic frame that differs from the conventional Landau or Eckart frames. This transformation is crucial for the correct application of the BDNK stress tensor, which is rewritten in the Landau frame using linearized all-order gradient-corrected redefinitions of temperature and velocity fields.

The authors highlight that while the BDNK formalism has a finite number of derivatives in a general frame, it may require an infinite number of derivatives or the introduction of non-fluid variables when expressed in the Landau frame. This complexity leads to non-unique methods for performing infinite-order summations, which are analyzed in the context of dispersion relations and spectra.

The findings of this research could have significant implications for the development of stable and causal hydrodynamic models, which are essential in various fields, including nuclear physics and cosmology. The paper emphasizes the importance of understanding these frameworks to enhance the accuracy and reliability of hydrodynamic simulations in relativistic contexts.

For further details, the paper can be accessed at arXiv:2312.16407.