Stable First-order Particle-frame Relativistic Hydrodynamics for Dissipative Systems

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.Comment: 4 pages, 3 figure

Uniqueness of Landau-Lifshitz Energy Frame in Relativistic Dissipative Hydrodynamics

We show that the relativistic dissipative hydrodynamic equation derived from the relativistic Boltzmann equation by the renormalization-group method uniquely leads to the one in the energy frame proposed by Landau and Lifshitz, provided that the macroscopic-frame vector, which defines the local rest frame of the fluid velocity, is independent of the momenta of constituent particles, as it should. We argue that the relativistic hydrodynamic equations for viscous fluids must be defined on the energy frame if it is consistent with the underlying relativistic kinetic equation.Comment: 6 page

Exact Solutions and the Attractor Mechanism in Non-BPS Black Holes

The attractor mechanism for the four-dimensional ${\cal N}=2$ supergravity black hole solution is analyzed in the case of the D0-D4 system. Our analyses are based on newly derived exact solutions, which exhibit explicitly the attractor mechanism for extremal non-BPS black holes. Our solutions account for the moduli as general complex fields, while in almost all non-BPS solutions obtained previously, the moduli fields are restricted to be purely imaginary. It is also pointed out that our moduli solutions contain an extra parameter that is not contained in solutions obtained by replacing the charges in the double extremal moduli solutions by the corresponding harmonic functions.Comment: 16 pages, added a few reference