Classification of Hypercylindrical Spacetimes with Momentum Flow

For the five-dimensional spacetimes whose four-dimensional sections are static, spherically symmetric ($SO(3)$) and flat asymptotically, we study the behavior of Arnowitt-Deser-Misner mass, tension and momentum densities characterizing such asymptotically hypercylindrical metrics under boosts along the cylindrical axis. For such stringlike metrics two boost-invariant quantities are found, which are a sort of "string rest mass-squared" and the sum of mass and tension densities. Analogous to the case of a moving point particle, we show that the asymptotically hypercylindrical geometries can be classified into three types depending on the value of the "string rest mass-squared", namely, "ordinary string", "null string" and "tachyonlike string" geometries. This asymptotic analysis shows that the extraordinary metrics reported recently by some of the authors belong to the tachyonlike string. Consequently, it is likely that such extraordinary solutions are the final states of tachyonic matter collapse. We also report two new vacuum solutions which belong to the null string and the tachyonlike string, respectively.Comment: 14 pages, 3 figure

Braided Statistics from Abelian Twist in κ\kappa-Minkowski Spacetime

$\kappa$-deformed commutation relation between quantum operators is constructed via abelian twist deformation in $\kappa$-Minkowski spacetime. The commutation relation is written in terms of universal $R$-matrix satisfying braided statistics. The equal-time commutator function turns out to vanish in this framework.Comment: 6pages, no figure

Heat conduction in general relativity

We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential. We pay attention to the fact that there are two additional degrees of freedom in choosing the relativistic analog of Cattaneo equation for the parts binormal to the caloric and the number flows. Including the contributions from the binormal parts, we find a $\textit{new}$ heat-flow equations and discover their dynamical role in thermodynamic systems. The benefit of introducing the binormal parts is that it allows room for a physical ansatz for describing the whole evolution of the thermodynamic system. Taking advantage of this platform, we propose a proper ansatz that deals with the binormal contributions starting from the physical properties of thermal equilibrium systems. We also consider the stability of a thermodynamic system in a flat background. We find that $\textit{new}$ "Klein" modes exist in addition to the known ones. We also find that the stability requirement is less stringent than those in the literature.Comment: 19 pages, 1 figur

Entropy of Self-Gravitating Anisotropic Matter

We examine the entropy of self-gravitating anisotropic matter confined to a box in the context of generalrelativity. The configuration of self-gravitating matter is spherically symmetric, but has anisotropic pressure of which angular part is different from the radial part. We deduce the entropy from the relation between the thermodynamical laws and the continuity equation. The variational equation for this entropy is shown to reproduce the gravitational field equation for the anisotropic matter. This result re-assures us the correspondence between gravity and thermodynamics. We apply this method to calculate the entropies of a few objects such as compact star and wormholes.Comment: 10 pages, 0 figur