G. Kang

Four dimensional string solutions in Hořava-Lifshitz gravity

We investigate string-like solutions in four dimensions based on Hořava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black strings are solutions in Hořava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the “conformal” lapse function is not constrained in Hořava-Lifshitz gravity. It turns out that if λ ≠ 1, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., λ = 1), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. We also point out that this solution is exactly the same with the black string solution obtained in a low-energy string theory action including the dilaton and the Kalb-Ramond fields.

Spacetime Structure of 5D Hypercylindrical Vacuum Solutions with Tension

We investigate geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and characterized by tension and mass densities. The solutions are classified by the tension-to-mass ratio. One particular example is the well-known Schwarzschild black string which has a curvature singularity enclosed by a horizon. We focus mainly on geometry of other solutions which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer with finite time, but is infinitely red-shifted.

Geometrical properties of the trans-spherical solutions in higher dimensions

We investigate the geometrical properties of static vacuum p-brane solutions of Einstein gravity in D=n+p+3 dimensions, which have spherical symmetry of S{sup n+1} orthogonal to the p directions and which are invariant under the translation along them. The solutions are characterized by the mass density and p number of tension densities. The causal structure of the higher-dimensional solutions is essentially the same as that of the five-dimensional ones. Namely, a naked singularity appears for most solutions except for the Schwarzschild black p-brane and the Kaluza-Klein bubble. We show that some important geometric properties such as the area of S{sup n+1} and the total spatial volume are characterized only by the three parameters (the mass density, the sum of tension densities, and the sum of tension density squares), rather than individual tension densities. These geometric properties are analyzed in detail in this parameter space and are compared with those of the five-dimensional case.

Equation of State in the Presence of Gravity

We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a characteristic variable that represents a weight per unit area relative to the average pressure is required in order to describe a macroscopic state of the gas. Although the density and the pressure are not uniform due to the presence of gravity, the ideal gas law itself is satisfied for the thermodynamic quantities when averaged over the system. Assuming that the system follows an adiabatic process further, we obtain a new relation between the averaged pressure and density, which differs from the conventional equation of state for the ideal gas in the absence of gravity. Applying our results to a small volume in a Newtonian star, however, we find that the conventional one is reliable for most astrophysical situations when the characteristic scale is small. On the other hand, gravity effects become significant near the surface of a Newtonian star.