Axisymmetric Stationary Spacetimes of Constant Scalar Curvature in Four Dimensions

In this paper we construct a special class of four dimensional axissymmetric stationary spacetimes whose Ricci scalar is constant in the Boyer-Lindquist coordinates. The first step is to construct Einstein metric by solving a modified Ernst equation for nonzero cosmological constant. Then, we modify the previous result by adding two additional functions to the metric to obtain a more general metric of constant scalar curvature which are not Einstein.Comment: 10 pages and no figure. Comments are welcom

N=1 Supergravity BPS Domain Walls on K\"ahler-Ricci Soliton

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four dimensional chiral N=1 supergravity. The scalar manifold can be viewed as a one-parameter family of K\"ahler manifolds generated by a K\"ahler-Ricci flow equation. Consequently, a vacuum manifold characterized by $(m,\lambda)$ where $m$ and $\lambda$ are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric K\"ahler-Ricci orbifolds.Comment: 19 pages, no figures; v2 some typos and grammar corrected; accepted in Rep. Math. Phy

Astrophysical Condition on the attolensing as a possible probe for a modified gravity theory

We investigate the wave effect in the gravitational lensing by a black hole with very tiny mass less than 10^-19 solar mass, which is called attolensing, motivated by a recent report that the lensing signature might be a possible probe of a modified gravity theory in the braneworld scenario. We focus on the finite source size effect and the effect of the relative motion of the source to the lens, which are influential to the wave effect in the attolensing. Astrophysical condition that the lensed interference signature can be a probe of the modified gravity theory is demonstrated. The interference signature in the microlensing system is also discussed.Comment: Accepted for publication in IJMP