Quasilocal energy and surface geometry of Kerr spacetime

Abstract

We study the quasi-local energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region $r\le 2m$, which is inside the ergosphere. For a certain region, $r>r_k(a)$, the Gaussian curvature of the surface with constant $t,r$ is positive, and for $r>\sqrt{3}a$ the critical value of the QLE is positive. We found that the three curves: the outer horizon $r=r_{+}(a)$, $r=r_k(a)$ and $r=\sqrt{3}a$ intersect at the point $a=\sqrt{3}m/2$, which is the limit for the horizon to be isometrically embedded into ${\mathbb{R}}^3$. The numerical result indicates that the Kerr QLE is monotonically decreasing to the ADM $m$ from the region inside the ergosphere to large $r$. Based on the second law of black hole dynamics, the QLE is increasing with respect to the irreducible mass $M_{\mathrm{ir}}$. From a results of Chen-Wang-Yau, we conclude that in a certain region, $r>r_h(a)$, the critical value of the Kerr QLE is a global minimum.

20 pages

References in corpus (5)

• Isometric embeddings into the Minkowski space and new quasi-local mass
• Rigidly rotating ZAMO surfaces in the Kerr spacetime
• Critical points of Wang-Yau quasi-local energy
• Chen-Nester-Tung quasi-local energy and Wang-Yau quasi-local mass
• Quasilocal Energy in Kerr Spacetime

Cited by in corpus (4)

• Wang and Yau's Quasi-Local Energy for an Extreme Kerr Spacetime
• Quasi-Local Energy of a Rotating Object Described by Kerr Spacetime
• Black Holes, Complex Curves, and Graph Theory: Revising a Conjecture by Kasner
• Strong field behavior of Wang-Yau Quasi-local energy