Electric/magnetic field deformed giant gravitons in Melvin geometry

The rotating D3-brane in the AdS5×S5 spacetime could be blowed up to the spherical BPS configuration which has the same energy and quantum number of the point-like graviton and is called as a giant graviton. The configuration is stable only if its angular momentum was less than a critical value of Pc. In this Letter we investigate the properties of the giant graviton in the electric/magnetic Melvin geometries of deformed AdS5×S5 spacetime which was obtained in our previous paper [W.-H. Huang, Phys. Rev. D 73 (2006) 026007, hep-th/0512117]. We find that in the magnetic Melvin spacetime the giant graviton has lower energy than the point-like graviton. Also, the critical value of the angular momentum is an increasing function of the magnetic field flux B. In particular, it is seen that while increasing the angular momentum the radius of giant graviton is initially an increasing function, then, after it reach its maximum value it becomes a decreasing function of the angular momentum. During these regions the giant graviton is still a stable configuration, contrast to that in the undeformed theory. Finally, beyond the critical value of angular momentum the giant graviton has higher energy than the point-like graviton and it eventually becomes unstable. Our analyzes show that the electric Melvin field will always render the giant graviton unstable.