Exact Collapse Solutions in D=4, N=4 Gauged Supergravity and Their Generalizations

We construct an exact time-dependent solution in $D=4$, ${\cal N}=4$ gauged supergravity, where the gauge fields of the $U(1)\times U(1)$ subgroup of the $SO(4)$ carry independent conserved charges. The solution describes a decaying white hole that settles down to the final state as a static charged black hole. We analyze the global structure and lift the solution back to $D=11$ supergravity. We further extend the theory by adding an extra term in the scalar potential and obtain a more general class of collapse solutions. The result constitutes a charged generalization of the Roberts solution and the dynamical scalar-hairy black hole solutions that have been very recently found by us. The generalized Roberts solutions demonstrate that a scalar coupled to gravity can be unstable even when it is confined by a scalar potential with a fixed point.Comment: 15 page

CR Structures and Twisting Vacuum Spacetimes with Two Killing Vectors and Cosmological Constant: Type II and More Special

Based on the CR formalism of algebraically special spacetimes by Hill, Lewandowski and Nurowski, we derive a nonlinear system of two real ODEs, of which the general solution determines a twisting type II (or more special) vacuum spacetime with two Killing vectors (commuting or not) and at most seven real parameters in addition to the cosmological constant Lambda. To demonstrate a broad range of interesting spacetimes that these ODEs can capture, special solutions of various Petrov types are presented and described as they appear in this approach. They include Kerr-NUT, Kerr and Debney/Demia\'{n}ski's type II, Lun's type II and III (subclasses of Held-Robinson), MacCallum and Siklos' type III (Lambda0) we found in an earlier paper, along with a new class of type II solutions as a nontrivial limit of Kerr and Debney's type II solutions. Also, we discuss a situation in which the two ODEs can be reduced to one. However, constructing the general solution still remains an open problem.Comment: 22 page

Exact Black Hole Formation in Asymptotically (A)dS and Flat Spacetimes

We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a static scalar-hairy black hole. The solution can be asymptotically AdS, flat or dS depending on the value of the cosmological constant parameter $\Lambda$ in the potential. As the advanced time $u$ increases, the spacetime reaches equilibrium in an exponential fashion, i.e., $e^{-u/u_0}$ with $u_0\sim1/(\alpha^4 M_0)^{1/3}$, where $M_0$ is the mass of the final black hole and $\alpha$ is the second parameter in the potential. Similar to the Vaidya solution, at $u=0$, the spacetime can be matched to an (A)dS or flat vacuum except that at the origin a naked singularity may occur. Moreover, a limiting case of our solution with $\alpha=0$ gives rise to an (A)dS generalization of the Roberts solution, thereby making it relevant to critical phenomena. Our results provide a new model for investigating formation of real life black holes with $\Lambda \geq 0$. For $\Lambda<0$, it can be instead used to study non-equilibrium thermalization of certain strongly-coupled field theory.Comment: Latex, 8 pages, typos corrected and references adde