Black strings, one class of higher dimensional analogues of black holes, were shown to be unstable to long wavelength perturbations by Gregory and Laflamme in 1992, via a linear analysis. We reexamine the problem through the numerical solution of the full equations of motion, and focus on trying to determine the end state of a perturbed, unstable black string. Our preliminary results show that such a spacetime tends towards a solution resembling a sequence of spherical black holes connected by thin black strings, at least at intermediate times. However, our code fails then, primarily due to large gradients that develop in metric functions, as the coordinate system we use is not well adapted to the nature of the unfolding solution. We are thus unable to determine how close the solution we see is to the final end state, though we do observe rich dynamical behavior of the system in the intermediate stages.

We study head-on collisions of boson stars in three dimensions. We consider evolutions of two boson stars which may differ in their phase or have opposite frequencies but are otherwise identical. Our studies show that these phase differences result in different late time behavior and gravitational wave output

We perform a numerical study of the critical regime at the threshold of black hole formation in the spherically symmetric, general relativistic collapse of collisionless matter. The coupled Einstein-Vlasov equations are solved using a particle-mesh method in which the evolution of the phase-space distribution function is approximated by a set of particles ͑or, more precisely, infinitesimally thin shells͒ moving along geodesics of the spacetime. Individual particles may have nonzero angular momenta, but spherical symmetry dictates that the total angular momentum of the matter distribution vanish. In accord with previous work by Rein, Rendall, and Schaeffer, our results indicate that the critical behavior in this model is type I; that is, the smallest black hole in each parametrized family has a finite mass. We present evidence that the critical solutions are characterized by unstable, static spacetimes, with nontrivial distributions of radial momenta for the particles. As expected for type I solutions, we also find power-law scaling relations for the lifetimes of near-critical configurations as a function of the parameter-space distance from criticality.

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We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same eigenvalue l of the angular momentum operator and calculate the equations of motion for the radial part of these scalar fields. We have found that the critical solutions for different values of l are discretely self-similar (as in the original l 0 case). The value of the discrete, self-similar period, l , decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass-scaling exponent, l , also decreases with l.

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We investigate the possibility to localize scalar field configurations as a model for black hole accretion. We analyze and resolve difficulties encountered when localizing scalar fields in General Relativity. We illustrate this ability with a simple spherically symmetric model which can be used to study features of accreting shells around a black hole. This is accomplished by prescribing a scalar field with a coordinate dependent potential. Numerical solutions to the Einstein-Klein-Gordon equations are shown, where a scalar filed is indeed confined within a region surrounding a black hole. The resulting spacetime can be described in terms of simple harmonic time dependence.

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