Abstract
We diagram the behavior of 5-dimensional anti-de Sitter spacetime against horizon formation in the gravitational collapse of a scalar field, treating the scalar field mass and width of initial data as free parameters, which we call the stability phase diagram. We find that the class of stable initial data becomes larger and shifts to smaller widths as the field mass increases. In addition to classifying initial data as stable or unstable, we identify two other classes based on nonperturbative behavior. The class of metastable initial data forms a horizon over longer time scales than suggested by the lowest order perturbation theory at computationally accessible amplitudes, and irregular initial data can exhibit non-monotonic and possibly chaotic behavior in the horizon formation times. Our results include evidence for chaotic behavior even in the collapse of a massless scalar field.
Highlights
Through the anti–de Sitter spacetime (AdS)/conformal field theory (CFT) correspondence, string theory on AdS5 × X5 is dual to a large N conformal field theory in four spacetime dimensions (R × S3 when considering global AdS5)
We diagram the behavior of five-dimensional anti–de Sitter spacetime against horizon formation in the gravitational collapse of a scalar field, treating the scalar field mass and width of initial data as free parameters, which we call the stability phase diagram
Starting with the pioneering work of [1,2,3,4], numerical studies have suggested that these dynamics may be generically unstable toward formation of AdSdþ1 black holes even for arbitrarily small amplitudes
Summary
Through the anti–de Sitter spacetime (AdS)/conformal field theory (CFT) correspondence, string theory on AdS5 × X5 is dual to a large N conformal field theory in four spacetime dimensions (R × S3 when considering global AdS5). Some initial scalar field profiles lead to quasiperiodic evolution (at least on the time scales accessible via numerical studies) at small but finite amplitudes; even early work [1,5] noted that it is possible to remove the secular growth terms in the evolution of a single perturbative eigenmode. Using numerical evolution of the full gravitational dynamics, we diagram classes of gravitational collapse behavior as a function of scalar field mass and initial scalar profile width, which we call a stability phase diagram in analogy to a phase diagram for phases of matter. This is the first systematic study of behavior for classes of initial data in AdS gravitational collapse using two tuning parameters.
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