The global structure of the scalar field critical solution was determined accurately in [157] by assuming analyticity at the centre of spherical symmetry and at the past light cone of the singularity (the self-similarity horizon, or SSH). The critical solution is then analytic up to the future lightcone of the singularity (the Cauchy horizon, or CH). Global adapted coordinates x and can be chosen so that the regular centre r = 0, the SSH and the CH are all lines of constant x, and surfaces of constant are never tangent to x lines. (A global is no longer a global time coordinate.) This is illustrated in Figure 4.

Approaching the CH, the scalar field oscillates an infinite number of times but with the amplitude of the oscillations decaying to zero. The scalar field in regular adapted coordinates is of the form

where , and are periodic with period , and the SSH is at x = 0. These functions have been computed numerically to high accuracy, together with the constants and . The scalar field itself is smooth with respect to , and as , it is continuous but not differentiable with respect to x on the CH itself. The same is true for the metric and the curvature. Surprisingly, the ratio m/r of the Hawking mass over the area radius on the CH is of order 10As the CH itself is regular with smooth null data except for the singular point at its base, it is not intuitively clear why the continuation is not unique. A partial explanation is given in [157], where all DSS continuations are considered. Within a DSS ansatz, the solution just to the future of the CH has the same form as Equation (31). is the same on both sides, but can be chosen freely on the future side of the CH. Within the restriction to DSS this function can be taken to parameterise the information that comes out of the naked singularity.

There is precisely one choice of on the future side that gives a regular centre to the future of the CH, with the exception of the naked singularity itself, which is then a point. This continuation was calculated numerically, and is almost but not quite Minkowski in the sense that m/r remains small everywhere to the future of the SSH.

All other DSS continuations have a naked, timelike central curvature singularity with negative mass. More exotic continuations including further CHs would be allowed kinematically [42] but are not achieved dynamically if we assume that the continuation is DSS. The spacetime diagram of the generic DSS continued solution is given in Figure 3.

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