Axi-symmetric example of an SPT between a non-singular isothermal sphere (solid blue curve), with core θc = 0.1θE, and other mass profiles. The other curves are transformed mass profiles, using the SPT, with different deformation functions f(β), all satisfying the power-law condition (20), and with slope ν = 0.5 (flatter curves) and ν = 1.4 (steeper curves). The dashed black curves correspond to the polynomial f(β) = f0 + f2β2/ 2, the red curves to , with β0 = 0.8θE, and the dotted blue curves to f(β) = 2f0/ cosh(β/β0) − f0, with . Here, θ is given in units of the Einstein radius θE.
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