Analytical conditions for a horizon-exterior bounce with a string cloud

Determine the exact analytical conditions under which the charged-AdS shellworld with a uniformly distributed bulk string cloud undergoes a bounce outside the horizons of both bulk spacetimes.

Background

When a uniformly distributed string cloud is added to the charged AdS bulk, the shellworld Friedmann equation acquires an effective matter contribution proportional to a{-3}. The paper finds numerically that suitable parameter choices can produce a bounce outside the bulk horizons.

However, the horizon locations and bounce points are determined by polynomial equations whose exact analytical solutions are difficult to obtain. The authors explicitly state that they cannot determine the exact parameter conditions analytically and rely instead on plots and numerical tuning.

References

Since obtaining analytical solutions of the polynomial equations corresponding to $f_{\pm}(a)=0$ and $U(a)=0$ is highly nontrivial in this case, we are unable to determine the exact conditions for the bounce to occur outside the horizons as was done in the previous section.

— Bouncing shellworld embedded in charged AdS spacetime  (2608.22855 - Sherpa et al., 24 Aug 2026) in Section “Charged AdS bulk with string cloud,” final paragraph before “Summary”