Collapsing domain walls generically form cuspidal edge and vertex singularities captured by Nambu-Goto and eikonal approximations and reproduced in field theory simulations.
Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization
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abstract
We present in detail the Einstein equations in the Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of $D$ dimensional spacetimes with $SO(D-d)$ isometry based on a method originally introduced in Ref.1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value $d=D-2$, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in $D=7$ spacetime dimensions with $SO(4)$ symmetry.
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Simulations of 5D black string instability in Einstein-Gauss-Bonnet gravity find that positive Gauss-Bonnet coupling caps curvature growth inside EFT validity, unlike negative coupling.
Chain-like transients in boson star collisions are controlled by a timing window set by matching binary collision time to the isolated breathing clock rather than excitation level alone.
Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.