Multidomain Galerkincollocation method: spherical collapse of scalar fields II
Abstract
We follow the strategy initiated in (Alcoforado 2021 Gen. Relativ. Gravit. 53 42) and proceed with the implementation of the Galerkincollocation domain decomposition applied to the dynamics of a spherical selfgravitating scalar field with the field equation in the Cauchy formulation. We have adopted the areal slicing gauge. We have presented a detailed implementation for an arbitrary number of subdomains and adopted the simplest form of the transmission conditions. Further, by an appropriate choice of the basis functions in the inner subdomain, we eliminated exactly the 1/r terms near the origin present in the field equations. The code is validated using two error measures: the conservation of the ADM mass and the Hamiltonian constraint that must be satisfied during the spacetime dynamics. In general, both error measures converge exponentially in all subdomains. As a useful illustration of placing more subdomains near the strongfield region, meaning an efficient concentrating of collocation points near the origin, we exhibited the formation of an apparent horizon even though the numerical integration diverges.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2021
 DOI:
 10.1088/13616382/ac2c1d
 arXiv:
 arXiv:2012.01302
 Bibcode:
 2021CQGra..38v5004A
 Keywords:

 numerical relativity;
 multidomain Garlerkincollocation;
 gravitational collapse;
 scalar fields;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 11 figures. Final version to appear in Classical and Quantum Gravity