\contentsline {section}{\numberline {1}Introduction}{2}{section.1}
\contentsline {section}{\numberline {2}Massless scalar in 4d extreme Reissner-Nordstr\"om (ERN) spacetime}{4}{section.2}
\contentsline {subsection}{\numberline {2.1}Couch-Torrence discrete conformal isometry}{4}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}Aretakis constants, Newman-Penrose constants, and initial static moments}{5}{subsection.2.2}
\contentsline {section}{\numberline {3}Late time behavior of scalar perturbation in 4d ERN spacetime}{8}{section.3}
\contentsline {subsection}{\numberline {3.1}Late time tails for non-compact initial data in flat space}{8}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Contributions due to asymptotic curvature of spacetime}{12}{subsection.3.2}
\contentsline {section}{\numberline {4}Discussion}{16}{section.4}