Axial ring‐down modes in general relativity and in its pseudo‐complex extension

Abstract

We calculate the axial ring-down frequencies of the merger of two black holes, using a modified version of the pseudo-complex General Relativity (pc-GR) and comparing it with the standard General Relativity (GR). The path, on how to determine the axial modes, serve as a starting point for more general extensions of GR, involving additions of r-dependent functions to g 00 .

Observable consequences of pseudo-complex General Relativity

“…There are two types of modes, the negative parity solutions, also called Regge-Wheeler modes [65], and the positive parity modes, also called Zerilli modes [66]. In [67] the axial modes where calculated for n = 3 and in [68] also the axial modes were calculated, now for n = 4. The time dependence of the ring-down modes is e −iωt = e −iω R t e ω I t , with ω = ω R + iω I , separated in its real and imaginary part.…”

“…The Regge-Wheeler equation is solved as explained in [67,68], using an iterative technique called the Asymptotic Iteration Method (AIM) [69], and in Fig. 8 the result for small −ω I is depicted (we defined ω = m 0 ω).…”