Testing pseudo‐complex general relativity with gravitational waves

Abstract

We show how the model of pseudo-complex general relativity can be tested using gravitational wave signals from coalescing compact objects. The model, which agrees with Einstein gravity in the weak-field limit, diverges dramatically in the near-horizon regime, with certain parameter ranges excluding the existence of black holes. We show that simple limits can be placed on the model in both the inspiral and ringdown phase of coalescing compact objects. We discuss further how these bounds relate to current observational limits. In particular, for minimal scenarios previously considered in the literature, gravitational wave observations are able to constrain pseudo-complex general relativity parameters to values that require the existence of black hole horizons.

Gravitational wave bounds on dirty black holes

“…In this work, we have focused on the inspiral regime, when the two objects are still orbiting each other. It is also possible to extend this to other regimes observable with gravitational waves, such as the post‐merger phase (Cardoso et al ; Nielsen et al ; Nielsen & Birnholtz ; Westerweck et al ). While we have compared our results to those of inspiralling, heavy BH‐like objects (Abbott et al ), it is also possible to use constraints from the inspiral of neutron stars, such as the system GW170817 (Abbott et al ).…”

“…The theory has been used to justify the nonexistence of horizons in gravitational collapse (Hess et al ; Hess & Boller ). The relationship between pcGR and gravitational waves has been previously studied in Hess (, ) and Nielsen & Birnholtz ().…”

Regge–Wheeler and Zerilli equations within a modified theory of general relativity

“…In Nielsen & Birnholz (), the pcGR was tested considering the orbital frequencies on a light ring. First indications were that the r ‐correction in the metric has to be modified.…”

Kerr Black Holes within a Modified Theory of Gravity

“…For b n = 0, the standard GR is recovered. In this review, we will not cover all aspects of the theory (please also consult [13]), but it would be interesting to vary the parameter b n from 0 to the value, from which no event horizon appears, as done also in [27,28] for gravitational waves. In this manner, the GR and pc-GR can be connected smoothly.…”