Gravitational wave bounds on dirty black holes

Abstract

Detection of gravitational waves has provided a new way to test black hole (BH) models. We show how simple constraints can be obtained for models that go beyond vacuum Einstein gravity solutions of binary BH mergers. Generic stationary metrics, termed dirty BHs in the literature, are not vacuum solutions of the Einstein equations. These models are, however, general enough to describe BHs surrounded by matter fields. Gravitational wave constraints already rule out certain parts of parameter space for these solutions, including certain parameters describing objects without horizons that have recently been studied in the context of pseudo-complex general relativity. KEYWORDgravitational waves -black hole physics -methods: observational -relativistic processes -binaries: general 1 How to cite this article: Nielsen AB, Birnholz O. Gravitational wave bounds on dirty black holes. Astron. Nachr. 2019;340:116-120.

Kerr Black Holes within a Modified Theory of Gravity

“…It is strong enough in order not to contribute to the known observations within the solar system and other systems with not too strong gravitational fields [1]. There may be other dependencies with n > 3 and, in fact, in [27,28], it was shown that the fall-off of the dark-energy density has to be stronger. We will discuss other cases of the fall-off, ordered by a number n as in (16); however, the main conclusions and structural predictions of the theory remain similar.…”

“…The two frequencies deduced in (35) and (36) have to be set equal, which leads to the following equation, deduced in [27,28] (we changed the variable r into y = r m 0 and defined a = a m ) √ ∆ y 3 − a 2 F + a 2y 2 m(y)…”

“…This equation and, thus, the position of the light-ring depends on the azimuth angle ϑ via g 22 . The expression is the same as in [27,28].…”

“…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.…”

Comparison of the predictions of the pseudocomplex general relativity to the observations of the Event Horizon Telescope collaboration

“…The case n = 2 is ruled out by solar system experiments (Will ), and n = 3 was recently ruled out in (Nielsen & Birnholz , ), investigating the in‐spiral frequency of a gravitational merger. Thus, here, we use n = 4, which is also in line with Visser ()) at large distances.…”