Perturbations from gravitationally decoupled hairy black holes
The detection of gravitational waves (GWs) by LIGO in 2015 [1, 2] gifted us with a new
tool to investigate the universe that can help us probe spacetime for strange entities such
as hairy black holes (HBHs). These entities are a priori precluded from existence due to
what is called the “no-hair conjecture” [10]. In this work, we implement the method of
gravitational decoupling (GD)[4, 7] capable of separating gravitational sources, which was
previously deemed impossible due to the high non-linear character of the Einstein field
equations [7]. Said process generates new terms in the metric that can be interpreted as
primary hair [5]. Having used this method to generate hair from the seed Schwarzschild
black hole solution [5], we apply perturbation theory in order to investigate the form and
properties of the gravitational waves produced by this object [3] thorugh the analysis of its
quasi-normal modes (QNMs). Using SageMath, we have constructed a code that produces
the Regge-Wheeler and Zerilli equations[9, 11] from any given spherically symmetric met-
ric, which govern the metric perturbation and which applies the 3rd-order WKB method
to obtain its QNMs. The main goal of this work is to search for hair signatures in these
modes that would distinguish them from the seed solution, and construct a database for
use in future GW observations.
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