Abstract
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO’s detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with D > 4 dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in D > 4. Here, we develop a numerical implementation of the formalism by Godazgar and Reall []—based on projections of the Weyl tensor analogous to the Newman–Penrose scalars—that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in D = 6 spacetime dimensions and find that a fraction of the Arnowitt–Deser–Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama–Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.
Highlights
Gravitational waves (GWs) entered the limelight with the recent detection of GW150914 [2]—soon followed by a second detection GW151226 [3]—which constitutes the first observation of a black-hole (BH) binary system, and marks a true milestone in gravitational physics
We will calibrate the numerical uncertainties arising from the numerical discretisation of the equations, the use of large but finite extraction radii and consider the dependency of the results on the initial separation of the BHs. This type of collisions has already been studied by Witek et al [69] who calculate the GW energy using the Kodama–Ishibashi formalism, which enables us to compare our findings with their values
The only prerequisite for implementing our formalism is the availability of the Arnowitt–Deser–Misner [84] (ADM) variables on each spatial hypersurface of the effective computational domain
Summary
Gravitational waves (GWs) entered the limelight with the recent detection of GW150914 [2]—soon followed by a second detection GW151226 [3]—which constitutes the first observation of a black-hole (BH) binary system, and marks a true milestone in gravitational physics. The main assumption there is that far away from the strong-field regime, the spacetime is perturbatively close to the Tangherlini [68] spacetime The deviations from this background facilitate the construction of master functions according to the KI formalism which in turn provide the energy flux in the different (l,m) radiation multipoles. Godazgar and Reall [1] have performed a decomposition of the Weyl tensor in higher dimensions, and derived a generalisation of the Newman–Penrose formalism for wave extraction to D > 4 This analysis provides us with a quantity analogous to the Weyl scalar Ψ4, from which we can calculate the energy radiated in gravitational waves in a similar fashion to the method in D = 4.
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