Towards numerical relativity in scalar Gauss-Bonnet gravity: 3+1 decomposition beyond the small-coupling limit

Abstract

Scalar Gauss-Bonnet gravity is the only theory with quadratic curvature corrections to general relativity whose field equations are of second differential order. This theory allows for nonperturbative dynamical corrections and is therefore one of the most compelling case studies for beyond-general relativity effects in the strong-curvature regime. However, having second-order field equations is not a guarantee for a healthy time evolution in generic configurations. As a first step toward evolving black-hole binaries in this theory, we here derive the 3 þ 1 decomposition of the field equations for any (not necessarily small) coupling constant, and we discuss potential challenges of its implementation.

Spin-Induced Scalarized Black Holes

“…[15], track the formation of scalar hair, and verify explicitly that the solutions found here are the end points of this instability. This has been achieved in simpler BH scalarization scenarios [33], but it is particularly challenging when one has a coupling with the Gauss-Bonnet invariant, although significant progress has recently been made in modeling nonlinear time-domain evolutions in these theories [54][55][56][57][58][59][60][61][62][63]. Finally, the astrophysical phenomenology and implications of the scalarized BHs reported herein is missing and our results hold the promise of non-negligible deviations from the Kerr phenomenology.…”

Scalarized black holes

“…Since these EsGB theories have so far survived the constraints that have emerged in the GW emission during binary mergers, when the scalar coupling function allows for a vanishing scalar field in the cosmological context, and thus leads to the same cosmological solutions as the standard cosmological CDM model [63], this makes them attractive also for dynamical numerical relativity studies. Recently several groups have already done work in this direction, studying, e.g., dynamical scalarization and descalarization in binary BH mergers, dynamics of rotating BH scalarization, or dynamical formation of scalarized BHs through stellar core collapse [28,33,51,65,74,75]. by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.…”

Compact Objects in Alternative Gravities

“…We end this discussion by mentioning that recent studies have applied techniques of numerical relativity to EsGB theories with spontaneous scalarization of black holes. These studies address, for instance, dynamical scalarization and descalarization in black hole mergers or the dynamical formation of scalarized black hole in the collapse of burned out stars [109][110][111][112][113][114].…”