Slowly rotating black holes in dynamical Chern-Simons gravity: Deformation quadratic in the spin

Abstract

We derive a stationary and axisymmetric black hole solution to quadratic order in the spin angular momentum. The previously found, linear-in-spin terms modify the odd-parity sector of the metric, while the new corrections appear in the even-parity sector. These corrections modify the quadrupole moment, as well as the (coordinate-dependent) location of the event horizon and the ergoregion. Although the linear-in-spin metric is of Petrov type D, the quadratic order terms render it of type I. The metric does not possess a second-order Killing tensor or a Carter-like constant. The new metric does not possess closed timelike curves or spacetime regions that violate causality outside of the event horizon. The new, even-parity modifications to the Kerr metric decay less rapidly at spatial infinity than the leading-order in spin, odd-parity ones, and thus, the former are more important when considering black holes that are rotating moderately fast. We calculate the modifications to the Hamiltonian, binding energy and Kepler's third law. These modifications are crucial for the construction of gravitational wave templates for black hole binaries, which will enter at second post-Newtonian order, just like dissipative modifications found previously.

Absorption of planar massless scalar waves by Kerr black holes

“…9 we show the main partial contributions for the total absorption cross section for fixed values of jmj, varying l, according to Eq. (12). We see from Fig.…”

“…One subtlety is that we need to take account of the spheroidal harmonics in Eq. (12). Progress can be made with an asymptotic relation, obtained using the WKB techniques of Ref.…”

“…This motivates careful study of the nature and observational consequences of the Kerr metric, which describes a rotating BH in GR. An improved understanding of the Kerr BH will also help us to understand more complicated structures, such as rotating BHs in modified theories of gravity [9][10][11][12].…”

Erratum: Slowly rotating black holes in dynamical Chern-Simons gravity: Deformation quadratic in the spin [Phys. Rev. D 86, 044037 (2012)]

“…Notice that the Chern-Simons corrections are unchanged. Since we have set VðϑÞ to zero throughout and we do not use ωðEÞ nor EðωÞ elsewhere in the original paper [1], all the other equations and figures are unaffected.…”

Signature of biased range in the non-dynamical Chern–Simons modified gravity and its measurements with satellite-satellite tracking missions: theoretical studies

“…For the tests of the dynamical CS gravity, the studies became active only recently. The vacuum solutions outside rotating black holes and stars in the dynamical formulation were studied with the slow rotation approximation [29][30][31], and their possible tests can be found in [32][33][34]. Moreover, the parity-violating term R R also leaves distinguishable signatures in gravitational waves, which may be captured by ground based or future space borne gravitational wave antennas [35][36][37][38].…”