Charges and fluxes on (perturbed) non-expanding horizons

Abstract

In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} $$ G of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $$ \mathfrak{B} $$ B at $$ \mathcal{I} $$ I +. For each infinitesimal generator of $$ \mathfrak{G} $$ G , we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries $$ \mathcal{N} $$ N along the lines of [2–6]. However, $$ \mathcal{N} $$ N is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $$ \mathfrak{G} $$ G are free of physically unsatisfactory features that can arise if $$ \mathcal{N} $$ N is allowed to be a general null boundary. In particular, all fluxes vanish if $$ \mathcal{N} $$ N is an NEH, just as one would hope; and fluxes associated with symmetries representing ‘time-translations’ are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in [1], $$ \mathcal{I} $$ I ±are NEHs in the conformally completed space-time but with an extra structure that reduces $$ \mathfrak{G} $$ G to $$ \mathfrak{B} $$ B . The flux expressions at $$ \mathcal{N} $$ N reflect this synergy between NEHs and $$ \mathcal{I} $$ I +. In a forthcoming paper, this close relation between NEHs and $$ \mathcal{I} $$ I + will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at $$ \mathcal{I} $$ I +.

Energy scales and black hole pseudospectra: the structural role of the scalar product

“…One can readily observe from figures 4 and 5 that the first two eigenvalues are recovered and that from the third eigenvalue onward the analytical and numerical results disagree. Additionally, the weak problem (119) gives direct access to the eigenvalues of L while the weak problem (120) renders the eigenvalues of L † . As extensively discussed in [57], in order to increase the number of correct eigenvalues recovered it is necessary to use enhanced machine precision and the numerical error can be reinterpreted as a perturbation of the operator L. The branches where the eigenvalues migrate to due to the numerical error are qualitatively similar to those reported in [57] giving confidence that this observed behavior, suitably interpreted as a random perturbation of the L operator, is not exclusive to the spectral approach used in [57].…”

Non-linear black hole dynamics and Carrollian fluids

“…A transparent way to this end was presented in [19,35]. Alternatively, insights can be gained through the dynamical horizon approach [36,37] or via a suitable second order perturbative approach [38,39]. However, we here want to keep a close connection with the Carrollian fluid structure and find it convenient to proceed as follows.…”

Airy-function approach to binary black hole merger waveforms: The fold-caustic diffraction model

“…There are other hints as well for linearity in black hole merg-ers: i) It has been suggested that the linear description of the ringdown phase can be extended all the way back to the merger itself [50][51][52][53] (though several open questions remain [54,55]). ii) Other studies find strong evidence for the presence of linear correlations between geometric fields in the strong field region and fields in the asymptotic wave-zone in a BBH merger [56][57][58][59][60][61][62][63]. These correlations are a dynamical feature difficult to understand without accepting some kind of underlying effective linear ingredient in the emission and propagation of the gravitational degrees of freedom captured in the BBH waveform.…”