Higher derivative asymptotic charges and internal Lorentz symmetries

Abstract

In line with a recent proposal for the study of asymptotic gravitational charges, we investigate higher derivative asymptotic charges. We show that the higher derivative BMS charges are related to the two-derivative BMS charges. Significantly, we find that internal Lorentz transformations are relevant in the higher derivative case in contrast to the two-derivative case. We give a prescription for their precise definition and derive the associated charges, finding, again, a relation with two-derivative BMS charges.

Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics

“…For the charges to be Lorentz invariant, one has to introduce compensating Lorentz transformations using the prescription outlined in Ref. [40]. In section 5 we compute the charges for alAdS spacetimes, verifying that the standard charges correspond to the wellknown Brown-York charges and finding that there are no dual charges.…”

“…Following [40], we fix the internal Lorentz transformation so that the combined action as given in equation (3.25) produces the required transformation of the vierbein components set out in (3.23).…”

Near horizon gravitational charges

“…Meanwhile boundary terms have their own contributions to the surface charges [12][13][14][15][16][17][18][19]. However it is shown that the surface charge from the Pontryagin term and Gauss-Bonnet term at null infinity is absent at the leading and subleading order in the inverse of a large r expansion [18,20]. This is somewhat under expected from the fact that those two are higher derivative terms which should have a faster fall-off behavior at large distance (see also [21] for relevant evidence).…”

Gravitational memory effects and higher derivative actions

“…Recently, it has been argued [15] that the most appropriate context in which to consider such questions is the first order tetrad formalism [41][42][43][44]. The relevant gravitational action then includes, in principle, any extra terms that do not contribute to the equations of motion, including higher derivative terms [45,46]. The result is that by applying the covariant phase space formalism [47][48][49][50][51][52][53] to the asymptotic BMS symmetries of the background, we obtain more charges than may have been expected.…”

“…The contribution of higher derivative terms in the action are not associated with any global charges, such as Bondi mass or angular momentum, or NUT charges. Nevertheless, the charges derived therefrom are non-trivial [45]. Moreover, in contrast with the two-derivative terms, there are charges derived from the higher derivative terms that are generated by internal Lorentz transformations.…”