Revisiting the ADT mass of the five-dimensional rotating black holes with squashed horizons

Abstract

We evaluate the Abbott-Deser-Tekin (ADT) mass of the five-dimensional rotating black holes with squashed horizons on two different on-shell reference backgrounds, which are the flat background and the boundary matched Kaluza-Klein (KK) monopole. The mass on the former, identified with the one on the background of the asymptotic geometry, differs from the mass on the latter by that of the KK monopole. However, each mass satisfies the first law of black hole thermodynamics. To test the results in five dimensions, we compute the mass in the context of the dimensionally reduced theory. Finally, in contrast with the original ADT formulation, its off-shell generalisation is applied to calculate the mass as well.

Mass and angular momentum of charged rotating Gödel black holes in five-dimensional minimal supergravity

“…Moreover, the Chern-Simons term contributes to the total charge as well. This is different from the cases in [38,46]. Therefore, a naive application of the off-shell generalized ADT foramlism without the contributions from the matter fields may fail to yield physical mass of the rotating charged Gödel black holes.…”

“…Therefore, for the completeness and universality of this formalism, it is of great necessity to simultaneously take into consideration of the effects of the matter fields. Like in [38], here we incorporate the contribution from the gauge field A µ within the potential associated with the Lagrangian (2.1) in full analogy with the rules of the original ADT formulation. Such an obviously extended potentialQ µν can be chosen as the one in Eq.…”

“…Consequently, in some sense, the offshell generalized ADT formalism could also be viewed as the cousin of both the BBC and phase space approaches. Till now, there have existed a series of developments and applications of the off-shell ADT formulation in a range of gravity theories regardless of the asymptotic behavior of the spacetime metrics [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46].…”

Hawking radiation of scalar particles and fermions from squashed Kaluza-Klein black holes based on a generalized uncertainty principle

“…Then we can regard a series of squashed Kaluza-Klein black hole solutions with a twisted compactified extra dimension as one of realistic higher-dimensional black hole models. Several aspects of squashed Kaluza-Klein black holes have been discussed, for example, thermodynamics [92][93][94][95][96][97][98][99], Hawking radiation [100][101][102][103][104][105][106][107][108][109][110][111], stabilities [112,113],…”