Abbott Deser Research Articles

Conserved charges of GMMG in arbitrary backgrounds

We extend the Abbott–Deser–Tekin (ADT) method to the computation of the global charges associated with Killing vectors of the background for solutions of general minimal massive gravity (GMMG) linearized about an arbitrary background. Then, we implement our result in various solutions to evaluate the mass and angular momentum with arbitrary asymptotics.

Off-shell ADT conserved quantities in Palatini gravity

In this paper we generalize the off-shell Abbott–Deser–Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein–Hilbert action, the most general theories and the teleparallel Palatini gravity.

Generalized off-shell ADT conserved charges in the presence of matter Chern–Simons term

In this paper we elevate the formalism for off-shell Abbott–Deser–Tekin (ADT) conserved charges in the presence of arbitrary matter fields to including the internal gauge transformation, when the gauge fields are present. For this purpose, we resort to exact symmetry, and the symmetry generator is combined by diffeomorphism and internal gauge transformation. For universality, we consider an apparently non-covariant Lagrangian, which contains a matter Chern–Simons term. We show that the elevated off-shell ADT formalism is equivalent to the covariant phase space method and the Barnich–Brandt–Compère (BBC) formalism. To check the validity of our method, we explicitly compute the conserved charges of general non-extremal rotating charged Gödel black holes in minimal five-dimensional gauged supergravity, reproducing the previously known results.

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

In this paper, for the sake of providing a concrete comparison between the usual Abbott–Deser–Tekin (ADT) formalism and its off-shell extension, as well as comparing the latter with the Barnich–Brandt–Compere (BBC) approach, we carry out these methods to compute the mass and angular momentum of the rotating charged Gödel black holes in five-dimensional minimal supergravity. We first present the off-shell ADT potential of the supergravity theories in arbitrary odd dimensions, which is consistent with the superpotential via the BBC approach. Then the off-shell generalized ADT method is applied to evaluate the mass and angular momentum of the Gödel-type black holes by including the contribution from the gauge field. Finally, we strictly obey the rules of the original ADT formalism to incorporate the contribution from the gauge field within the potential. With the help of the modified potential, we try to seek for appropriate reference backgrounds to produce the mass and angular momentum. It is observed that the ADT formalism has to incorporate the contribution from the matter fields to yield physical charges for the Gödel-type black holes.

Field-theoretical construction of currents and superpotentials in Lovelock gravity

Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether–Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved currents, energy-momentum tensors out of them, and related superpotentials with arbitrary displacement vectors, not restricting to Killing vectors. A comparison with the well known Abbott–Deser–Tekin approach is given. The developed general formalism is applied to give conserved quantities for perturbations on anti-de Sitter (AdS) backgrounds. As a test we calculate mass of the Schwarzschild–AdS black hole in the Lovelock theory in arbitrary D dimensions. Proposals for future applications are presented.

Abbott–Deser–Tekin like conserved quantities in Lanczos–Lovelock gravity: beyond Killing diffeomorphisms

We obtain the conserved Abbott–Deser–Tekin (ADT)- like current for the Lanczos–Lovelock gravity for a diffeomorphism vector, which defines the horizon of a spacetime and, importantly, is not necessarily a Killing vector. As the original ADT current is defined only for the presence of a background Killing vector, one cannot use it extensively for the thermodynamic description of the wide classes of non-Killing horizons which appear in gravity. On the other hand, this general approach can be utilized for those horizons. Here, the conserved current can be written as the derivative of the two-rank anti-symmetric potential, the connection of which is apparent with the conserved Noether potential from our analysis. If one assumes the diffeomorphism vector as the Killing one, the results match to the ADT case, whereas non-trivial result comes for the conformal Killing vectors and other horizon defining vectors.

Thermodynamics of new black hole solutions in the Einstein–Maxwell-dilaton gravity

In the present work, thermodynamics of the new black hole solutions to the four-dimensional Einstein–Maxwell-dilaton gravity theory have been studied. The dilaton potential, as the solution to the scalar field equations, has been constructed out by a linear combination of three Liouville-type potentials. Three new classes of charged dilatonic black hole solutions, as the exact solutions to the coupled equations of gravitational, electromagnetic and scalar fields, have been introduced. The conserved charge and mass of the new black holes have been calculated by utilizing Gauss's electric law and Abbott–Deser mass proposal, respectively. Also, the temperature, entropy and the electric potential of these new classes of charged dilatonic black holes have been calculated, making use of the geometrical approaches. Through a Smarr-type mass formula, the intensive parameters of the black holes have been calculated and validity of the first law of black hole thermodynamics has been confirmed. A thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. The heat capacity of the new black holes has been calculated and the points of type one- and type two-phase transitions as well as the ranges at which the new charged dilatonic black holes are locally stable have been determined, precisely.

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

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.

A note on the mass of Kerr–AdS black holes in the off-shell generalized ADT formalism☆☆Project supported by the National Natural Science Foundation of China (Grant Nos. 11505036 and 11275157) and partially supported by the Science Fund from the Technology Department of Guizhou Province, China (Grant No. (2016)1104).

In this note, the off-shell generalized Abbott–Deser–Tekin (ADT) formalism is applied to explore the mass of Kerr–anti-de Sitter (Kerr–AdS) black holes in various dimensions within asymptotically rotating frames. The cases in four and five dimensions are explicitly investigated. It is demonstrated that the asymptotically rotating effect may make the charge non-integrable or unphysical when the asymptotic non-rotating timelike Killing vector associated with the charge is allowed to vary and the fluctuation of the metric is determined by the variation of all the mass and rotation parameters. To obtain a physically meaningful mass, it is proposed that one can let the non-rotating timelike Killing vector be fixed or perform calculations in the asymptotically static frame. The results further support that the ADT formalism is background-dependent.

Thermodynamics of novel charged dilatonic BTZ black holes

In this paper, the three-dimensional Einstein–Maxwell theory in the presence of a dilatonic scalar field has been studied. It has been shown that the dilatonic potential must be considered as the linear combination of two Liouville-type potentials. Two new classes of charged dilatonic BTZ black holes, as the exact solutions to the coupled scalar, vector and tensor field equations, have been obtained and their properties have been studied. The conserved charge and mass of the new black holes have been calculated, making use of the Gauss's law and Abbott–Deser proposal, respectively. Through comparison of the thermodynamical extensive quantities (i.e. temperature and entropy) obtained from both, the geometrical and the thermodynamical methods, the validity of the first law of black hole thermodynamics has been confirmed for both of the new black holes we just obtained. A black hole thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. Regarding the black hole heat capacity, it has been found that for either of the new black hole solutions there are some specific ranges in such a way that the black holes with the horizon radius in these ranges are locally stable. The points of type one and type two phase transitions have been determined. The black holes, with the horizon radius equal to the transition points are unstable. They undergo type one or type two phase transitions to be stabilized.

The mass and angular momentum of reconstructed metric perturbations

We prove a key result regarding the mass and angular momentum content of linear vacuum perturbations of the Kerr metric obtained through the formalism developed by Chrzarnowski, Cohen, and Kegeles (CCK). More precisely, we prove that the Abbott–Deser mass and angular momentum integrals of any such perturbation vanish when that perturbation was obtained from a regular Fourier mode of the Hertz potential. As a corollary we obtain a generalization of previous results on the completion of the ‘no string’ radiation gauge metric perturbation generated by a point particle. We find that for any bound orbit around a Kerr black hole, the mass and angular momentum perturbations completing the CCK metric are simply the energy and angular momentum of the particle ‘outside’ the orbit and vanish ‘inside’ the orbit.

Abbott–Deser–Tekin Charge of Dilaton Black Holes with Squashed Horizons**Supported by the National Natural Science Foundation of China under Grant Nos 11275157 and 11505036, the Doctoral Research Fund of Guizhou Normal University in 2014, the Technology Department of Guizhou Province Fund under Grant No [2015]2114, and the Science and Technology Innovation Talent Team of Guizhou Province under Grant No (2015)4015.

We consider the conserved charge of static black holes with squashed horizons in the Einstein-Maxwell-dilaton theory via both the Abbott–Deser–Tekin (ADT) method and its off-shell generalization. We first make use of the original ADT method to compute the mass of the dilaton squashed black holes in terms of three different reference spacetimes, which are the asymptotic geometry, the flat background and the spacetime of the Kaluza-Klein monopole with boundary matched to the original metric, respectively. Each mass satisfies the first law of black hole thermodynamics, although the mass computed on the basis of the boundary matching the Kaluza-Klein monopole is different from that of the other two reference spacetimes. Then the mass of the black holes is evaluated through the off-shell generalized ADT method.

Mass and angular momentum of black holes in low-energy heterotic string theory

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott–Deser–Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr–Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

A New Strategy for Solving Two Cosmological Constant Problems in Hadron Physics

A new approach to solving two of the cosmological problems (CCPs) is proposed by introducing the Abbott-Deser (AD) method for defining Killing charges in asymptotic de Sitter space as the only consistent means for defining the ground-state vacuum for the CCP. That granted, Einstein gravity will also need to be modified at short-distance nuclear scales, using instead a nonminimally coupled scalar-tensor theory of gravitation that provides for the existence of QCD's two-phase vacuum having two different zero-point energy states as a function of temperature. Einstein gravity alone cannot accomplish this. The scalar field will be taken from bag theory in hadron physics, and the origin of the bag constant B is accounted for by gravity's cosmological constant - noting that the Higgs mechanism does not account for either the curved-space origin of lambda or the mass of composite hadrons. A small Hubble-scale graviton mass naturally appears external to the hadron bag, induced by lambda. This mass is unobservable and gravitationally gauge-dependent. It is shown to be related to the cosmological event horizon in asmyptotic de Sitter space.

Critical gravity with a scalar field in four dimensions

We consider the critical gravity theory with a scalar field in four dimensions. We find that this theory has the solution corresponding to the de Sitter (dS), anti-de Sitter (AdS), and Minkowski background depending on whether the action includes the cosmological term or not. The Minkowski background is the solution which cannot be obtained in the model without a scalar field. At the critical point, we show that the Abbott-Deser (AD) mass of the Schwarzschild-de Sitter (SdS) black hole and the energy for the massless graviton vanish, whose situation is not changed from the model without a scalar field.

Witten–Nester energy in topologically massive gravity

We formulate topologically massive supergravity with a cosmological constant in the first-order formalism and construct the Noether supercurrent and superpotential associated with its local supersymmetry. Using these results, we construct in ordinary topologically massive gravity the Witten–Nester integral for conserved charges containing spinors which satisfy a generalized version of the Witten equation on the initial value surface. We show that the Witten–Nester charge, represented as an integral over the boundary of the initial value surface, produces the Abbott–Deser–Tekin energy for asymptotically anti-de Sitter spacetimes. We consider all values of the Chern–Simons coupling constant, including the critical value known as the chiral point, and study the cases of standard Brown–Henneaux boundary conditions, as well as their weaker version that allows a slower fall-off. Studying the Witten–Nester energy as a bulk integral over the initial value surface instead, we find a bound on the energy, and through it the sufficient condition for the positivity of the energy. In particular, we find that spacetimes of Petrov type N that admit globally well-defined solutions of the generalized Witten equation have positive energy.

Black hole mass and angular momentum in topologically massive gravity

We extend the Abbott–Deser–Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.

Mass and free energy in the thermodynamics of squashed Kaluza–Klein black holes

The Abbott–Deser mass, the Hamiltonian and the Komar mass of the five-dimensional Kaluza–Klein black hole with squashed horizons take different values. Introducing a new couple of thermodynamic variables for the Komar mass, we show that each mass can be interpreted as a thermodynamic potential with its own natural variables, i.e. all masses are related to each other by the Legendre transformations. It is found that the new variables and the gravitational tension represent the squashing of the outer horizon.

Mass of rotating black holes in gauged supergravities

The masses of several recently-constructed rotating black holes in gauged supergravities, including the general such solution in minimal gauged supergravity in five dimensions, have until now been calculated only by integrating the first law of thermodynamics. In some respects it is more satisfactory to have a calculation of the mass that is based directly upon the integration of a conserved quantity derived from a symmetry principal. In this paper, we evaluate the masses for the newly-discovered rotating black holes using the conformal definition of Ashtekar, Magnon and Das (AMD), and show that the results agree with the earlier thermodynamic calculations. We also consider the Abbott-Deser (AD) approach, and show that this yields an identical answer for the mass of the general rotating black hole in five-dimensional minimal gauged supergravity. In other cases we encounter discrepancies when applying the AD procedure. We attribute these to ambiguities or pathologies of the chosen decomposition into background AdS metric plus deviations when scalar fields are present. The AMD approach, involving no decomposition into background plus deviation, is not subject to such complications. Finally, we also calculate the Euclidean action for the five-dimensional solution in minimal gauged supergravity, showing that it is consistent with the quantum statistical relation.

Gravitational energy in quadratic-curvature gravities.

We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.