arXiv subjects

Jun-Jin Peng

Publications and source records attributed to Jun-Jin Peng.

At least 19 recordsLinked to original sources

arXiv2025

Extracting the expression for the field equations of a diffeomorphism invariant theory of gravity from surface term

As a contribution towards the understanding for the field equations of diffeomorphism invariant theories of pure gravity, we demonstrate in great detail that the expression for the field equations of such theories can be derived within the perspective of the surface term coming from the variation of the Lagrangian. Specifically, starting with the surface term, we extract a symmetric rank-two tensor together with an anti-symmetric one out of this term with the variation operator replaced with the Lie derivative along an arbitrary vector field. By utilizing an equality stemming from the Lie derivative of the Lagrangian density along an arbitrary vector field, it is proved that the resulting symmetric rank-two tensor is identified with the functional derivative of the Lagrangian density with respect to the metric. Such a result further brings forth the expression for the field equations constructed from the symmetric rank-two tensor, which naturally rules out the derivative of the Lagrangian density with respect to the metric and coincides with the one for the Euler-Lagrange equations of motion. Furthermore, it is illustrated that the construction of the expression for the field equations from the symmetric rank-two tensor must be feasible as long as the variation operator in the variation equation of the Lagrangian is allowed to be substituted by the Lie derivative along an arbitrary vector field. On the other hand, as a byproduct, the anti-symmetric rank-two tensor turns out to be the Noether charge two-form. Our results offer a straightforward support on the proposal in our previous work that the surface term gives a unified description for field equations and Noether charges in the context of theories of gravity admitting diffeomorphism invariance symmetry.

gr-qc↗

arXiv2025

The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term

We figure out the explicit expression for the trace of the field equations associated to generic higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order covariant derivatives of the Riemann tensor. Then an equality linking the Lagrangian density with the covariant divergence of a vector field is put forward in terms of the trace of the field equations. As a significant application, we particularly concentrate on a broad range of higher derivative theories of gravity with the Lagrangian density constructed from the contraction of the product for metric tensors with the product of the Riemann tensors and the arbitrary order covariant derivatives of the Riemann tensor. By utilizing the trace for the equations of motion, such a type of Lagrangian density is expressed as the covariant divergence of a vector field.

gr-qc↗

arXiv2024

Field equations and Noether potentials for higher-order theories of gravity with Lagrangians involving $\Box^i R$, $\Box^i R_{μν}$ and $\Box^i R_{μνρσ}$

In this paper, we aim to perform a systematical investigation on the field equations and Noether potentials for the higher-order gravity theories endowed with Lagrangians depending on the metric and the Riemann curvature tensor, together with $i$th ($i=1,2,\cdot\cdot\cdot$) powers of the Beltrami-d'Alembertian operator $\Box$ acting on the latter. We start with a detailed derivation of the field equations and the Noether potential corresponding to the Lagrangian $\sqrt{-g}L_R(R,\Box R,\cdot\cdot\cdot,\Box^m R)$ through the direct variation of the Lagrangian and a method based upon the conserved current. Next the parallel analysis is extended to a more generic Lagrangian $\sqrt{-g}L_{\text{Ric}}(g^{μν}, R_{μν},\Box R_{μν}, \cdot\cdot\cdot,\Box^m R_{μν})$, as well as to the generalization of the Lagrangian $\sqrt{-g}L_{\text{Ric}}$, which depends on the metric $g^{μν}$, the Riemann tensor $R_{μνρσ}$ and $\Box^i R_{μνρσ}$s. Finally, all the results associated to the three types of Lagrangians are extended to the Lagrangian relying on an arbitrary tensor and the variables via $\Box^i$ acting on such a tensor. In particular, we take into consideration of equations of motion and Noether potentials for nonlocal gravity models. For Lagrangians involving the variables $\Box^i R$, $\Box^i R_{μν}$ and $\Box^i R_{μνρσ}$, our investigation provides their concrete Noether potentials and the field equations without the derivative of the Lagrangian density with respect to the metric. Besides, the Iyer-Wald potentials associated to these Lagrangians are also presented.

gr-qc↗

arXiv2024

A note on field equations in generalized theories of gravity

In the work (arXiv:1109.3846 [gr-qc]), to obtain a simple and economic formulation of field equations for generalised theories of gravity described by the Lagrangian $\sqrt{-g}L\big(g^{αβ},R_{μνρσ}\big)$, the key equality $\big(\partial L/\partial g^{μν}\big)_{R_{αβκω}} =2P_μ^{~λρσ}R_{νλρσ}$ was derived. In this note, it is demonstrated that such an equality can be directly derived from an off-shell Noether current associated with an arbitrary vector field. As byproducts, a generalized Bianchi identity related to the divergence for the expression of field equations, together with the Noether potential, is obtained. On the basis of the above, we further propose a systematic procedure to derive the equations of motion from the Noether current, and then this procedure is extended to more general higher-order gravities endowed with the Lagrangian encompassing additional terms of the covariant derivatives of the Riemann tensor. To our knowledge, both the detailed expressions for field equations and the Noether potential associated with such theories are first given at a general level. All the results reveal that using the Noether current to determine field equations establishes a straightforward connection between the symmetry of the Lagrangian and the equations of motion and such a remedy even can avoid calculating the derivative of the Lagrangian density with respect to the metric.

gr-qc↗

arXiv2023

Conserved quantities for asymptotically AdS spacetimes in quadratic curvature gravity in terms of a rank-4 tensor

We investigate the conserved quantities associated to Killing isometries for asymptotically AdS spacetimes within the framework of quadratic-curvature gravity. By constructing a rank-4 tensor possessing the same index symmetries as the ones of the Riemann tensor, we propose a 2-form potential resembling the Noether one for quadratic-curvature gravity. Such a potential is compared with the results via other methods existing in the literature to establish the equivalence. Then this potential is adopted to define conserved quantities of asymptotically AdS spacetimes. As applications, we explicitly compute the mass of static spherically-symmetric spacetimes, as well as the mass and the angular momentum for rotating spacetimes, such as the four(higher)-dimensional Kerr-AdS black holes and black strings embedded in quadratic-curvature gravities. Particularly, we emphasize the conserved charges of Einstein-Gauss-Bonnet, Weyl and critical gravities, together with the ones for the asymptotically AdS solutions satisfying vacuum Einstein field equations.

gr-qc↗

arXiv2022

Generalized Komar currents for vector fields

In this paper, on basis of three quadratic differential operators leaving the form degree of an arbitrary differential form unchanged, that is, the d'Alembertian operator and two combined ones from the Hodge coderivative and the exterior derivative, the usual Komar current for a Killing vector is formulated into another equivalent form. Then it is extended to more general currents in the absence of the linearity in the Killing vector field. Moreover, motivated by this equivalent of the usual Komar current, we put forward a conserved current corresponding to a generic vector with some constraint. Such a current can be generalized to the one with higher-order derivatives of the vector. The applications to some specific vector fields, such as the almost-Killing vectors, the conformal Killing vectors and the divergence-free vectors, are investigated. It is demonstrated that the above generalizations of the Killing vector can be uniformly described by a second-order derivative equation.

gr-qc↗

arXiv2020

A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity

The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d'Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d'Alembertian. The surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, we make use of such a formula to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results coincide with the ones in the literature.

gr-qc↗

arXiv2020

A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization

Within the framework of the Lovelock gravity theory, we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters. Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically anti-de Sitter (AdS) spacetimes. Besides, inspired with the case of the Lovelock gravity, we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor. On basis of the newly-constructed tensor, we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.

gr-qc↗

arXiv2020

Constructing $p,n$-forms from $p$-forms via the Hodge star operator and the exterior derivative

In this paper, we aim to explore the properties and applications on the operators consisting of the Hodge star operator together with the exterior derivative, whose action on an arbitrary $p$-form field in $n$-dimensional spacetimes makes its form degree remain invariant. Such operations are able to generate a variety of $p$-forms with the even-order derivatives of the $p$-form. To do this, we first investigate the properties of the operators, such as the Laplace-de Rham operator, the codifferential and their combinations, as well as the applications of the operators in the construction of conserved currents. On basis of two general p-forms, then we construct a general n-form with higher-order derivatives. Finally, we propose that such an n-form could be applied to define a generalized Lagrangian with respect to a p-form field according to the fact that it incudes the ordinary Lagrangians for the $p$-form and scalar fields as special cases.

gr-qc↗

arXiv2020

A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization

Within the framework of four-dimensional quadratic curvature gravities in the appearance of a negative cosmological constant, a definition for the gravitational energy of solutions with anti-de Sitter (AdS) asymptotics was put forward in Ref. [1]. This was achieved by adding proper topological invariant terms to the gravity action to render the variation problem well-posed. In the present note, we prove that the definition via the procedure of topological regularization can be covered by the one given in Ref. [3] in four dimensions. Motivated by this, we further generalize the results to generic gravity theories in arbitrary even dimensions.

gr-qc↗

arXiv2019

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.

gr-qc↗

arXiv2017

A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism

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 be 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 avoid such a dilemma, we can let the non-rotating timelike Killing vector be fixed or perform calculations in the asymptotically static frame. Our results further support that the ADT formalism is background-dependent.

gr-qc↗

arXiv2017

Conserved charge of a gravity theory with $p$-form gauge fields and its property under Kaluza-Klein reduction

In this paper, we investigate the conserved charges of generally diffeomorphism invariant gravity theories with a wide variety of matter fields, particularly of the theories with multiple scalar fields and $p$-form potentials, in the context of the off-shell generalized Abbott-Deser-Tekin (ADT) formalism. We first construct a new off-shell ADT current that consists of the terms for the variation of a Killing vector and expressions of the field equations as well as the Lie derivative of a surface term with respect to the Killing vector within the framework of generally diffeomorphism invariant gravity theories involving various matter fields. After deriving the off-shell ADT potential corresponding to this current, we propose a formula of conserved charges for these theories. Next, we derive the off-shell ADT potential associated with the generic Lagrangian that describes a large range of gravity theories with a number of scalar fields and $p$-form potentials. Finally, the properties of the off-shell generalized ADT charges for the theory of Einstein gravity and the gravity theories with a single $p$-form potential are investigated by performing Kaluza-Klein dimensional reduction along a compactified direction. The results indicate that the charge contributed by all the fields in the lower-dimensional theory is equal to that of the higher-dimensional one at mathematical level with the hypothesis that the higher-dimensional spacetime allows for the existence of the compactified dimension. In order to illustrate our calculations, the mass and angular momentum for the five-dimensional rotating Kaluza-Klein black holes are explicitly evaluated as an example.

hep-th↗

arXiv2016

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.

gr-qc↗

arXiv2015

Off-shell Noether current and conserved charge in Horndeski theory

We derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar-tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar-tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor.

gr-qc↗

arXiv2014

Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of motion equation, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those through other methods in the literature.

gr-qc↗

arXiv2011

Thermodynamics and Hawking radiation of five-dimensional rotating charged Gödel black holes

We study the thermodynamics of Gödel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed time-like curves and the absence of globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, We extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and effective action give the same Hawking fluxes as those from Planck distribution for blackbody radiation in the background of the charged rotating Gödel black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.

hep-th↗

arXiv2010

Hawking Radiation of Black Holes in Infrared Modified Hořava-Lifshitz Gravity

We study the Hawking radiation of the spherically symmetric, asymptotically flat black holes in the infrared modified Horava-Lifshitz gravity by applying the methods of covariant anomaly cancellation and effective action, as well as the approach of Damour-Ruffini-Sannan's. These black holes behave as the usual Schwarzschild ones of the general relativity when the radial distance is very large. We also extend the method of covariant anomaly cancellation to derive the Hawking temperature of the spherically symmetric, asymptotically AdS black holes that represent the analogues of the Schwarzschild AdS ones.

hep-th↗