Motivated by the study of conserved Aretakis charges for a scalar field on the horizon of an extremal black hole, we construct the metrics for certain classes of four-dimensional and five-dimensional extremal rotating black holes in Gaussian null coordinates. We obtain these as expansions in powers of the radial coordinate, up to sufficient order to be able to compute the Aretakis charges. The metrics we consider are for 4-charge black holes in four-dimensional STU supergravity (including the Kerr-Newman black hole in the equal-charge case) and the general 3-charge black holes in five-dimensional STU supergravity. We also investigate the circumstances under which the Aretakis charges of an extremal black hole can be mapped by conformal inversion of the metric into Newman-Penrose charges at null infinity. We show that while this works for four-dimensional static black holes, a simple radial inversion fails in rotating cases because a necessary conformal symmetry of the massless scalar equation breaks down. We also discuss that a massless scalar field in dimensions higher than four does not have any conserved Newman-Penrose charge, even in a static asymptotically flat spacetime.
We propose the modified form of the conventional holographic conserved charges which provides us the frame-independent expressions for charges. This form is also preferable to the conventional one since it is independent of the holographic renormalization scheme. We show the frame and scheme independence through the matching of our holographic expression to the covariant bulk expression of conserved charges. As an explicit example, we consider five-dimensional AdS Kerr black holes and show that our form of holographic conserved charges gives us the identical expressions in the rotating and non…
In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-$r$ expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a $1/r$-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. $1/r^0$, one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. A…
We explore the quadratic form of the $f(R)=R+bR^2$ gravitational theory to derive rotating $N$-dimensions black hole solutions with $a_i, i\geq 1$ rotation parameters. Here, $R$ is the Ricci scalar, and $b$ is the dimensional parameter. We assumed that the $N$-dimensional spacetime is static and has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that in the four-dimensional case,the higher-order curvature does not contribute to the black hole,i.…
In this paper, we examine the emergence of conserved charges on the horizon of a particular class of extremal non-dilatonic black $p$-branes (which reduce to extremal dilatonic black holes in $D=4$ dimensions upon toroidal compactification) in the presence of a probe massless scalar field in the bulk. This result is achieved by writing the black $p$-brane geometry in a Gaussian null coordinate system which allows us to get a non-singular near-horizon geometry description. We find that the near-horizon geometry is $AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal structure …
In this paper we consider a generally covariant theory of gravity, and extend the generalized off-shell ADT current such that it becomes conserved for field dependent (asymptotically) Killing vector field. Then we define the extended off-shell ADT current and the extended off-shell ADT charge. Consequently, we define the conserved charge perturbation by integrating from the extended off-shell ADT charge over a spacelike codimension two surface. Eventually, we use the presented formalism to find the conserved charge perturbation of an asymptotically flat spacetime. The conserved charge perturba…
We investigate the tendency in variations of the dual CFT$_2$ when a rotating AdS$_3$ black hole changes by fluxes transferred by the scattering of a massive scalar field according to the AdS/CFT correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities, so the black hole cannot be extremal under the scattering. This is naturally preferred. By the relationship between the rotating AdS$_3$ black hole and dual CFT$_2$, we find that such chang…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general prescription for defining quasi-local ``conserved quantities'' (i.e. in the situation when the gravitating system has a non-vanishing energy flux). Applications include energy-momentum and angular momentum at spatial and null infinity, asymptotically anti-deSitter spacetimes, and thermodynamics of the isolated horizons.
We compute the mass, angular momenta and charge of the Godel-type rotating black hole solution to 5 dimensional minimal supergravity. A generalized Smarr formula is derived and the first law of thermodynamics is verified. The computation rests on a new approach to conserved charges in gauge theories that allows for their computation at finite radius.
In this paper, using the combined Lorentz-diffeomorphism symmetry, we find a general formula for quasi-local conserved charge of the covariant gravity theories in first order formalism of gravity. We simplify the general formula for Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain energy and angular momentum of the rotating OTT black hole solution in the context of this theory.
In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions are anti-deSitter, but for power Maxwell invariant solutions, depend on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti-deSitter for all values of the nonlinearity parameter. Next, we calcul…
We obtain the magnetic counterpart of the BTZ solution, i.e., the rotating spacetime of a point source generating a magnetic field in three dimensional Einstein gravity with a negative cosmological constant. The static (non-rotating) magnetic solution was found by Clement, by Hirschmann and Welch and by Cataldo and Salgado. This paper is an extension of their work in order to include (i) angular momentum, (ii) the definition of conserved quantities (this is possible since spacetime is asymptotically anti-de Sitter), (iii) upper bounds for the conserved quantities themselves, and (iv) a new int…
We consider an extension of a special class of conformal sigma models (`chiral null models') which describe extreme supersymmetric string solutions. The new models contain both `left' and `right' vector couplings and should correspond to non-BPS backgrounds. In particular, we discuss a conformal six-dimensional model which is a combination of fundamental string and 5-brane models with two extra couplings representing rotations in orthogonal planes. If the two rotational parameters are independent the resulting background is found to be either singular or not asymptotically flat. The non asympt…
The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r_{ph}(a/M;cos i) of these spherical null geodesics, where a/M is the dimensionless angular-momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known…
We obtain exact rotating membrane solutions and explicit expressions for the conserved charges on a manifold with exactly known metric of G_2 holonomy in M-theory, with four dimensional N=1 field theory dual. After that, we investigate their semiclassical limits and derive different relations between the energy and the other conserved quantities, which is a step towards M-theory lift of the semiclassical string/gauge theory correspondence for N=1 field theories.
We present arguments for the existence of five-dimensional rotating black holes with equal magnitude angular momenta in Einstein-Gauss-Bonnet theory with negative cosmological constant. These solutions posses a regular horizon of spherical topology and approach asymptotically an Anti-de Sitter spacetime background. We discuss the general properties of these solutions and, using an adapted counterterm prescription, we compute their entropy and conserved charges.
The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency. Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact obj…
In this work we have constructed axially symmetric vacuum solutions of the gravitational field equations in a Randall-Sundrum brane. A non-null effective cosmological constant is considered, and asymptotically de Sitter and anti-de Sitter spacetimes are obtained. The solutions describe rotating black holes in a four-dimensional brane. Optical features of the solutions are treated, emphasizing the rotation of the polarization vector along null congruences.
Depending on five parameters, rotating counterparts of Einstein--Maxwell--dilaton black holes are derived. We discuss their physical and geometric properties and investigate their null and time-like geodesics including circular orbits. The Lense--Thirring effect is considered.
We consider Einstein gravity coupled to an $U(1)$ gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as $d/4$. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the…
We construct a new class of charged rotating black string solutions coupled to a nonlinear electromagnetic field in the background of anti-de Sitter spaces. We consider two types of nonlinear electromagnetic field namely, logarithmic and exponential forms. We investigate the geometric effects of nonlinearity parameter and find that for large $r$, these solutions recover the rotating back string solutions of Einstein-Maxwell theory. We calculate the conserved and thermodynamic quantities of the rotating black string. We also analyze thermodynamics of the spacetime and verify the validity of the…
In this paper we construct mass, angular momentum and entropy of black hole solution of Generalized Minimal Massive Gravity (GMMG) in asymptotically Anti-de Sitter (AdS) spacetimes. The generalized minimal massive gravity theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. We apply our result for conserved charge $Q^μ (\barξ)$ to the rotating BTZ black hole solution of GMMG, and find energy, angular momentum and entropy. Then we show our results for these quantities are c…
It is shown that the conserved charges on the event horizon and the Cauchy horizon associated to scalar perturbations on extremal black holes are externally measurable from null infinity. This suggests that these charges have the potential to serve as an observational signature. The proof of this result is based on obtaining precise late-time asymptotics for the radiation field of outgoing perturbations.
We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effcetive values of mass and angular momentum are then used to derive an identity ($K_{χ^μ}=2ST$) which relates the Komar conserved charge ($K_{χ^μ}$) corresponding to the null Killing vector ($χ^μ$) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of …
A black hole is superentropic if it violates the reverse isoperimetric inequality. Recently, some studies have indicated that some four dimensional superentropic black holes have the null hypersurface caustics (NHC) outside their event horizons. In this paper, we extend to explore whether or not the NHC exists in the cases of high dimensional superentropic black holes. We consider the singly rotating Kerr-AdS superentropic black holes in arbitrary dimensions and the singly rotating charged superentropic black hole in five-dimensional minimal gauged supergravity, and find that the NHC exists ou…
There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more general null-fronted metrics, field quantization cannot be interpreted in terms of particle creation and annihilation operators, and the physical meaning of the theory becomes obscure.
We construct the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case with only one rotation parameter and two independent charges. Using the Boyer-Lindquist coordinates, the metric is expressed in a generalized form of the ansatz previously presented in [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], which may be helpful to find the most general non-extremal two-charged rotating black hole with three unequal rotation parameters. The conserved charges for thermodynamics are also computed.
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-Com…
We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacet…
In this paper, we aim to examine the relationship between the unstable circular photon orbit and the thermodynamic phase transition for a rotating Kerr-AdS black hole. On one side, we give a brief review of the phase transition for the Kerr-AdS black hole. The coexistence curve and the metastable curve corresponding to the phase transition are clearly shown. On the other side, we calculate the radius and the angular momentum of the unstable circular orbits for a photon by analyzing the effective potential. Then combining these two sides, we find the following results. i) The radius and the ang…
Recently, a general method for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Kerr-dS black holes. Furthermore, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermody…
We use the anti-de Sitter (AdS) conformal field theory correspondence to calculate the conserved charges and the Euclidean actions of the charged rotating black string in four dimensions both in the canonical and the grand-canonical ensemble. The four-dimensional solution of the Einstein-Maxwell equations with a positive cosmological constant is introduced, and its conserved quantities and actions for fixed charge and fixed electric potential are calculated. We also study the thermodynamics of the asymptotically AdS black strings and perform a stability analysis both in the canonical and the g…
We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed a…
We investigate the thermodynamics of rotating Lovelock-Lifshitz black branes. We calculate the conserved and thermodynamic quantities of the solutions and obtain a relation between temperature, angular velocity, energy density, entropy density and angular momentum density. We, also, obtain a Smarr-type formula for the energy density as a function of entropy and angular momentum densities, and show that the thermodynamic quantities calculated in this paper satisfy the first law of thermodynamics. Finally, we investigate the stability of black brane solutions in both canonical and grand-canonica…
We investigate a stress-energy tensor for a CFT at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad (arXiv:1207.2305), and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons, and that the energy density is negative just outside …
A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, $P$. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. Howe…
In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor memories, the Penrose's conformal completion method is used to analyze the asymptotic structures and asymptotic symmetries, and then, conserved charges for the Bondi-Metzner-Sachs algebra are constructed with the Wald-Zoupas formalism. These charges take very similar forms to those in Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is rewri…
We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.
In this work, we generalized the Kerr-Newman-NUT black hole solution in Rastall gravity from Ref. 1. Here we are more focused on the black hole dynamics such as the event horizons, ergosurface, ZAMO, thermodynamic properties, and the equatorial circular orbit around the black hole such as static radius limit, null equatorial circular orbit, and innermost stable circular orbit. We present how the NUT and Rastall parameter affects the dynamic of the black hole.
Recently Gibbons {\it et al.} in hep-th/0408217 defined a set of conserved quantities for Kerr-AdS black holes with the maximal number of rotation parameters in arbitrary dimension. This set of conserved quantities is defined with respect to a frame which is non-rotating at infinity. On the other hand, there is another set of conserved quantities for Kerr-AdS black holes, defined by Hawking {\it et al.} in hep-th/9811056, which is measured relative to a frame rotating at infinity. Gibbons {\it et al.} explicitly showed that the quantities defined by them satisfy the first law of black hole the…
In this paper, we explore the photon region and the shadow of the rotating counterpart of a static charged Weyl black hole, which has been previously discussed according to null and time-like geodesics. The rotating black hole shows strong sensitivity to the electric charge and the spin parameter, and its shadow changes from being oblate to being sharp by increasing in the spin parameter. Comparing the calculated vertical angular diameter of the shadow with that of M87*, we found that the latter may possess about $10^36$ protons as its source of electric charge, if it is a rotating charged Wey…
We describe the most general asymptotically flat, stationary, non-extremal, dyonic black hole of the four-dimensional N = 2 supergravity coupled to 3 vector multiplets that describes the low-energy regime of the STU model. Under U-dualities, this can be used as a seed to generate all single-centered stationary black holes of N = 8 supergravity. The independent conserved charges are the mass, angular momentum, four electric charges and four magnetic charges; an independent NUT charge can also be added. Several aspects of the black hole are presented, including thermodynamics, the BPS limit, the…
Rotating Black Holes and the Kerr/CFT Correspondence in Einstein-Bumblebee Gravity
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）
Modes emerging out of a collapsing black hole are red-shifted to such an extent that Hawking radiation at future null infinity consists of modes that have energies beyond the Planck scale at past null infinity. This indicates that physics at the Planck scale may modify the spectrum of Hawking radiation and the associated stress-energy tensor of the quantum field. Recently, it has been shown that, the T-duality symmetry of string fluctuations along compact extra dimensions leads to a modification of the standard propagator of point particles in quantum field theory. At low energies (when compar…
We consider the Gauss-Bonnet gravity in the presence of a new class of nonlinear electromagnetic field, namely, power Maxwell invariant. By use of a suitable transformation, we obtain a class of real rotating solutions with $k$ rotation parameters and investigate some properties of the solutions such as existence of singularity(ies) and asymptotic behavior of them. Also, we calculate the finite action, thermodynamic and conserved quantities of the solutions and using the the Smarr-type formula to check the first law of thermodynamics.
We consider rotating strings and D2-branes on type IIA background, which arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to N=1 gauge theory in four dimensions. We obtain exact solutions and explicit expressions for the conserved charges. By taking the semiclassical limit, we show that the rotating strings can reproduce only one type of semiclassical behavior, exhibited by rotating M2-branes on G2 manifolds. Our further investigation leads to the conclusion that the rotating D2-branes reproduce two types of the semiclassical energy-charge relations known for membra…
We present the metric for the $(n+1)$-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.
In this paper, we construct a class of (n+1)-dimensional $(n\geq4)$ slowly rotating black hole solutions in Brans-Dicke-Maxwell theory with a quadratic potential. These solutions can represent black holes with inner and outer event horizons, an extreme black hole and a naked singularity and they are neither asymptotically flat nor (anti)-de Sitter. We compute the Euclidean action and use it to obtain the conserved and thermodynamics quantities such as entropy, which does not obey the area law. We also compute the angular momentum and the gyromagnetic ratio for these type of black holes where t…
We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl t…
We construct the general solution for non-extremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterised by four non-trivial parameters, namely the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTC's) are avoided. We calculate the conserved energy, angular momenta and charge for the solutions, and show how supersymmetric solutions arise in a BPS limit. These have n…
We consider null warped AdS(3) solutions of three-dimensional gravity coupled to a massive vector field. We isolate a certain set of non-propagating solutions to the equations of motion, which we argue are the ones relevant for understanding the stress tensor sector of the dual field theory. We construct a map from these modes to solutions of three-dimensional Einstein gravity with a negative cosmological constant, and thus show that they admit a Fefferman-Graham-like asymptotic expansion. We also compute the renormalized on-shell action for these modes at full non-linear level and propose tha…
It has recently been revealed that spinning black holes of the photon-fluid model can support acoustic `clouds', stationary density fluctuations whose spatially regular radial eigenfunctions are determined by the $(2+1)$-dimensional Klein-Gordon equation of an effective massive scalar field. Motivated by this intriguing observation, we use {\it analytical} techniques in order to prove a no-short hair theorem for the composed acoustic-black-hole-scalar-clouds configurations. In particular, it is proved that the effective lengths of the stationary bound-state co-rotating acoustic scalar clouds a…
We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic resonant frequencies of the black hole, including quasinormal modes, total-transmission modes and total-reflection modes. We identify these modes with semiclassical bound states of a one-dimensional Schrodinger equation, localized along contours in the complexified r-plane which connect turning points of corresponding null geodesics. Each family of modes has …
