While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theories allows to partially remove the degeneracy of these theories, leading to a three-parameter family of Lagrangians of order four in the Riemann tensor. This shows that the parallel with Lovelock theory observed on spherical symmetry, extends to the realm of slowly rotating solutions. In the quartic case, the equations for the slowly rotating black hole are obtained from a consistent, reduced action principle. These functions admit a simple integration in terms of quadratures. Finally, in order to go beyond the slowly rotating regime, we explore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological gravity. Requiring the spacetime to asymptotically match with the rotating black hole in GR, for equal oblateness parameters, the Kerr-Schild deformation of an AdS vacuum, does not lead to a solution for generic values of the coupling. This result suggests that in order to have solutions with finite rotation in Quasi-topological gravity, one must go beyond the Kerr-Schild ansatz.
It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of slowly rotating black holes in the Einstein-scalar-Chern-Simons (EsCS) theory. In the slow rotation approximation, the CS term takes a linear form of rotation parameter $a$ which determines the tachyonic instability. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. It is shown that the slowly rotating black holes are unstable against a spherically symmetric scalar-mode perturbation for positive coupling $α$, whereas these bla…
We investigate the area spectrum for rotating black holes which are Kerr and BTZ black holes. For slowly rotating black holes, we use the Maggiore's idea combined with Kunstatter's method to derive their area spectra, which are equally spaced.
We investigate slowly rotating black holes in the Hořava-Lifshitz (HL) gravity. For $Λ_W=0$ and $λ=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.
Stationary, axisymmetric and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptoti…
It is shown that the well-known non-Abelian static SU(2) black hole solutions have rotating generalizations, provided that the hypothesis of linearization stability is accepted. Surprisingly, this rotating branch has an asymptotically Abelian gauge field with an electric charge that cannot vanish, although the non-rotating limit is uncharged. We argue that this may be related to our second finding, namely that there are no globally regular slowly rotating excitations of the particle-like Bartnik-McKinnon solutions.
By using a new approach, we demonstrate analytic expressions for slowly rotating Gauss-Bonnet charged black holes with negative cosmological constant. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the charged black holes get no corrections from rotation.
Slowly rotating black holes in the non-projectable Hořava-Lifshitz (HL) theory were studied recently in Phys. Rev. Lett. {\bf 109}, 181101 (2012), and claimed that they do not exist. In this Comment, we show that this is incorrect, and such solutions indeed exist in the IR limit of the non-projectable HL theory.
In this paper, we study slowly rotating black hole solutions in Lovelock gravity (n=3). These exact slowly rotating black hole solutions are obtained in uncharged and charged cases, respectively. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the uncharged black holes get no corrections from rotation. In charged case, we compute magnetic dipole moment and gyromagnetic ratio of the black holes. It is shown that the gyromagnetic ratio keeps invariant after introducing the Gauss-Bonnet and third order Lovelock interactions.
We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is given by a term for Schwarzschild black hole, whereas the CS term takes a linear term of $a$. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. We use the (2+1)-dimensional hyperboloidal foliation method to show the tachyonic instability for slowly rotating black holes by considering the time evolution of a spherically symmetric…
We present a slowly rotating generalization of a black hole modeled by a Solv horizon geometry, in five dimensional General Relativity. A separable ansatz compatible with Einstein equations is proposed, which is integrated in terms of hypergeometric and exponential functions. The solution highly simplifies after requiring to maintain the same asymptotic behaviour as the non-rotating black hole and to have finite, non-vanishing charges. We compute the charges of the solution and also comment on its importance for studying the phase space of the theory in this sector.
In a recent paper we claimed that there there are no slowly rotating, stationary, axisymmetric black holes in the infrared limit of Horava-Lifshitz gravity, provided that they are regular everywhere apart from the central singularity. Here we point out a subtlety in the equivalence between Einstein-aether theory and the infrared limit of Horava-Lifshitz gravity which was missed in our earlier derivation and drastically modifies our conclusion: our earlier calculations (which are otherwise technically correct) do not really imply that there are no slowly rotating black holes in Horava-Lifshitz …
We study the Gregory-Laflamme instability of a 5-dimensional slowly rotating black string in which the 4-dimensional section is described by the Kerr black hole. We treat the rotation in a perturbative way introducing a small parameter for the rotation. It is found that rotation makes the Gregory-Laflamme instability stronger. Both the critical wavelength at the onset of instability and the growth time-scale are found to decrease as the rotation increases.
Rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit with an appropriate combination of three Liouville-type dilaton potentials. The angular momentum, magnetic dipole moment and the gyromagnetic ratio of such a black hole are determined for arbitrary values of the dilaton-electromagnetic coupling parameter.
We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding $rr$ and $tϕ$ components of the gravitational field equations in both cases: A, $b_μ=(0,b(r),0,0)$; B, $b_μ=(0,b(r),\mathfrak{b}(θ),0)$. Then we check the other gravitational field equations and the bumblebee field motion equations by using this solution. We find that in the case A, there exists a slowly rotating black hole solution indeed for arbitrary LV (Lorentz violation) coupling constant $\ell$; however as in the case B, there exists this slowly rotating solution if and only if the coup…
We show how (at least in principle) one can construct electrically and magnetically charged slowly rotating black hole solutions coupled to non-linear electrodynamics (NLE). Our generalized Lense-Thirring ansatz is, apart from the static metric function $f$ and the electrostatic potential $ϕ$ inherited from the corresponding spherical solution, characterized by two new functions $h$ (in the metric) and $ω$ (in the vector potential) encoding the effect of rotation. In the linear Maxwell case, the rotating solutions are completely characterized by static solution, featuring $h=(f-1)/r^2$ and $ω=…
In the Einstein-Cartan formulation, an iterative procedure to find solutions in non-dynamical Chern-Simons (CS) gravity in vacuum is proposed. The iterations, in powers of a small parameter $β$ which codifies the CS coupling, start from an arbitrary torsionless solution of Einstein equations. With Schwarzschild as the zeroth-order choice, we derive a second-order differential equation for the $\mathcal{O}(β)$ corrections to the metric, for an arbitrary zeroth-order embedding parameter. In particular, the slowly rotating Kerr metric is an $\mathcal{O}(β)$ solution in either the canonical or the…
We study the Vainshtein mechanism in the context of slowly rotating stars in scalar-tensor theories. While the Vainshtein screening is well established for spherically symmetric spacetimes, we examine its validity in the axisymmetric case for slowly rotating sources. We show that the deviations from the general relativity solution are small in the weak-field approximation outside the star: the solution for the frame-dragging function is the same as in general relativity at leading order. Moreover, in most cases the corrections are suppressed by powers of the Vainshtein radius provided that the…
We study slowly rotating black hole solutions in the six independent theories of Einstein Quartic Gravity (EQG) in four dimensions. Unlike in the static case for which all six theories yield the same solution, for rotating black holes we obtain distinct results for five out of the six theories. Working to leading order in the rotation parameter, we find that the equations characterizing these black holes can be reduced to second order for each theory, similar to what has already been done for Einstein Cubic Gravity. We construct approximate and numerical solutions to these equations, and study…
We develop the effective theory for perturbations around black holes with scalar hair, in two directions. First, we show that the scalar-Gauss--Bonnet theory, often used as an example exhibiting scalar black hole hair, can be deformed by galileon operators leading to order unity changes to its predictions. The effective theory for perturbations thus provides an efficient framework for describing and constraining broad classes of scalar-tensor theories, of which the addition of galileon operators is an example. Second, we extend the effective theory to perturbations around an axisymmetric, slow…
Nonminimally coupled free scalar fields may be unstable in the spacetime of compact objects. Such instability can be triggered by classical seeds or, more simply, by quantum fluctuations giving rise to the so-called {\em vacuum awakening effect}. Here, we investigate how the parameter space which characterizes the instability is affected when the object gains some rotation. For this purpose, we focus on the stability analysis of nonminimally coupled scalar fields in the spacetime of slowly spinning matter shells.
A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was considered. Having used the obtained solution we investigated thermodynamic functions such as black hole's temperature, entropy and heat capacity. In addition to examine thermodynamic properties of the black hole extended technique was applied. The equation of state of Van der Waals type was obtained and investigated. It has been shown that the given system has phase transitions of the first as well as of the zeroth order for the temperatures below a critical one which is notable feature of the black hole. A coexiste…
Black hole solutions in higher dimensional Einstein and Einstein-Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner-Nordstrom and Kerr solutions of four-dimensional general relativity. However, higher dimensional generalization of the Kerr-Newman solution in four dimensions has not been found yet. As a first step in this direction I shall report on a new solution of the Einstein-Maxwell system of equations that describes an electrically charged and slowly rotating black h…
We study the effect of rotation on the spectrum of bound states for dust cores that source (quantum) black holes found in Eur. Phys. J. C 82 (2022) 10. The dust ball is assumed to spin rigidly with sufficiently slow angular velocity that perturbation theory can be applied. Like the total mass, the total angular momentum is shown to be quantised in Planck units, hence so is the horizon area. For sufficiently small fraction of mass in the outermost layer, the model admits ground states which can spin fast enough within the perturbative regime so as to describe regular rotating objects rather tha…
We consider slowly rotating, stationary, axisymmetric black holes in the infrared limit of Horava-Lifshitz gravity. We show that such solutions do not exist, provided that they are regular everywhere apart from the central singularity. This has profound implications for the viability of the theory, considering the astrophysical evidence for the existence of black holes with non-zero spin. NOTE ADDED: A subtlety in the dynamical equivalence between Horava-Lifshitz gravity and Einstein-aether theory has been missed and this has seriously affected the conclusions of this paper. Please see arXiv:1…
In the present work, we consider the possibility of observationally testing Hořava gravity by using the accretion disk properties around slowly rotating black holes of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard slowly rotating general relativistic Kerr solution. Comparing the mass accretion in a slowly rotating Kehagias-Sfetsos geometry in Hořava gravity with the one of a slowly rotating Kerr black hole, we verify that the…
We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a non-vanishing $g_{tϕ}$ component. Similarly to the static case, the order of the equation determining such component can be reduced twice, giving rise to a second-order differential equation which can be easily solved numerically as a function of the ECG coupling. We study how various physical properties of the solutions are modified with resp…
We study the superradiant instability of slowly rotating Kerr-Newman (sKN) black holes under a charged massive scalar perturbation. These black holes resemble closer the Reissner-Nordström black holes than the Kerr-Newman black holes. We compute the negative absorption cross section of a massive scalar for superradiant scattering in the low frequency limit. From the scalar potential analysis, we find that the superradiant instability is not allowed in the sKN black holes because the condition for a trapping well is not compatible with the superradiance condition. However, the rate of energy ex…
We show that, independently of the scalar field potential and of specific asymptotic properties of the spacetime (asymptotically flat, de Sitter or anti-de Sitter), any static, spherically symmetric or planar, black hole or soliton solution of the Einstein theory minimally coupled to a real scalar field with a general potential is mode stable under linear odd-parity perturbations. To this end, we generalize the Regge-Wheeler equation for a generic self-interacting scalar field, and show that the potential of the relevant Schrödinger operator can be mapped, by the so-called S-deformation, to a …
We present a novel family of slowly rotating black hole solutions in four, and higher dimensions, that extend the well known Lense-Thirring spacetime and solve the field equations to linear order in rotation parameter. As "exact metrics" in their own right, the new (non-vacuum) spacetimes feature the following two remarkable properties: i) near the black hole horizon they can be cast in the, manifestly regular, Painlevé-Gullstrand form and ii) they admit exact Killing tensor symmetries. We show these symmetries are inherited from the principal Killing-Yano tensor of the exact rotating black ho…
In this paper, with considering the nonlinear electromagnetic field coupled to Einstein gravity, we obtain the higher dimensional slowly rotating charged black hole solutions. By use of the fact that the temperature of the extreme black hole is zero, we find that these solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons provide that the mass parameter $m$ is greater than an extremal value $m_{ext}$, an extreme black hole if $m=m_{ext}$ and a naked singularity otherwise. Also, we find that the asymptotic behavior of the spacetime is not anti deSit…
We study slowly rotating, asymptotically flat black holes in Einstein-aether theory and show that solutions that are free from naked finite area singularities form a two-parameter family. These parameters can be thought of as the mass and angular momentum of the black hole, while there are no independent aether charges. We also show that the aether has non-vanishing vorticity throughout the spacetime, as a result of which there is no hypersurface that resembles the universal horizon found in static, spherically symmetric solutions. Moreover, for experimentally viable choices of the coupling co…
Slowly rotating charged BTZ black hole solutions in Palatini Chern-Simons gravity
Instituto de Física Corpuscular (IFIC), CSIC‐Universitat de València（粒子物理研究所 (IFIC)，西班牙瓦伦西亚大学）；Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）；Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）
Rotating charged Gauss-Bonnet black hole solutions in higher dimensional ($d >4$), asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit. The angular momentum, magnetic dipole moment, and the gyromagnetic ratio of the black holes are calculated and it turns out that the Gauss-Bonnet term does not affect to the gyromagnetic ratio.
We present a new stationary solution to the field equations of Hořava-Lifshitz gravity with the detailed balance condition and for any value of the coupling constant λ> 1/3 . This is the generalization of the corresponding spherically symmetric solution earlier found by Lü, Mei and Pope to include a small amount of angular momentum. For the relativistic value λ= 1, the solution describes slowly rotating AdS type black holes. With a soft violation of the detailed balance condition and for λ= 1 , we also find such a generalization for the Schwarzschild type black hole solution of the theory. Fin…
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift an…
Campbell et al. demonstrated the existence of axion ``hair'' for Kerr black holes due to the non-trivial Lorentz Chern-Simons term and calculated it explicitly for the case of slow rotation. Here we consider the dilaton coupling to the axion field strength, consistent with low energy string theory and calculate the dilaton ``hair'' arising from this specific axion source.
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…
The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined,…
Employing the Quark Mass Denisity- and temperature- dependent model and the Hartle's method, We have studied the slowly rotating strange star with uniform angular velocity. The mass-radius relation, the moment of inertia and the frame dragging for different frequencies are given. We found that we cannot use the strange star to solve the challenges of Stella and Vietri for the horizontal branch oscillations and the moment of inertia $I_{45}/(M/M_ s)>2.3$. Furthermore, we extended the Hartle's method to study the differential rotating strange star and found that the differential rotation is an e…
We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented by all possible quadratic, algebraic curvature invariants coupled to a scalar field. The solution is found as a deformation of the Schwarzschild metric in General Relativity. We explicitly derive the changes to the orbital frequency at the innermost stable circular orbit and at the light ring in closed form. These results could be useful when comparing Gener…
We consider a further extension of our previous works in the treatment of the three-dimensional general relativistic Poynting-Robertson effect, which describes the motion of a test particle around a compact object as affected by the radiation field originating from a rigidly rotating and spherical emitting source, which produces a radiation pressure, opposite to the gravitational pull, and a radiation drag force, which removes energy and angular momentum from the test particle. The gravitational source is modeled as a non-spherical and slowly rotating compact object endowed with a mass quadrup…
We calculate the renormalized vacuum energy density for a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed very close to the surface of a rotating spherical gravitational source with mass $M$, radius $R$ and momentum angular $J$, at the equatorial region. We consider that the source rotates slowly and that the gravitational field is weak. Corrections to the Casimir energy density induced by the gravitational field generated by this source are calculated up to $M/R^2$ order. The obtained results show us that there is an important mod…
We obtain a slowly rotating black hole solution in the scalar-tensor theory of gravity with nonminimal derivative coupling to the Einstein tensor. Properties of the obtained solution have been examined carefully. We also investigate the thermodynamics of the given black hole. To obtain thermodynamic functions, namely its entropy we use the Wald procedure which is suitable for quite general diffeomorphism-invariant theories. The applied approach allowed us to obtain the expression for entropy and the first law of black hole thermodynamics. Having introduced thermodynamic pressure which is relat…
In this paper, we take the slowly rotating black three-brane background and perturb it by introducing a vector gauge field. We find the components of the gauge field through Maxwell equations and Bianchi identities. Using currents and some ansatz we find Fick's first law at long wavelength regime. An interesting result for this non-trivial supergravity background is that the diffusion constant on the stretched horizon which emerges from Fick's first law is a complex constant. The pure imaginary part of the diffusion constant appears because the black three-brane has angular momentum. By taking…
Coulomb Sectors and Scattering for Maxwell-Higgs Fields on Schwarzschild and Slowly Rotating Kerr Backgrounds
Theoretical Physics Laboratory, Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung（万隆理工学院数学与自然科学学院理论物理实验室、理论高能物理研究部）
We study black hole solutions at first order in the Hartle-Thorne slow-rotation approximation in Horndeski gravity theories. We derive the equations of motion including also cases where the scalar depends linearly on time. In the Hartle-Thorne formalism, all first-order rotational corrections are described by a single frame-dragging function. We show that the frame-dragging function is exactly the same as in general relativity for all known black hole solutions in shift symmetric Horndeski theories, with the exception of theories with a linear coupling to the Gauss-Bonnet invariant. Our result…
