In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.
We construct new axially symmetric solutions of SU(2) Yang-Mills theory in a four dimensional anti-de Sitter spacetime. Possessing nonvanishing nonabelian charges, these regular configurations have also a nonzero angular momentum. Numerical arguments are also presented for the existence of rotating solutions of Einstein-Yang-Mills equations in an asymptotically anti-de Sitter spacetime.
A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the …
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 construct a model of a rotating wormhole made by cutting and pasting two Kerr spacetimes. As a result, we obtain a rotating thin-shell wormhole with exotic matter at the throat. Two candidates for the exotic matter are considered: (i) a perfect fluid; (ii) an anisotropic fluid. We show that a perfect fluid is unable to support a rotating thin-shall wormhole. On the contrary, the anisotropic fluid with the negative energy density can be a source for such a geometry.
We use the $ζ$-function regularization method to evaluate the finite temperature 1-loop effective potential for $ϕ^4$ theory in the Godel spacetime. It is used to study the effects of temperature and curvature coupling on the cosmological phase transition in the rotational spacetime. From our results the critical temperature of symmetry restoration, which is a function of curvature coupling and magnitude of spacetime rotation, can be determined.
Well-known results demonstrate the uniqueness of extremal isolated horizons (equivalently near-horizon spacetimes) in (3+1)-dimensions. This paper briefly reviews some of these results and then explicitly constructs families of non-asymptotically flat, non-spherically symmetric spacetimes that nevertheless contain spherically symmetric extremal horizons that are isomorphic to those found in Reissner-Nordstrom spacetimes.
This is a short pedagogical introduction to the subject of Killing-Stackel and Killing-Yano tensors and their role in the integrability of various types of equations that are of physical interest in curved spacetime, the main application being higher dimensional rotating black holes with cosmological constant.
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…
General higher-dimensional rotating black hole spacetimes of any dimensions admit the Killing and Killing-Yano tensors, which generate the hidden symmetries just as in four-dimensional Kerr spacetime. We study these properties of the black holes using the formalism of supersymmetric mechanics of pseudo-classical spinning point particles. We present two nontrivial supercharges, corresponding to the Killing-Yano and conformal Killing-Yano tensors of the second rank. We demonstrate that an unusual extended Poisson-Dirac algebra of these supercharges results in two independent Killing tensors in s…
In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of ve…
We analyse vacuum decay in rotating BTZ black hole spacetimes with the thin wall approximation. Possible parameter regions for the vacuum decay are clarified. We find that the nucleation rate is dominated by the bounce solution with the static shell configuration. The nucleation rate of the static shell decreases with the mass of the initial black hole. For a larger/smaller value of the initial black hole, the nucleation rate can be smaller/larger than that of the Coleman De Luccia vacuum decay in the pure AdS spacetime. Through the vacuum decay, the black hole gains its mass and loses the hor…
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…
We show that the spacetime of the near-horizon limit of the extreme rotating d=5 black hole, which is maximally supersymmetric in N=2,d=5 supergravity for any value of the rotation parameter j in [-1,1], is locally isomorphic to a homogeneous non-symmetric spacetime corresponding to an element of the 1-parameter family of coset spaces SO(2,1)x SO(3)/SO(2)_j in which the subgroup SO(2)_j is a combination of the two SO(2) subgroups of SO(2,1) and SO(3).
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.
We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separabil…
We present covariant symmetry operators for the conformal wave equation in the (off-shell) Kerr-NUT-AdS spacetimes. These operators, that are constructed from the principal Killing-Yano tensor, its `symmetry descendants', and the curvature tensor, guarantee separability of the conformal wave equation in these spacetimes. We next discuss how these operators give rise to a full set of conformally invariant mutually commuting operators for the conformally rescaled spacetimes and underlie the $R$-separability of the conformal wave equation therein. Finally, by employing the WKB approximation we de…
The Brown-York quasi-local energy of a rotating black hole described by the Kerr metric and enclosed by a fixed-radius surface is calculated by direct computation. No special assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were placed. The arbitrary reference term has been set to zero. The result may be relevant for applications in astrophysics, for modeling elementary particles or for extensions of the framework of quasi-local quantities. An analytic expression in terms of incomplete elliptic integrals is given.
We demonstrate separability of conformally coupled scalar field equation in general (off-shell) Kerr-NUT-AdS spacetimes in all dimensions. The separability is intrinsically characterized by the existence of a complete set of mutually commuting conformal wave operators that can be constructed from a hidden symmetry of the principal Killing-Yano tensor. By token of conformal symmetry, the separability also works for any Weyl rescaled (off-shell) metrics. This is especially interesting in four dimensions where it guarantees separability of a conformally coupled scalar field in the general Plebans…
In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is…
We study the collision of two geodesic particles in the accelerating and rotating black hole spacetime and probe the effects of the acceleration of black hole on the center-of-mass energy of the colliding particles and on the high-velocity collision belts. We find that the dependence of the center-of-mass energy on the acceleration in the near event-horizon collision is different from that in the near acceleration-horizon case. Moreover, the presence of the acceleration changes the shape and position of the high-velocity collision belts. Our results show that the acceleration of black holes br…
We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Bañados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational…
Recently, two kinds of deformed schwarzschild spacetime have been proposed, which are the black-bounces metric (\cite{2019JCAP...02..042S,2021PhRvD.103h4052L}) and quantum deformed black hole (BH) (\cite{2021arXiv210202471B}). In present work, we investigate the rotating spacetime of these deformed Schwarzschild metric. They are exact solutions to the Einstein$'$s field equation. We analyzed the properties of these rotating spacetimes, such as event horizon (EH), stationary limit surface (SIS), structure of singularity ring, energy condition (EC), etc., and found that these rotating spacetime …
In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new five-dimensional metric describes a (rotating) black string. The geodesics in the Schwarzschild and Kerr spacetime have been studied in great detail, however, when a compact dimension is added new behaviour occurs. We present the analytical solutions of the geodesic equations and discuss the possible orbits. The motion in the ordinary four-dimensional Schwarzschild and…
Zero-Mass Rotating Spacetimes in Four-Dimensional Horava Gravity
Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）；Institute of Basic Science and College of AI Convergence, Inje University（基础科学研究院及庆熙大学AI融合学院）
A stationary observer in the Kerr spacetime has zero angular momentum if his/her angular velocity $ω$ has a particular value, which depends on the position of the observer. Worldlines of such zero angular momentum observers (ZAMOs) with the same value of the angular velocity $ω$ form a three dimensional surface, which has the property that the Killing vectors generating time translation and rotation are tangent to it. We call such a surface a rigidly rotating ZAMO surface. This definition allows a natural generalization to the surfaces inside the black hole, where ZAMO's trajectories formally …
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi-Civita connection. In extended teleparallel theories, for instance in $f(T)$ or scalar-torsion gravity, the connection must obey its antisymmetric field equations. So far only a few analytic solutions were known. In this note we solve the $f(T,ϕ)$ gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformat…
The effective action for QED in curved spacetime includes equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions admit the possibility of superluminal yet causal photon propagation in gravitational fields. In this paper, we extend our analysis of photon propagation in gravitational backgrounds to the Kerr spacetime describing a rotating black hole. The results support two general theorems -- a polarisation sum rule and a `horizon theorem'. The implications for the stationary limit surface bounding the ergosphere are also d…
We investigate the deflection of light by a rotating global monopole spacetime and a rotating Letelier spacetime in the weak deflection approximation. To this end, we apply the Gauss-Bonnet theorem to the corresponding osculating optical geometries and show that the deflection of light increases due to the presence of the global monopole parameter and the string cloud parameter, respectively. The results obtained for the deflection angle in the equatorial plane generalize known results for the corresponding non-rotating global monopole and Letelier spacetimes as well as the Kerr solution.
We present a spinning hairy black hole in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. The black hole is characterized by having a single horizon which encloses a curvature singularity and the scalar field is regular everywhere. The mass and angular momentum are shown to be finite. The presence of a scalar field with a slower fall-off at infinity leads an anti-de Sitter asymptotic behavior which differs from the one found by Brown and Henneaux, but has the same symmetry group as in pure gravity. A scalar soliton, which is a finite mass regula…
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in a perfect agreement with those of the recent numerical study where the full coupled partial differential e…
We propose the metric for general rotating spacetimes. These spacetimes are stationary, axially symmetric and spatially asymptotically flat. They can be the spacetimes outside of rotating black holes or rotating celestial bodies such as the Sun and the Earth. The metric functions are expanded in power series of distance and the angle variable is included in the expansion coefficients.
We consider generic axially symmetric rotating spacetimes and examine particle collisions in the ergoregion. The results are generic and agree with those obtained in the particular case of the rotating Teo wormhole in N. Tsukamoto and C. Bambi, Phys. Rev. D 91, 104040 (2015). It is shown that for sufficiently rapid rotation, the energy of a particle escaping to infinity can become arbitrary large (so-called super-Penrose process). Moreover, this energy is typically much larger than the center-of mass energy of colliding particles. In this sense the situation differs radically from that for col…
We show that under certain conditions an axisymmetric rotating spacetime contains a ring of points in the equatorial plane, where a particle at rest with respect to an asymptotic static observer remains at rest in a static orbit. We illustrate the emergence of such orbits for boson stars. Further examples are wormholes, hairy black holes and Kerr-Newman solutions.
We discuss various physical aspects of nonextremal, extremal and supersymmetric black holes in asymptotically anti-de Sitter (ADS) spacetimes. Specifically, we discuss how the isolated horizon (IH) framework leads to an ambiguity-free description of rotating black holes in these spacetimes. We then apply this framework to investigate the properties of supersymmetric isolated horizons (SIHs) in four-dimensional N = 2 gauged supergravity. Among other results we find that they are necessarily extremal, that rotating SIHs must have non-trivial electromagnetic fields, and that non-rotating SIHs nec…
We study gravitational perturbations sourced by a rotating test shell collapsing into five-dimensional Myers-Perry black holes in anti-de Sitter (AdS). Our attention is restricted to the case in which the two possible angular momenta of the geometry are set equal. In this situation the background is cohomogeneity-1, which amounts to a crucial technical simplification. It is found that the linearized Einstein equations are consistent only when the test shell is corotating with the spacetime. However, it is argued that this is a consequence of the matter on the shell being described by dust or, …
Motivated by the success of the recently proposed method of anomaly cancellation to derive Hawking fluxes from black hole horizons of spacetimes in various dimensions, we have further extended the covariant anomaly cancellation method shortly simplified by Banerjee and Kulkarni to explore the Hawking radiation of the (3+1)-dimensional charged rotating black strings and their higher dimensional extensions in anti-de Sitter spacetimes, whose horizons are not spherical but can be toroidal, cylindrical or planar, according to their global identifications. It should be emphasized that our analysis …
We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-ho…
The energy-momentum distribution of spatially homogeneous rotating spacetimes in the context of teleparallel theory of gravity is investigated. For this purpose, we use the teleparallel version of Moller prescription. It is found that the components of energy-momentum density are finite and well-defined but are different from General Relativity. However, the energy-momentum density components become the same in both theories under certain assumptions. We also analyse these quantities for some special solutions of the spatially homogeneous rotating spacetimes.
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schroedinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle …
We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing-Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong-Cvetic-Lu-Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.
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 the literature, the Newman-Janis algorithm (NJA) has been widely used to construct stationary and axisymmetric spacetimes to describe rotating black holes. In addition, it has been recently shown that the general stationary and axisymmetric spacetime generated through NJA allows the complete separability of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this spacetime is also separable if one of the metric functions is additively separable. In this work, we further study the conditions for a separable Klein-Gordon equation in such a general spacetime. The relations be…
We examine the separability properties of the equation of motion for a stationary string near a rotating charged black hole with two independent angular momenta in five-dimensional minimal gauged supergravity. It is known that the separability problem for the stationary string in a general stationary spacetime is reduced to that for the usual Hamilton-Jacobi equation for geodesics of its quotient space with one dimension fewer. Using this fact, we show that the "effective metric" of the quotient space does not allow the complete separability for the Hamilton-Jacobi equation, albeit such a sepa…
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Ker…
In this paper, with an appropriate combination of three Liouville-type dilaton potentials, we obtain the higher dimensional charged slowly rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime. The angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. It is shown that the dilaton field modifies the gyromagnetic ratio of the rotating dilaton black holes.
The behavior of a arbitrary coupled quantum scalar field is studied in the background of the Gödel spacetime. Closed forms are derived for the effective action and the vacuum expectation value of quadratic field fluctuations by using $ζ$-function regularization. Based on these results, we argue that causality violation presented in this spacetime can not be removed by quantum effects.
In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier-Stocks equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier-Stocks system.
In a (2+1)-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter (AdS) spacetime, respectively. By applying the first law of thermodynamics to the extremal shell one shows that its entropy is an arbitrary function of the gravitational area $A_+$ alone, $S=S(A_+)$. When the shell approaches its own gravitational radius $r_+$ and turns in…
In the interface between general relativity and relativistic quantum mechanics, we analyse rotating effects on the scalar field subject to a hard-wall confining potential. We consider three different scenarios of general relativity given by the cosmic string spacetime, the spacetime with space-like dislocation and the spacetime with a spiral dislocation. Then, by searching for a discrete spectrum of energy, we analyse analogues effects of the Aharonov-Bohm effect for bound states and the Sagnac effect.
In this paper, we construct the rotating Janis-Newman-Winicour (JNW) naked singularity spacetime using Newman-Janis Algorithm (NJA). We analyse NJA with and without complexification methods and find that the energy conditions do satisfied when we skip the complexification step. We study the shadows cast by rotating JNW naked singularity and compare them with the shadows cast by the Kerr black hole. We find that the shadow of the rotating naked singularity can be distinguished from the shadow of the Kerr black hole. While we analyse the precession of timelike bound orbits in rotating JNW spacet…
