Kerr–Schild metrics and gravitational radiation

We describe conditions assuring that the Kerr–Schild type solutions of Einstein's equations with pure radiation fields are asymptotically flat at future null infinity. Such metrics cannot describe “true” gravitational radiation from bounded sources—it is shown that the Bondi news function vanishes identically. We obtain formulae for the total energy and angular momentum at ℐ. As an example we consider a non-stationary generalization of the Kerr metric given by Vaidya and Patel. Angular momentum and total energy are expressed in closed form as functions of retarded time.     

Electromagnetic waves in the Kerr–Schild metric

A short electromagnetic wavelength approximation is used to obtain general solutions to the Maxwell equations for electromagnetic radiation in a Kerr–Schild plane gravitational wave metric. Their properties are then investigated for the specific case of a light beam in a weak, harmonic gravitational wave.     

Kerr–Schild metric in topological massive (2+1) gravity

In the framework of the (2+1)-dimensional topologically massive theory of gravity put forward by Deser, Jackiw, and Templeton, we analyze the (2+1) Kerr–Schild metric, in order to search for exact solutions, and to obtain plane-fronted wave solutions, which in the standard (2+1) Einstein theory (whose dynamics is provided by a cosmological constant term) do not exist.     

Spectroscopy of a Kerr–Newman–Kasuya Black Hole

Majhi and Vagenas’s work showed that the entropy spectrum of a spherically symmetric black hole can be obtained without quasinormal modes. In this paper, we extend this work to a Kerr–Newman–Kasuya black hole and discuss its spectra of entropy and area. We find that the spectra are equally spaced and are independent on the parameters of black hole.     

Families of Quintic Calabi–Yau 3–Folds with Discrete Symmetries

At special loci in their moduli spaces, Calabi–Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi–Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez–Villegas, we find a calculationally tractable means of finding the Picard–Fuchs equations satisfied by the periods of all 3–forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self–contained.     

Nongeneric SUSY in Spinning NUT–Kerr–Newman Space–Time

The supersymmetric extension of theNUT–Kerr–Newman (NUT–KN)space–time is investigated. Along with fourstandard supersymmetries, this type of space–timeadmits fermionic symmetry generated by the square root of the bosonic constant of motion exceptthe Hamiltonian. Such a new supersymmetry corresponds tothe Killing–Yano tensor, which plays an importantrole in solving various field equations in thisspace–time.     

Painleve Analysis and Symmetries of the Hirota–Satsuma Equation

Abstract

The singular manifold expansion of Weiss, Tabor and Carnevale [1] has been successfully applied to integrable ordinary and partial differential equations. They yield information such as Lax pairs, Bäcklund transformations, symmetries, recursion operators, pole dynamics, and special solutions. On the other hand, several recent developments have made the application of group theory to the solution of the differential equations more powerful then ever. More recently, Gibbon et. al. [2] revealed interrelations between the Painlevè property and Hirota’s bilinear method. And W. Strampp [3] hase shown that symmetries and recursion operators for an integrable nonlinear partial differential equation can be obtained from the Painlevè expansion. In this paper, it has been shown that the Hirota–Satsuma equation passes the Painlevé test given by Weiss et al. for nonlinear partial differential equations. Furthermore, the data obtained by the truncation technique is used to obtain the symmetries, recursion operators, some analytical solutions of the Hirota–Satsuma equation.     

Kerr–Newman Solution as a Dirac Particle

For m ² < a ² + q ², with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr–Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4 rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.     

Entropy of the Kerr–Sen black hole

We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.     

Generalized Kerr–NUT–de Sitter metrics in all dimensions

We classify all spacetimes with a closed rank-2 conformal Killing–Yano tensor. They give a generalization of Kerr–NUT–de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness conditions of the Einstein metrics over compact Riemannian manifolds.     

Hawking radiation of Kerr–Newman–de Sitter black hole

We extend the classical Damour–Ruffini method and discuss Hawking radiation in Kerr–Newman–de Sitter (KNdS) black hole. Under the condition that the total energy, angular momentum and charge of spacetime are conserved, taking the reaction of the radiation of the particle to the spacetime and the relation between the black hole event horizon and the cosmological horizon into consideration, we derive the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal one. It is related to the change of the Bekenstein–Hawking entropy corresponding the black hole event horizon and the cosmological horizon. It is consistent with the underlying unitary theory.     

Area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes from quasinormal modes

The area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes are investigated from quasinormal modes via Maggiore’s physical interpretation of quasinormal modes. Using the first law of black hole thermodynamics and the action variable quantization, we arrive at consistent equally spaced area and entropy spectra. Results show that the spectra are irrelevant to the parameters of the black holes and the perturbation fields, which fully agree with Bekensteins original conjecture. In the calculations, we have defined the corresponding Hawking temperatures of the black holes following the suggestion of Mäkelä et al. to avoid the zero temperature and to guarantee the (nearly-) extreme black holes quantizable.     

On hidden symmetries of extremal Kerr–NUT–AdS–dS black holes

It is well known that the Kerr–NUT–AdS–dS black hole admits two linearly independent Killing vectors and possesses a hidden symmetry generated by a rank-2 Killing tensor. The near-horizon geometry of an extremal Kerr–NUT–AdS–dS black hole admits four linearly independent Killing vectors, and we show how the hidden symmetry of the black hole itself is carried over by means of a modified Killing–Yano potential which is given explicitly. We demonstrate that the corresponding Killing tensor of the near-horizon geometry is reducible as it can be expressed in terms of the Casimir operators formed by the four Killing vectors.     

Universal properties of distorted Kerr–Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein–Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr–Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.     

Non-Existence of Multiple-Black-Hole Solutions Close to Kerr–Newman

We show that a stationary asymptotically flat electro-vacuum solution of Einstein’s equations that is everywhere locally “almost isometric” to a Kerr–Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular this implies that the assumption of a single event horizon in Alexakis–Ionescu–Klainerman’s proof of perturbative uniqueness of Kerr black holes is in fact unnecessary.     

Charged fermions tunnelling from Kerr–Newman black holes

We consider the tunnelling of charged spin 1/2 fermions from a Kerr–Newman black hole and demonstrate that the expected Hawking temperature is recovered. We discuss certain technical subtleties related to the obtention of this result.     

Photon emission of extremal Kerr–Newman black holes

In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr–Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained.     

Bosonized Supersymmetric Sawada–Kotera Equations: Symmetries and Exact Solutions

The Bosonized Supersymmetric Sawada–Kotera(BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.