arXiv subjects
Publications and source records attributed to Jutta Kunz.
We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalised Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion is defined locally, using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the $θ$-divisor. For a representation of the hyperelliptic functions the Klein--Weierstraß multivariable $σ$-function is introduced. It is shown that all parameters needed for the calculations like period matrices and abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and $θ$-constants. The cases of genus two, three and four are considered in detail. The method is exemplified by the particle motion associated with genus one elliptic and genus three hyperelliptic curves. Applications are for instance solutions to the geodesic equations in the space-times of static, spherically symmetric Hořava-Lifshitz black holes.
We analyze the physical properties of boson stars, which possess counterparts in flat space-time, Q-balls. Applying a stability analysis via catastrophe theory, we show that the families of rotating and non-rotating boson stars exhibit two stable regions, separated by an unstable region. Analogous to the case of white dwarfs and neutron stars, these two regions correspond to compact stars of lower and higher density. Moreover, the high density phase ends when the black hole limit is approached. Here another unstable phase is encountered, exhibiting the typical spiralling phenomenon close to the black hole limit. When the interaction terms in the scalar field potential become negligible, the properties of mini boson stars are recovered, which possess only a single stable phase.
We study the particle motion in the space-time of a Kehagias-Sfetsos (KS) black hole. This is a static spherically symmetric solution of a Horava-Lifshitz gravity model that reduces to General Relativity in the IR limit and deviates slightly from detailed balance. Taking the viewpoint that the model is essentially a (3+1)-dimensional modification of General Relativity we use the geodesic equation to determine the motion of massive and massless particles. We solve the geodesic equation exactly by using numerical techniques. We find that neither massless nor massive particles with non-vanishing angular momentum can reach the singularity at r=0. Next to bound and escape orbits that are also present in the Schwarzschild space-time we find that new types of orbits exist: manyworld bound orbits as well as two-world escape orbits. We also discuss observables such as the perihelion shift and the light deflection.
We consider black holes localized on the brane in the Randall-Sundrum infinite braneworld model. These configurations are static and charged with respect to a spherically symmetric, electric Maxwell field living on the brane. We start by attempting to construct vacuum black holes, in which case our conclusions are in agreement with those of Yoshino in JHEP 0901:068, 2009 (arXiv:0812.0465). Although approximate solutions appear to exist for sufficiently small brane tension, these are likely only numerical artifacts. The qualitative features of the configurations in the presence of a brane U(1) electric field are similar to those in the vacuum case. In particular, we find a systematic unnatural behaviour of the metric functions in the asymptotic region in the vicinity of the AdS horizon. Our results are most naturally interpreted as evidence for the nonexistence of static, nonextremal charged black holes on the brane. In contrast, extremal black holes are more likely to exist on the brane. We determine their near-horizon form by employing both analytical and numerical methods. For any bulk dimension d>4, we find good agreement between the properties of large extremal black holes and the predictions of general relativity, with calculable subleading corrections.
We construct generalizations of the Kerr black holes by including higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EBGd) black holes is bounded by the Kerr black holes, the critical EGBd black holes, and the singular extremal EGBd solutions. The angular momentum of the EGBd black holes can exceed the Kerr bound. The EGBd black holes satisfy a generalised Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.
We present balanced black ring solutions of pure Einstein-Maxwell theory in five dimensions. The solutions are asymptotically flat, and their tension and gravitational self-attraction are balanced by the repulsion due to rotation and electrical charge. Hence the solutions are free of conical singularities and possess a regular horizon which exhibits the topology S1 x S2 of a torus. We discuss the global charges and the horizon properties of the solutions and show that they satisfy a Smarr relation. We construct these black rings numerically, restricting to the case of black rings with a rotation in the direction of the S1.
In recent years higher-dimensional black holes have attracted much interest because of various developments in gravity and high energy physics. But whereas higher-dimensional charged static (Tangherlini) and uncharged rotating (Myers-Perry) black holes were found long ago, black hole solutions of Einstein-Maxwell theory, are not yet known in closed form in more than 4 dimensions, when both electric charge and rotation are present. Here we therefore study these solutions and those of Einstein-Maxwell-dilaton theory, by using numerical and perturbative methods, and by exploiting the existence of spacetime symmetries. The properties of these black holes reveal new interesting features, not seen in D=4. For instance, unlike the D=4 Kerr-Newman solution, they possess a non-constant gyromagnetic factor.
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the $θ$--divisor. For a representation of the hyperelliptic functions the Klein--Weierstraß multivariable sigma function is introduced. It is shown that all parameters needed for the calculations like period matrices and Abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and theta-constants. The cases of genus two and three are considered in detail. The method is exemplified by particle motion associated with a genus three hyperelliptic curve.
We present numerical evidence for the existence of several types of static black hole solutions with a nonspherical event horizon topology in $d\geq 6$ spacetime dimensions. These asymptotically flat configurations are found for a specific metric ansatz and can be viewed as higher dimensional counterparts of the $d=5$ static black rings, dirings and black Saturn. Similar to that case, they are supported against collapse by conical singularities. The issue of rotating generalizations of these solutions is also considered.
We perform a systematic study of stationary sphaleron-antisphaleron systems of Weinberg-Salam theory at the physical value of the weak mixing angle. These systems include rotating sphaleron-antisphaleron pairs, chains and vortex rings. We show that the angular momentum of these solutions is proportional to their electric charge. We study the dependence of their energy and magnetic moment on their angular momentum. We also investigate the influence of their angular momentum on their local properties, in particular on their energy density and on the node structure of their Higgs field configuration. Furthermore, we discuss the equilibrium condition for these solutions.
We construct rotating black hole solutions in Einstein-Gauss-Bonnet theory in five spacetime dimensions. These black holes are asymptotically flat, and possess a regular horizon of spherical topology and two equal-magnitude angular momenta associated with two distinct planes of rotation. The action and global charges of the solutions are obtained by using the quasilocal formalism with boundary counterterms generalized for the case of Einstein-Gauss-Bonnet theory. We discuss the general properties of these black holes and study their dependence on the Gauss-Bonnet coupling constant $α$. We argue that most of the properties of the configurations are not affected by the higher derivative terms. For fixed $α$ the set of black hole solutions terminates at an extremal black hole with a regular horizon, where the Hawking temperature vanishes and the angular momenta attain their extremal values. The domain of existence of regular black hole solutions is studied. The near horizon geometry of the extremal solutions is determined by employing the entropy function formalism.
The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic Kleinian sigma functions restricted to the one-dimensional theta-divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.
We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sixtic potential the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.
Employing higher order perturbation theory, we find a new class of charged rotating black hole solutions of Einstein-Maxwell-dilaton theory with general dilaton coupling constant. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter, and focus on extremal black holes with equal-magnitude angular momenta in odd dimensions. We perform the perturbations up to 4th order for black holes in 5 dimensions and up to 3rd order in higher odd dimensions. We calculate the physical properties of these black holes and study their dependence on the charge and the dilaton coupling constant.
We consider boson shells in scalar electrodynamics coupled to Einstein gravity. The interior of the shells can be empty space, or harbour a black hole or a naked singularity. We analyze the properties of these types of solutions and determine their domains of existence. We investigate the energy conditions and present mass formulae for the composite black hole--boson shell systems. We demonstrate that these types of solutions violate black hole uniqueness.
We construct new static, asymptotically AdS solutions where the conformal infinity is the product of Minkowski spacetime $M_n$ and a sphere $S^m$. Both globally regular, soliton-type solutions and black hole solutions are considered. The black holes can be viewed as natural AdS generalizations of the Schwarzschild black branes in Kaluza-Klein theory. The solitons provide new brane-world models with compact extra-dimensions. Different from the Randall-Sundrum single-brane scenario, a Schwarzschild black hole on the Ricci flat part of these branes does not lead to a naked singularity in the bulk.
We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with the Reissner-Nordström space-time.