arXiv subjects

Saskia Grunau

Publications and source records attributed to Saskia Grunau.

18 recordsLinked to original sources

arXiv2022

Hyperelliptic functions and motion in general relativity

Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with set a of examples of genus $g=2$.

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arXiv2021

Topological black holes in mimetic gravity

We construct some new classes of topological black hole solutions in the context of mimetic gravity. We study the uncharged and charged black holes, separately. In the absence of a potential for the mimetic field, our solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking any kind of particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modification of the Schwarzschild spacetime. We also investigate the casual structure and physical properties of the solutions. The presence of the mimetic field changes the asymptotic behaviour of the spacetime. We observe that in the absence of a potential, our solutions are not asymptotically flat, while, in the presence of a negative constant potential for the mimetic field, the asymptotic behaviour of the solutions can be anti de-Sitter (AdS). Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in Einstein gravity and in mimentic gravity. In contrast to Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimentic gravity. Furthermore, we find stable bound orbits for massless particles.

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arXiv2020

The ISCO of charged particles in Reissner-Nordström, Kerr-Newman and Kerr-Sen spacetime

In this article we study the innermost stable circular orbit (ISCO) of electrically charged particles in the electrically charged Reissner-Nordström spacetime, the Kerr-Newman spacetime and the Kerr-Sen spacetime. We find that the radius of the ISCO increases with an increasing particle-black hole charge product $|qQ|$ in the case of attractive Coulomb interaction $qQ<0$. For repulsive Coulomb interaction, the ISCO radius first decreases to a minimum and then increases again, until it diverges as the charge product approaches one. If the charge $Q$ of the black hole is very small, the minimum of the ISCO radius lies at $qQ=0$. Repulsive and attractive Coulomb interactions will always increase the ISCO radius in this limit. Stable bound orbits of charged particles cease to exist in the Reissner-Nordström and Kerr-Newman spacetime for $qQ\geq 1$. In the Kerr-Sen spacetime the limiting case depends on the charge of the black hole and if dilaton coupling is applied to the test particle. We find $qQ\geq 1+Q^2$ without dilaton-coupling and $qQ\geq 1+\frac{3}{2}Q^2$ with dilaton coupling $α=1$.

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arXiv2020

Geodesic motion around a supersymmetric AdS5 black hole

In this article the geodesic motion of test particles in the spacetime of a supersymmetric AdS$_5$ black hole is studied. The equations of motion are derived and solved in terms of the Weierstrass $\wp$, $σ$ and $ζ$ functions. Effective potentials and parametric diagrams are used to analyze and characterize timelike, lightlike and spacelike particle motion and a list of possible orbit types is given. Furthermore, various plots of orbits are presented.

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arXiv2020

Motion of charged particles around a scalarized black hole in Kaluza-Klein theory

In this article we study the geodesic motion of charged particles in the spacetime of an extremal rotating dyonic black hole in Kaluza-Klein theory. We derive the equations of motion and present their analytical solutions in terns of elliptic and hyperelliptic functions. Furthermore, we analyze the geodesic motions with the help of parametric diagrams and effective potentials.

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arXiv2018

Geodesic motion around traversable wormholes supported by a massless conformally-coupled scalar field

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the JNWW spacetime. We study the geodesic motion of time-, light- and space-like particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß\ functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for time-like geodesics only in one of the two worlds. Moreover, under no conditions there exist time-like two world bound orbits.

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arXiv2018

Geodesic motion in the five-dimensional Myers-Perry-AdS spacetime

In this article we study the geodesic motion of test particles and light in the five-dimensional Myers-Perry-anti de Sitter spacetime. We derive the equations of motion and present their solutions in terms of the Weierstraß $\wp$-, $σ$- and $ζ$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types for timelike, null and spacelike geodesics. We plot examples of the orbits and take a look at the photon region in five dimensions. Furthermore we study spacelike geodesics and their relation to the AdS/CFT correspondence.

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arXiv2016

Analytic treatment of complete geodesics in a static cylindrically symmetric conformal spacetime

We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass {\wp} function and the Kleinian σ function. Using parametric diagrams and effective potentials we analyze the possible orbits and characterize them in terms of the energy and the angular momentum of the test particles. Finally we show some examples of orbits.

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arXiv2016

Geodesic motion in the spacetime of a static charged black hole in $f(R)$ gravity

In the present paper we study the geodesic motion of test particles and light rays in the spacetime of a static charged black hole in $f(R)$ gravity. The complete set of analytic solutions of the geodesic equations in the spacetime of this black hole are presented. The geodesic equations are solved in terms of Weierstrass elliptic $\wp$ function and derivatives of Kleinian $σ$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types. The different types of the resulting orbits are characterized in terms of the conserved energy, angular momentum, charge and cosmological constant.

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arXiv2016

Detailed study of geodesics in the Kerr-Newman-(A)dS spactime and the rotating charged black hole spacetime in $f(R)$ gravity

We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\wp$, $ζ$ and $σ$ functions as well as the Kleinian $σ$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of $f(R)$ gravity with a constant curvature scalar.

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arXiv2016

Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes

In this article we derive the geodesic equations in the $\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $σ$-function and in special cases in terms of the Weierstraß $\wp$-, $σ$- and $ζ$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.

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arXiv2015

Analytic solutions of the geodesic equation for Einstein-Maxwell-dilaton-axion black holes

In this article we study the geodesic motion of test particles and light in the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstraß $\wp$-, $σ$- and $ζ$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types.

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arXiv2015

Thermodynamics of a rotating black hole in minimal five-dimensional gauged supergravity

In this article we study the thermodynamics of a general non-extremal rotating black hole in minimal five-dimensional gauged supergravity. We analyse the entropy-temperature diagram and the free energy. Additionally we consider the thermodynamic stability by calculating the specific heat, the isothermal moment of inertia tensor and the adiabatic compressibility.

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arXiv2014

Charged dilatonic black rings and black saturns and their thermodynamics

In this article charged black rings and black saturns are constructed in Einstein-Maxwell-dilaton theory in five dimensions. The neutral black ring and black saturn solutions are embedded in six dimensions and boosted with respect to the time coordinate and the added sixth dimension. Then the charged solutions are obtained by a Kaluza-Klein reduction. The influence of the charge is studied by analysing the physical properties and the phase diagram. The different dilatonic solutions are compared and their thermodynamic stability is considered.

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arXiv2013

Geodesic motion in the (rotating) black string 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 Kerr spacetime is compared to the motion in the (rotating) black string spacetime.

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arXiv2012

Geodesic Motion in the Singly Spinning Black Ring Spacetime

We present analytical solutions of the geodesic equations of test particles and light in the five dimensional singly spinning black ring spacetime for special cases, since it does not appear possible to separate the Hamilton-Jacobi-equation for singly spinning black rings in general. Based on the study of the polynomials in the equations of motion we characterize the motion of test particles and light and discuss the associated orbits.

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arXiv2012

Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime

In this article we analyze the geodesics of test particles and light in the five dimensional (charged) doubly spinning black ring spacetime. Apparently it is not possible to separate the Hamilton-Jacobi-equation for (charged) doubly spinning black rings in general, so we concentrate on special cases: null geodesics in the ergosphere and geodesics on the two rotational axes of the (charged) doubly spinning black ring. We present analytical solutions to the geodesic equations for these special cases. Using effective potential techniques we study the motion of test particles and light and discuss the corresponding orbits.

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arXiv2010

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordström space-time in terms of the Weierstraß $\wp$, $σ$ and $ζ$ elliptic functions. Based on the study of the polynomials in the $\vartheta$ and $r$ equations we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordström space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordström space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

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