arXiv subjects

Betti Hartmann

Publications and source records attributed to Betti Hartmann.

At least 19 recordsLinked to original sources

arXiv2026

Circular orbits and particle collisions close to charged black holes surrounded by scalar clouds

We study the motion of massive (un)charged test particles in space-times of electric and dyonic black holes which carry scalar hair. We determine the stable and unstable circular orbits and discuss the collision of massive test particles. In particular, we aim at demonstrating how the presence of the scalar hair of the black hole changes the circular orbits and particle collisions, respectively, as compared to the Reissner-Nordstr\"om (RN) space-time. We find that in the presence of scalar hair, up to four circular orbits (two unstable and two stable) as well as static orbits with $L=0$ can exist. Particle collisions can generate infinite center-of-mass energy when at least one of the particles is charged, very similar to the RN case. We find, however, that the value of the charge at which this divergence happens depends on the value of the scalar field on the horizon.

gr-qc↗

arXiv2025

Photon rings and shadows of Kerr black holes immersed in a swirling universe

We discuss photon rings around as well as shadows of Kerr black holes immersed in a swirling spacetime (KBHSU). We find that the spin-spin interaction between the angular momentum of the black hole and the swirling of the background leads to new interesting effects as it breaks the symmetry between the upper and lower hemispheres. We find that a pair of light rings exists for all values of the parameter space. Using a topological argument, we prove that there should be, indeed, two light rings and that, additionally, these light rings are unstable. In comparison to the Schwarzschild black hole immersed in a swirling universe, the light rings typically all possess different radii. Interestingly, as the value of the swirling parameter is increased at fixed angular momentum of the black hole the two disconnected patches of the ergoregions eventually merge. The light ring at this merger possesses no angular velocity (as measured by an observer at infinity) and is called a \textit{light point}. To our knowledge, this is the first time the existence of such a light point in a black hole space-time is reported. Finally, we also present the shadows of KBHSU for various parameter values and observe that, due to the presence of the swirling background, the shadows are twisted.

gr-qc↗

arXiv2025

Frozen states of charged boson stars

In this paper, we study frozen states of charged boson stars. These solutions are globally regular and exist in a U(1) gauged scalar field model minimally coupled to gravity for suitable choices of the coupling constants. These configurations are field theoretical realizations of the Mazur-Mottola solution with a de Sitter interior, a black hole exterior and a thin shell that interpolates between the two and replaces the event horizon. We demonstrate that standard electrodynamics is sufficient to find these frozen states, but that the self-interaction of the scalar field is crucial. Adding Horndeski vector-tensor gravity to the model allows the frozen states to exist without self-interaction though. The frozen states possess one stable and one unstable lightring, the former inside the thin shell, the latter in the black hole exterior.

gr-qc↗

arXiv2025

Hairy charged black holes in a model with bounded scalar field potential

Electrically and magnetically charged (a.k.a. dyonic) black holes with scalar hair have recently been constructed for a sextic scalar field potential. Here, we re-investigate this model, but with a bounded scalar field potential of exponential form. We demonstrate that qualitative differences appear. First, we present scalar clouds on (dyonic) Reissner-Nordstr\"om black holes as well as (dyonically) charged clouds on Schwarzschild black holes, respectively. We then extend our results to the fully backreacted case and put the focus on the comparison of the electrically charged black holes with their dyonic counterparts.

gr-qc↗

arXiv2024

Boson stars and black holes with (complex and) real scalar hair

We discuss boson stars and black holes with scalar hair in a model where the complex scalar field forming the boson star and the hair on the black hole, respectively, interacts with a real scalar field via a H\'enon-Heiles-type potential. We demonstrate that black holes and boson stars carrying only a real scalar field with cubic self-interaction are possible and that black holes with both real and complex scalar field branch off from these solutions for sufficiently large interaction between the two fields and/or sufficiently large horizon radius $r_h$. The latter possess lower mass for the same choice of coupling constants than the former, however seem to be thermodynamically preferred only for high enough temperature.

gr-qc↗

arXiv2024

Born-Infeld stars and charged black holes surrounded by scalar clouds

We discuss the formation of scalar clouds on charged, spherically symmetric and static stars and black holes. We first discuss Reissner-Nordstr\"om black holes with electric and magnetic charge and present new results demonstrating the existence of a second branch of solutions. Moreover, we find that the presence of the magnetic charge allows for smaller mass and Noether charge when the clouds are close to their minimal possible mean radius. Replacing standard electrodynamics by Born-Infeld (BI) electrodynamics, the background model possesses globally regular, star-like as well as black hole solutions. We show that the former can be scalarized as well and that the scalar clouds become more compact when decreasing the electric charge of the BI star. Finally, we discuss a magnetic dipole field in the background of the scalarized BI star and show that the strong gravitational field of this star leads to a significant change.

gr-qc↗

arXiv2024

Motion of charged particles in an electromagnetic swirling universe: The complete set of solutions

We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth constant of motion. The equations of motion can be analytically integrated. The solutions are presented in terms of elementary and elliptic functions. In addition, we discuss the possible orbits for both uncharged particles (in which case the motion is geodesic) and charged particles, respectively. A typical orbit is bounded in the radial direction and escapes to infinity in the $z-$ direction. However, the presence of the electromagnetic fields also leads to the existence of planar orbits.

gr-qc↗

arXiv2024

Azimuthal geodesics in closed FLRW cosmological models

We study geodesics in Friedmann-Lema{\^\i}tre-Robertson-Walker (FLRW) cosmological models and give the full set of solutions. For azimuthal geodesics, in a closed universe, we give the angular distance travelled by a test particle moving along such a geodesic during one cycle of expansion and re-collapse of the universe. We extend previous results regarding the path followed by light rays to the two-fluid case, also including a cosmological constant, as well as to massive test particles. Our work contains various new results and explicit formulae, often using special functions which naturally appear in this setting.

gr-qc↗

arXiv2024

Azimuthal geodesics in closed FLRW cosmologies

Modern cosmology is closely linked to our understanding of radial null geodesics as these model the propagation of light signals through an expanding universe. Azimuthal geodesics, on the other hand, are perhaps best known for their relevance within closed cosmological models. Such models typically have a finite lifetime: the universe expands up to a maximum size after which it recollapses during the so-called big crunch. An azimuthal geodesic starting at the beginning of the universe will travel a finite angular distance during the expansion and recollapse. It is well-known that this angle is $2\pi$ for a matter-dominated universe and $\pi$ for a radiation-dominated solution. Here we derive the simple formula $$\Delta \varphi = \frac{2\pi}{1+3w}$$ for an arbitrary linear equation of state parameter $w$. To the best of our knowledge this result has not been reported elsewhere and fills a small gap in the literature.

gr-qc↗

arXiv2023

Geodesic Motion in a Swirling Universe: The complete set of solutions

We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions to the geodesic equations can be given in terms of elementary and elliptic functions. We also consider a space-time describing a static black hole immersed in a swirling universe. In this case, full separation of variables is not possible and the geodesic equations have to be solved numerically.

gr-qc↗

arXiv2023

Note on super-critical charged boson stars

We study the transition of charged boson stars from sub- to super-criticality. This transition is defined as that choice of coupling constants for which the Coulomb repulsion of two individual bosons (that make up the star) exactly cancels their gravitational attraction. It was recently shown that without self-interaction super-critical boson stars are unstable to decay into their individual constituents. Here we show that this is no longer true for the self-interacting case and that boson stars can possess spatial oscillations in the scalar field. We also discuss the corresponding black hole solutions that carry charged scalar hair.

gr-qc↗

arXiv2023

Charged and rotating boson stars in 5-dimensional Einstein-Maxwell(-Chern-Simons) theory

We study charged and rotating boson stars in 5-dimensional Einstein-Maxwell(-Chern-Simons) theory assuming the two angular momenta associated to the two orthogonal planes of rotation to be equal. Next to the angular momenta, the boson stars carry electric charge and magnetic moment. Interestingly, we find new branches of Einstein-Maxwell-Chern-Simons solutions for which the spatial part of the gauge potential possesses nodes. Consequently, the magnetic moment and the gyromagnetic ratio have opposite sign as compared to the solutions on the main branch. For sufficiently large energy density we find that the solutions possess ergoregions.

gr-qc↗

arXiv2021

Boson stars and black holes with wavy scalar hair

In this paper, we follow up on the discovery of a new type of solution in the Einstein-Maxwell system coupled minimally to a self-interacting complex scalar field. For sufficiently large gravitational coupling and sufficiently small electromagnetic coupling we demonstrate that boson stars as well as black holes can carry scalar hair that shows a distinct new feature~: a number of spatial oscillations in the scalar field away from the core or horizon, respectively. These spatial oscillations appear also in the curvature invariants and hence should be a detectable feature of the space-time. As a first hint that this is true, we show that the effective potential for null geodesics in this space-time possesses a local minimum indicating that in the spatial region where oscillations occur a new stable photon sphere should be possible. We also study the interior of the black holes with scalar hair and show that the curvature singularity appears at a finite value of the radius and that black holes with wavy scalar hair have this singularity very close to the center.

gr-qc↗

arXiv2021

(Un)balanced holographic superconductors with electric and spin motive force coupling

We study holographic phase transitions in (2+1) dimensions that possess interacting phases which result from a direct coupling between the two U(1) gauge fields. This can be interpreted as a non-minimal interaction between the electric and spin motive forces of the dual model. We first present a new analytical solution of the Einstein-Maxwell equations that describes a black hole with charge non-equivalent to the sum of the asymptotic charges of the two U(1) gauge fields and briefly discuss formation of uncharged scalar hair on this solution. We then study the formation of charged scalar hair on an uncharged black hole background and discuss the dual description of balanced as well as unbalanced superconductors.

hep-th↗

arXiv2021

Spontaneous scalarization of self-gravitating magnetic fields

In this paper, we study the spontaneous scalarization of an extended, self-gravitating system which is static, cylindrically symmetric and possesses electromagnetic fields. We demonstrate that a real massive scalar field condenses on this Melvin magnetic universe solution when introducing a non-minimal coupling between the scalar field and (a) the magnetic field and (b) the curvature of the space-time, respectively. We find that in both cases, the solutions exist on a finite interval of the coupling constant and that solutions with a number of nodes $k$ in the scalar field exist. For case (a) we observe that the intervals of existence are mutually exclusive for different $k$.

gr-qc↗

arXiv2021

Spontaneously vectorized Einstein-Gauss-Bonnet black holes

We construct spontaneously vectorized black holes where a real vector field is coupled to the Gauss-Bonnet invariant. We employ three coupling functions for the vector field, and determine the respective domains of existence of the vectorized black holes. These domains of existence are bounded by the marginally stable Schwarzschild black holes and the critical vectorized black holes. We also address the effects of a mass term. For a given black hole mass the horizon radius is smaller for the vectorized black holes than for the Schwarzschild black holes. Since the vector field vanishes at the horizon, there is no contribution from the Gauss-Bonnet term to the entropy of the vectorized black holes.

gr-qc↗

arXiv2020

Calculation of multipole moments of axistationary electrovacuum spacetimes

The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more efficient calculation of the multipole moments, applying methods introduced by B\"ackdahl and Herberthson. For the non-vacuum electromagnetic case, our results for the octupole and higher moments differ from the results already published in the literature. The reason for this difference is that we correct an earlier unnoticed mistake in the power series solution of the Ernst equations. We also apply the presented method to directly calculate the multipole moments of a 5-parameter charged magnetized generalization of the Kerr and Tomimatsu-Sato exact solutions.

gr-qc↗

arXiv2020

Strong gravity effects of charged Q-clouds and inflating black holes

In this paper, we re-examine charged Q-clouds around spherically symmetric, static black holes. In particular, we demonstrate that for fixed coupling constants two different branches of charged scalar clouds exist around Schwarzschild black holes. This had not been noticed previously. We find that the new solutions possess a "hard wall" at maximal possible gauge coupling. This wall separates the interior (containing the black hole horizon), in which the scalar field is trapped in the "false vacuum", from the "true vacuum" exterior. When taking back-reaction onto the space-time into account, we find that at maximal possible back reaction, the black hole solutions corresponding to these two branches either become extremal black holes with diverging scalar field derivative on the horizon or inflating black holes with a second, "cosmological" horizon which - outside this second horizon - correspond to extremal Reissner-Nordstr\"om black holes.

gr-qc↗