## About

68

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Introduction

Eva Hackmann leads a research group on gravitational theory at the Center of Applied Space Technology and Microgravity at Bremen University. She is interested in classical general relativity, accretion disks, clock effects in relativity, and relativistic geodesy.
Find more information on her personal homepage
(evahackmann.org)
and on the homepage of her research group
(https://www.zarm.uni-bremen.de/en/research/space-science/gravitational-theory.html)

Additional affiliations

April 2018 - September 2018

April 2016 - September 2016

January 2014 - present

## Publications

Publications (68)

We study the conditions for stability of electrically charged, nonconductive perfect fluid tori with respect to linear perturbations. To this end, we employ Lagrangian perturbation formalism, and we assume a system where the fluid orbits a central body. Gravitational field of the latter is described in the Newtonian framework. We first formulate th...

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parametrized explicitly by constants of motion—the energy, the angular momentum, and the Carter constant—and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial a...

Lunar Laser Ranging (LLR) measures the distance between observatories on Earth and retro-reflectors on the Moon since 1969. In this Letter, we study the possible violation of the equivalence of passive and active gravitational mass (ma/mp), for aluminum (Al) and iron (Fe), using LLR data. Our new limit of 3.9×10−14 is about 100 times better than th...

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their r...

LLR measures the distance between observatories on Earth and retro-reflectors on Moon since 1969. In this paper, we study the possible violation of the equality of passive and active gravitational mass (m_a/m_p), for Aluminium (Al) and Iron (Fe), using LLR data. Our new limit of 3.9x10^-14 is about 100 times better than that of Bartlett and Van Bur...

The main goal of this paper is to investigate one of the important astrophysical systems, namely Thick accretion disks, in the background of the spherically symmetric solution in Born-Infeld teleparallel gravity to examine observable predictions of the theory in the vicinity of black holes. Thus, the properties of the non-self-gravitating equilibri...

The main goal of this paper is to investigate one of the important astrophysical systems, namely Thick accretion disks, in the background of the spherically symmetric solution in Born-Infeld teleparallel gravity to examine observable predictions of the theory in the vicinity of black holes. Thus, the properties of the non-self-gravitating equilibri...

Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the center of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity and alternative modified gravity theories. An important relativistic effect which has to be taken into account in the timing...

Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the center of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity and alternative modified gravity theories. An important relativistic effect which has to be taken into account in the timing...

It has been shown by Bañados, Silk and West (BSW) that the center of mass energy (Ecm) of test particles starting from rest at infinity and colliding near the horizon of a Schwarzschild black hole is always finite. In this short note, we extent the BSW scenario and study two particles with different energies colliding near the horizon of a static s...

We construct the relativistic standard steady, optically thick, cold and geometrically thin accretion disk around a distorted Schwarzschild black hole. The distortion of this static and axially symmetric black hole solution, is connected to an external distribution of matter. If the effects due to the rotation are negligible, this distribution can...

We study the collision of two massive particles with nonzero intrinsic spin moving in the equatorial plane in the background of a Schwarzschild black hole surrounded by quintessential matter field (SBHQ). For the quintessential matter equation of state (EOS) parameter, we assume three different values. It is shown that for collisions outside the ev...

We study the collision of two massive particles with non-zero intrinsic spin moving in the equatorial plane in the background of a Schwarzschild black hole surrounded by quintessential matter field (SBHQ). For the quintessential matter equation of state (EOS) parameter, we assume three different values. It is shown that for collisions outside the e...

It has been shown by Ba\~{n}ados, Silk and West (BSW) that the center of mass energy (E cm ) of test particles starting from rest at infinity and colliding near the horizon of a Schwarzschild black hole is always finite. In this communication, we extent the BSW scenario and study two particles with different energies colliding near the horizon of a...

In order to classify and understand structure of the spacetime, investigation of the geodesic motions of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of...

Equilibrium configurations of a circling electrically charged fluid surrounding a central static black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Various configurations of the fluid are influenced by the balance between the gravitational and electromagnetic actions; pr...

The Earth’s geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (inclu...

Astrophysical black holes are often embedded into electromagnetic fields, that can usually be treated as test fields not influencing the spacetime geometry. Here we analyse the innermost stable circular orbit (ISCO) of charged particles moving around a Schwarzschild black hole in the presence of a radial electric test field and an asymptotically un...

In order to classify and understand the spacetime structure, investigation of the geodesic motion of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of geod...

We construct the relativistic standard steady, optically thick, cold, and geometrically thin accretion disk around a distorted Schwarzschild black hole. The distortion of this static and axially symmetric black hole solution is connected to an external distribution of matter. If the effects due to the rotation are negligible, this distribution can...

The Earth's geoid is one of the most important fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including...

Astrophysical black holes are often embedded into electromagnetic fields, that can usually be treated as test fields not influencing the spacetime geometry. Here we analyse the innermost stable circular orbit (ISCO) of charged particles moving around a Schwarzschild black hole in the presence of a radial electric test field and an asymptotically un...

In this contribution, we summarize our results concerning the observational constraints on the electric charge associated with the Galactic centre black hole – Sgr A*. According to the no-hair theorem, every astrophysical black hole, including supermassive black holes, is characterized by at most three classical, externally observable parameters –...

The observation of a pulsar closely orbiting the galactic center supermassive black hole would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravi...

In this contribution, we summarize our results concerning the observational constraints on the electric charge associated with the Galactic centre black hole - Sgr A*. According to the no-hair theorem, every astrophysical black hole, including supermassive black holes, is characterized by at most three classical, externally observable parameters -...

We study stationary, electrically charged fluid structures encircling a rotating compact object with a dipole magnetic field oriented along the rotation axis. This situation is described in an idealized way by the Kerr metric and a magnetic dipole “test” field, that does not affect the spacetime. The self-gravitational and self-electromagnetic fiel...

The observation of a pulsar closely orbiting the galactic center supermassive black hole would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravi...

We study stationary, electrically charged fluid structures encircling a rotating compact object with a dipole magnetic field oriented along the rotation axis. This situation is described in an idealized way by the Kerr metric and a magnetic dipole "test" field, that does not affect the spacetime. The self-gravitational and self-electromagnetic fiel...

Equilibrium configurations of electrically charged perfect fluid surrounding a central rotating black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Following our previous studies considering the central black hole non-rotating, we show that in the rotating case, condition...

We derive exact expressions for the relativistic redshift between an Earth-bound observer, that is meant to model a standard clock on the Earth's surface, and various (geodesic) observers in the Schwarzschild spacetime. We assume that the observers exchange radial light signals to compare the frequencies of standard clocks, which they transport alo...

Accurate orbit determination and modeling plays a key role in contemporary and future space missions. To fully exploit the technological capabilities, and to correctly interpret all measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, the equations of motion for freely falling test objec...

We describe a new analytical model for the accretion of particles from a rotating and charged spherical shell of dilute collisionless plasma onto a rotating and charged black hole. By assuming a continuous injection of particles at the spherical shell and by treating the black hole and a featureless accretion disc located in the equatorial plane as...

We present a definition of the geoid that is based on the formalism of general relativity without approximations, i.e. it allows for arbitrarily strong gravitational fields. For this reason it applies not only to the Earth and other planets but also to compact objects such as neutron stars. We define the geoid as a level surface of a time-independe...

Detailed and long-term VLBI (Very Long Baseline Interferometry) studies of the variable jets of supermassive black holes helps us to understand the emission processes of these fascinating phenomena. When observed and traced precisely, jet component kinematics reveals details about the potential motion of the jet base. Following this motion over dec...

We review the analytical solution methods for the geodesic equations in
Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of
elliptic and hyperelliptic functions. A short guide to corresponding literature
for general timelike and lightlike motion is also presented.

For an investigation of the physical properties of gravitational fields the
observation of massive test particles and light is very useful. The
characteristic features of a given space-time may be decoded by studying the
complete set of all possible geodesic motions. Such a thorough analysis can be
accomplished most effectively by using analytical...

We investigate the motion of spinning test bodies in General Relativity. By
means of a multipolar approximation method for extended test bodies we derive
the equations of motion, and classify the orbital motion of pole-dipole test
bodies in the equatorial plane of the Kerr geometry. An exact expression for
the periastron shift of a spinning test bo...

In General Relativity the rotation of a gravitating body like the Earth
influences the motion of orbiting test particles or satellites in a
non-Newtonian way. This causes e.g. a precession of the orbital plane, known as
the Lense-Thirring effect, and a precession of the spin of a gyroscope, known
as the Schiff effect. Here we discuss a third effect...

The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole
solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related t...

The requirements for accurate numerical simulations are increasing steadily. Modern high precision physics experiments now exceed the achievable numerical accuracy of standard commercial and scientific simulation tools. One example are optical resonators for which changes in the optical length are now commonly measured to 10-15 precision. The achie...

We consider the motion of test particles in the regular black hole space-time
given by Ay\'{o}n-Beato and Garc\'{\i}a in Phys. Rev. Lett. 80:5056 (1998). The
complete set of orbits for neutral and weakly charged test particles is
discussed, including for neutral particles the extreme and over-extreme metric.
We also derive the analytical solutions...

The motion of charged test-particles in the gravitational field of a rotating
and electromagnetically charged black hole as described by the Kerr-Newman
metric is considered. We completely classify the colatitudinal and radial
motion on the extended manifold $-\infty \leq r \leq \infty$, including orbits
crossing the horizons or $r=0$. Analytical s...

The Square Kilometre Array (SKA) is the most ambitious radio telescope ever
planned. With a collecting area of about a square kilometre, the SKA will be
far superior in sensitivity and observing speed to all current radio
facilities. The scientific capability promised by the SKA and its technological
challenges provide an ideal base for interdiscip...

The no-hair conjecture statement is enhanced to include static regular and singular black-hole solutions, based on the class of nonlinear electrodynamics proposed by Plebański coupled to Einstein theory. In particular, we focus, as example, on regular black-hole solutions, i.e., black holes where the space-time metric everywhere is nonsingular, in...

It has been shown that the Hamilton-Jacobi equation corresponding to the geodesic equation in a Petrov type D space-time is separable and, thus, integrable. All Petrov type D space-times are exhausted by the Plebański-Demiański electrovac solutions with vanishing acceleration of the gravitating source. Here we present the analytical integration of...

The periastron shift and the Lense-Thirring effect of bound orbital motion in
a general axially symmetric space-time given by Pleba\'nski and Demia\'nski are
analyzed. We also define a measure for the conicity of the orbit and give
analytic expressions for all three observables in terms of hyperelliptic
integrals and Lauricella's $F_D$ function. Fo...

The requirements for accurate numerical simulation are increasing constantly.
Modern high precision physics experiments now exceed the achievable numerical
accuracy of standard commercial and scientific simulation tools. One example
are optical resonators for which changes in the optical length are now commonly
measured to 10^{-15} precision. The a...

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...

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 geo...

We study the geodesic equation in the space-time of a Kerr black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles in terms of Mino time that allows to decouple the r- and theta-component of the geodesic equation. The solutions of the geodesic equat...

The complete structure of geodesics in fast Kerr and Kerr-(anti-)de Sitter space-times are analyzed and classified. The analysis is based on the determination of the zeros of the polynomials underlying the equation of motion for the altitudinal and the radial coordinates.

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 inter...

The physics of a gravitational field can be explored by studying the geodesic motion of test particles and light. Although the majority of gravitational effects can be discussed using approximations and numerics, a systematic study of all effects can only be achieved by using analytical methods. In particular, exact analytic treatments can finally...

We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular mo...

The complete sets of analytic solutions of the geodesic equation in
Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general
Plebanski--Demianski space--times without acceleration are presented. The
solutions are given in terms of the Kleinian sigma functions.

The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild–(anti)de Sitter, Reissner-Nordström and Reissner–Nordström–(anti)de Sitter spacetimes are presented. Using the Jacobi inversion problem restricted to the theta divisor the explicit solution is given in terms of Kle...

A method for solving geodesic equations in Schwarzschild–de Sitter space–times and higher dimensional Schwarzschild space–times is presented. The solutions are derived from Jacobi's inversion problem on a Riemann surface of genus 2 restricted to the set of zeros of the theta function, which is called a theta–divisor. In its final form, the solution...

The OPTIS mission is a satellite equipped with a variety of clocks and laser ranging and tracking facilities for performing
improved tests of the foundations as well as predictions of special and general relativity. This mission makes advantage of
the space conditions of large differences in the velocity and the gravitational potential. Here, we re...

The complete set of analytic solutions of the geodesic equation in a
Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are
derived from the Jacobi inversion problem restricted to the set of zeros of the
theta function, called the theta divisor. In its final form the solutions can
be expressed in terms of derivatives of Kleinia...

The complete set of analytic solutions of the geodesic equation in a
Schwarzschild--(anti) de Sitter space--time is presented. The solutions are
derived from the Jacobi inversion problem restricted to the theta--divisor. In
its final form the solutions can be expressed in terms of derivatives of
Kleinian sigma functions. The solutions are completel...

The complete set of analytic solutions of the geodesic equation in Schwarzschild-(anti)de Sitter space-times is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta-divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian si...

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti)de Sitter space-time is presented. The solutions are derived from Jacobi's inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sig...

An analysis of Doppler tracking data from the NASA satellites Pioneer 10 and 11 (Anderson et al., 2002) has detected an anomalous, constant, acceleration of magnitude 8 x 10-10 m/s2 directed toward the sun. The studied range corresponded to a heliocentric distance interval of 40.0 to 70.5 AU in the case of Pioneer 10 and of 22.4 to 31.7 AU for Pion...