Georgios Lukes-Gerakopoulos

How to Observe a Non-Kerr Spacetime Using Gravitational Waves

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr spacetime. We exploit the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form Birkhoff chains on a surface of section. The KAM curves of the islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. However the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime.

Observable signature of a background deviating from the Kerr metric

By detecting gravitational wave signals from extreme mass ratio inspiraling sources (EMRIs) we will be given the opportunity to check our theoretical expectations regarding the nature of supermassive bodies that inhabit the central regions of galaxies. We have explored some qualitatively new features that a perturbed Kerr metric induces in its geodesic orbits. Since a generic perturbed Kerr metric does not possess all the special symmetries of a Kerr metric, the geodesic equations in the former case are described by a slightly nonintegrable Hamiltonian system. According to the

The non-integrability of the Zipoy-Voorhees metric

The low frequency gravitational wave detectors like eLISA/NGO will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. A way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the

Adjusting chaotic indicators to curved spacetimes

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ORBITS IN A NON-KERR DYNAMICAL SYSTEM

spacetime) can be included in the bumpy black hole family, because it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, in the present article it is shown by numerical examples that in general ZV belongs to the family of non-integrable systems.

Dynamics and chaos in the unified scalar field cosmology

In this work, chaotic indicators, which have been established in the framework of classical mechanics, are reformulated in the framework of general relativity in such a way that they are invariant under coordinate transformation. For achieving this, the prescription for reformulating mLCE given by [Y. Sota, S. Suzuki, and K.-I. Maeda, Classical Quantum Gravity 13, 1241 (1996)] is adopted. Thus, the geodesic deviation vector approach is applied, and the proper time is utilized as measure of time. Following the aforementioned prescription, the chaotic indicators FLI, MEGNO, GALI, and APLE are reformulated. In fact, FLI has been reformulated by adapting other prescriptions in the past, but not by adapting the Sota et al. one. By using one of these previous reformulations of FLI, an approximative expression giving MEGNO as function of FLI has been applied on non-integrable curved spacetimes in a recent work. In the present work the reformulation of MEGNO is provided by adjusting the definition of the indicator to the Sota et al. prescription. GALI, and APLE are reformulated in the framework of general relativity for the first time. All the reformulated indicators by the Sota et al. prescription are tested and compared for their efficiency to discern order from chaos.

Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole

We study the orbits in a Manko–Novikov type metric (MN) which is a perturbed Kerr metric. There are periodic, quasi-periodic, and chaotic orbits, which are found in configuration space and on a surface of section for various values of the energy E and the z-component of the angular momentum Lz. For relatively large Lz there are two permissible regions of nonplunging motion bounded by two closed curves of zero velocity (CZV), while in the Kerr metric there is only one closed CZV of nonplunging motion. The inner permissible region of the MN metric contains mainly chaotic orbits, but it contains also a large island of stability. When Lz decreases, the two permissible regions join and chaos increases. Below a certain value of Lz, most orbits escape inwards and plunge through the horizon. On the other hand, as the energy E decreases (for fixed Lz) the outer permissible region shrinks and disappears. In the inner permissible region, chaos increases and for sufficiently small E most orbits are plunging. We find the positions of the main periodic orbits as functions of Lz and E, and their bifurcations. Around the main periodic orbit of the outer region, there are islands of stability that do not appear in the Kerr metric (integrable case). In a realistic binary system, because of the gravitational radiation, the energy E and the angular momentum Lz of an inspiraling compact object decrease and therefore the orbit of the object is nongeodesic. In fact, in an extreme mass ratio inspiraling (EMRI) system the energy E and the angular momentum Lz decrease adiabatically and therefore the motion of the inspiraling object is characterized by the fundamental frequencies which are drifting slowly in time. In the Kerr metric, the ratio of the fundamental frequencies changes strictly monotonically in time. However, in the MN metric when an orbit is trapped inside an island the ratio of the fundamental frequencies remains constant for some time. Hence, if such a phenomenon is observed this will indicate that the system is nonintegrable and therefore the central object is not a Kerr black hole.

Spinning test body orbiting around a Schwarzschild black hole: Circular dynamics and gravitational-wave fluxes

We study the dynamics of the closed scalar field FRW cosmological models in the framework of the so-called unified dark matter (UDM) scenario. Performing a theoretical as well as a numerical analysis we find that there is a strong indication of chaos in agreement with previous studies. We find that a positive value of the spatial curvature is essential for the appearance of chaoticity, though the Lyapunov number seems to be independent of the curvature value. Models that are close to flat (k{yields}0{sup +}) exhibit a chaotic behavior after a long time while pure flat models do not exhibit any chaos. Moreover, we find that some of the semiflat models in the UDM scenario exhibit similar dynamical behavior with the {lambda} cosmology despite their chaoticity. Finally, we compare the measured evolution of the Hubble parameter derived from the differential ages of passively evolving galaxies with that expected in the semiflat unified scalar field cosmology. Based on a specific set of initial conditions we find that the UDM scalar field model matches well the observational data.

Investigating spinning test particles: Spin supplementary conditions and the Hamiltonian formalism

We present a new computation of the asymptotic gravitational wave energy fluxes emitted by a {\it spinning} particle in circular equatorial orbits about a Kerr black hole. The particle dynamics is computed in the pole-dipole approximation, solving the Mathisson-Papapetrou equations with the Tulczyjew spin-supplementary-condition. The fluxes are computed, for the first time, by solving the 2+1 Teukolsky equation in the time-domain using hyperboloidal and horizon-penetrating coordinates. Denoting by

Dynamics and constraints of the unified dark matter flat cosmologies

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