Although the orbits of comparable mass, spinning black holes seem to defy simple decoding, we find a means to decipher all such orbits. The dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. We are able to quantitatively define and describe the fully three dimensional motion of comparable mass binaries with one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by capturing the motion in the orbital plane. Our results are twofold: (1) We derive highly simplified equations of motion in a non-orthogonal orbital basis, and (2) we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rationals, we are able to show that zoom-whirl behavior is prevalent in comparable mass binaries in the strong-field regime. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves and that no orbit will behave like the tightly precessing ellipse of Mercury. The gravitational waveform produced by these low-leaf clovers will reflect the natural harmonics of the orbital basis -- harmonics that, importantly, depend only on radius. The significance for gravitational wave astronomy will depend on the number of windings the pair executes in the strong-field regime and could be more conspicuous for intermediate mass pairs than for stellar mass pairs.
Understanding the dynamics around rotating black holes is imperative to the success of the future gravitational wave observatories. Although integrable in principle, test particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxono…
The masses of elementary particles and hadrons can be calculated from the periodic table of elementary particles. The periodic table is derived from dimensional hierarchy for the seven extra spatial dimensions. As a molecule is the composite of atoms with chemical bonds, a hadron is the composite of elementary particles with hadronic bonds. The masses of elementary particles and hadrons can be calculated using the periodic table with only four known constants: the number of the extra spatial dimensions in the superstring, the mass of electron, the mass of Z=B0, and the fine structure constant.…
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell m…
We investigate periodic orbits and zoom-whirl behaviors around a Kerr Sen black hole with a rational number $q$ in terms of three integers $(z,w,v)$, from which one can immediately read off the number of leaves(or zooms), the ordering of the leaves, and the number of whirls. The characteristic of zoom-whirl periodic orbits is the precession of multi-leaf orbits in the strong field regime. This feature is analogous to the counterpart in the Kerr space-time. Finally, we analyze the impact of the charge parameter $b$ on the zoom-whirl periodic orbits. Compared to the periodic orbits around the Ke…
In calculations of the inspiral of binary black holes an intermediate approximation is needed that can bridge the post-Newtonian methods of the early inspiral and the numerical relativity computations of the final plunge. We describe here the periodic standing wave approximation: A numerical solution is found to the problem of a periodic rotating binary with helically symmetric standing wave fields, and from this solution an approximation is extracted for the physically relevant problem of inspiral with outgoing waves. The approximation underlying this approach has been recently confirmed with…
We extend firstly the regular phantom black hole solution to a slowly rotating black hole case and find that the phantom field depresses the angular velocity of the event horizon and suppresses the super-radiation of black hole. We also probe the dependence of quasi-periodic oscillations frequencies in relativistic precession model on the phantom parameter. With the observation data of GRO J1655-40, we make a constraint on the parameters of the regular and slowly rotating phantom black hole. Our results show that although the best-fit value of the phantom parameter $b$ is small, the allowed va…
The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momen…
Quasi-periodic oscillations (QPOs) observed in the power spectrum of black holes are unique observational probes to the background spacetime since they can be directly related to the timescales associated with the motion of matter orbiting in the vicinity of the black hole horizon. In this regard, the high frequency QPOs (HFQPOs) are particularly interesting as they occur in commensurable pairs, the most common ratio being the 3:2 twin peak QPOs. The theoretical models which aim to explain these QPOs express the observed frequencies in terms of the epicyclic motion of test particles in a given…
It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordstrom black hole background; in particular, there are no static solutions of the Dirac equation in such a background field. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.
The idea of black-hole lattices as models for the large-scale structure of the universe has been under scrutiny for several decades, and some of the properties of these systems have been elucidated recently in the context of the problem of cosmological backreaction. The complete, three-dimensional and fully relativistic evolution of these system has, however, never been tackled. We explicitly construct the first of these solutions by numerically integrating Einstein's equation in the case of an eight-black-hole lattice with the topology of S3.
By using the relativistic precession model, we have studied frequencies of quasi-periodic oscillations in the spacetime of a disformal Kerr black hole. This black hole owns an extra disformal parameter and belongs to a class of non-stealth solutions in quadratic degenerate higher-order scalar-tensor (DHOST) theories. Our result shows that only the periastron precession frequency is related to the disformal parameter, while the azimuthal frequency and the nodal precession frequency are identical with those in the usual Kerr black hole in general relativity. Combing with the observation data of …
The measurements of quasi-periodic oscillations (QPOs) provide a quite powerful tool to test the nature of astrophysical black hole candidates in the strong gravitational field regime. In this paper, we use QPOs within the relativistic precession model to test a recently proposed family of rotating black hole mimickers, which reduce to the Kerr metric in a limiting case, and can represent traversable wormholes or regular black holes with one or two horizons, depending on the values of the parameters. In particular, assuming that the compact object of GRO J1655-40 is described by a rotating bla…
The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of three dimensional black holes. We use the period of motion of an outgoing wave which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon area of rotating and non-rotating BTZ black holes. It is shown that the equally spaced area spectrum takes the same form as the obtained in the literature using the quasinormal mode analysis for both metrics. Using this method, we do not need to use the small angular …
The motion of a massive test particle around a Kehagias-Sfetsos black hole in deformed Hourava-Lifshitz gravity is studied. Employing the effective potential, the marginally bound orbits and the innermost stable circular orbits are analyzed. For the marginally bound orbits, their radius and angular momentum decrease with the parameter $ω$ of the gravity. For the innermost stable circular orbits, the energy and angular momentum also decrease with $ω$. Based on these results, we investigate the periodic orbits in the Kehagias-Sfetsos black holes. It is found that the apsidal angle parameter incr…
In this paper we investigate scalar perturbations of black holes embedded in a five dimensional bulk space. It is calculated the quasinormal frequencies of a such black holes using the third order of Wentzel, Kramers, Brillouin (WKB) approximation for scalar perturbations. The results are presented in tables along the text.
Quasi-periodic oscillations (QPOs), in particular, the ones with high frequencies, often observed in the power spectrum of black holes, are useful in understanding the nature of strong gravity since they are associated with the motion of matter in the vicinity of the black hole horizon. Interestingly, these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the most common ratio being 3:2. Several theoretical models are proposed in the literature which explain the HFQPOs in terms of the orbital and epicyclic frequencies of matter rotating around the central object. Since these f…
Taxonomy of periodic orbits and gravitational waves in a non-rotating Destounis-Suvorov-Kokkotas black hole spacetime
University of Chinese Academy of Sciences（中国科学院大学）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（亚太理论物理中心，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Imposing extendibility on Kasner-Fronsdal black hole local isometric embedding is equivalent to removing conic singularities in Kruskal representation. Allowing for globally non-trivial (living in $M_{5}\times S_{1}$) embeddings, parameterized by $k$, extendibility can be achieved for apparently forbidden frequencies $ω_{1}(k)\leω(k)\le ω_{2}(k)$. The Hawking-Gibbons limit, say $\displaystyle{ω_{1,2}(0)= {1\over{4M}}}$ for Schwarzschild geometry, is respected. The corresponding Kruskal sheets are viewed as slices in some Kaluza-Klein background. Euclidean $k$ discreteness, dictated by imaginar…
Quasi-periodic oscillations, often present in the power density spectrum of accretion disk around black holes, are useful probes for the understanding of gravitational interaction in the near-horizon regime of black holes. Since the presence of an extra spatial dimension modifies the near horizon geometry of black holes, it is expected that the study of these quasi-periodic oscillations may shed some light on the possible existence of these extra dimensions. Intriguingly, most of the extra dimensional models, which are of significant interest to the scientific community, predicts the existence…
We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast with the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity.
Supermassive black holes (SMBHs; $M\gtrsim10^5\msun$) are known to exist at the centre of most galaxies with sufficient stellar mass. In the local Universe, it is possible to infer their properties from the surrounding stars or gas. However, at high redshifts we require active, continuous accretion to infer the presence of the SMBHs, often coming in the form of long-term accretion in active galactic nuclei. SMBHs can also capture and tidally disrupt stars orbiting nearby, resulting in bright flares from otherwise quiescent black holes. Here, we report on a $\sim200$-s X-ray quasi-periodicity a…
