In presence of magnetic fields, the orbits of charged particles can be displaced from the equatorial plane. We study circular orbits of electrically charged massive objects around a magnetic black hole in the probe approximation. We show that there exist a one-parameter family of circular orbits at constant polar angle $θ$ and constant radius $r$, parameterized by the angular momentum. The angle $θ$ can be made arbitrarily small by increasing the charge-to-mass ratio of the orbiting particle, but when this is a Reissner-Nordstr\" om black hole, the condition $q\leq m$ implies that orbits exist only for $|θ-\fracπ{2}|<
{\rm arccot}(2\sqrt{2})$. We show that the circular orbits are stable under small perturbations in the $θ$ and $r$ directions. We also discuss the Newtonian approximation and a binary system of electric and magnetic black holes, each one describing a circular orbit with no central force.
We consider gravitational radiation and electromagnetic radiation from point mass binary with electric charges in a Keplerian orbit, and calculate the merger rate distribution of primordial black hole binaries with charges and a general mass function by taking into account gravitational torque and electromagnetic torque by the nearest primordial black hole. We apply the formalism to the extremal charged case and find that $α=-(m_i+m_j)^2\partial^2 \ln {\cal R}(m_i,m_j)/\partial m_i \partial m_j=12/11$, which is independent of the mass function.
We derive the equations of motion of dyonic black hole binaries with electric and magnetic charges and explore features of static orbits. By using a Newtonian method with the inclusion of radiation reaction, we calculate the total emission rate of energy and angular momentum due to gravitational radiation and electromagnetic radiation for circular orbits. Moreover, we obtain the evolutions of orbits and calculate merger times of dyonic binaries. We show that electric and magnetic charges significantly suppress the merger times of dyonic binaries. Our results provide rich information about dyon…
Inspiral waveforms of charged compact binaries and observational constraints
University of Chinese Academy of Sciences（中国科学院大学）；Taiji Laboratory for GW Universe, University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室）；Hunan Normal University（湖南师范大学）；Yangtze University（长江大学）
It is still an open issue if astrophysical black holes have electric charges or not. In this work, we analytically calculate gravitational and electromagnetic waveforms in the frequency domain for charged black hole binaries during the inspiral phase. In addition to the well-known $f^{-7/6}$ waveforms, we also get a $-11/6$ power law gravitational wave component. The phase of waveforms for charged binary is fully derived. In the case of electromagnetic counterparts, we focus on the electromagnetic dipole radiation, but we include the quadrupole contribution to complete our discussion. We also …
Post-Newtonian dynamics of charged compact binaries
International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（国际理论物理中心亚太区，中国科学院大学）；Taiji Laboratory for GW Universe, University of Chinese Academy of Sciences（引力波宇宙太极实验室，中国科学院大学）；School of Physics and Optoelectronic Engineering, Yangtze University（长江大学物理与光电工程学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
It is expected on both evolutionary and empirical grounds that many merging neutron star (NS) binaries are composed of a highly magnetized NS in orbit with a relatively low magnetic field NS. I study the magnetic interactions of these binaries using the framework of a unipolar inductor model. The e.m.f. generated across the non-magnetic NS as it moves through the magnetosphere sets up a circuit connecting the two stars. The exact features of this circuit depend on the uncertain resistance in the space between the stars R_space. Nevertheless, I show that there are interesting observational and/…
We extend the gravitational self-force methodology to identify and compute new $O(μ)$ tidal invariants for a compact body of mass $μ$ on a quasi-circular orbit about a black hole of mass $M \gg μ$. In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative `electric' invariants and 3+1 `magnetic' invariants, satisfying 1+1 and 1+0 trace conditions. After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the function…
Transition of gravitational waves, produced in the process of coalescence of black hole binaries, into electromagnetic radiation in magnetic field is discussed. The magnetic field is assumed to be created by rotating electrically charged black holes. The process of electric charging of black holes due to different mobilities of protons and electrons in the surrounding plasma is described.
The observation of a possible electromagnetic counterpart by the Fermi GBM group to the aLIGO detection of the merger of a black hole binary has spawned a number of ideas about its source. Furthermore, observations of fast radio bursts (FRBs) have similarly resulted in a range of new models that might endow black hole binaries with electromagnetic signatures. In this context, even the unlikely idea that astrophysical black holes may have significant charge is worth exploring, and here we present results from the simulation of weakly charged black holes as they orbit and merge. Our simulations …
The primary optical caustic surface behind a Kerr black hole is a four-cusped tube displaced from the line of sight. We derive the caustic surface in the nearly asymptotic region far from the black hole through a Taylor expansion of the lightlike geodesics up to and including fourth-order terms in m/b and a/b, where $m$ is the black hole mass, a the spin and b the impact parameter. The corresponding critical locus in the observer's sky is elliptical and a point-like source inside the caustics will be imaged as an Einstein cross. With regard to lensing near critical points, a Kerr lens is analo…
Inspiral gravitational waveforms from charged compact binaries with scalar hair
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力波物理与量子信息研究中心）；Department of Physics, Waseda University（早稻田大学物理学部）
In this paper we propose the model that the coalescence of primordial black holes (PBHs) binaries with equal mass $M \sim 10^{28}$g can emit luminous gigahertz (GHz) radio transient, which may be candidate sources for the observed fast radio bursts (FRBs), if at least one black hole holds appropriate amount of net electric charge $Q$. Using a dimensionless quantity for the charge $q = Q/\sqrt{G}M$, our analyses infer that $q\sim O(10^{-4.5})$ can explain the FRBs with released energy of order $O(10^{40}) {\rm ergs}$. With the current sample of FRBs and assuming a distribution of charge $ϕ(q)$ …
We extend the gravitational self-force approach to encompass `self-interaction' tidal effects for a compact body of mass $μ$ on a quasi-circular orbit around a black hole of mass $M \gg μ$. Specifically, we define and calculate at $O(μ)$ (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of …
Ambient magnetic fields are thought to play a critical role in black hole jet formation. Furthermore, dual electromagnetic signals could be produced during the inspiral and merger of binary black hole systems. However, due to the absence of theoretical models, the physical status of binary black hole arrays with dual jets has remained unresolved. In this paper, we derive the exact solution for the electromagnetic field occurring when a static, axisymmetric binary black hole system is placed in the field of two magnetic or electric monopoles. As a by-product of this derivation, we also find the…
Electromagnetic duality degeneracy in dynamical black hole mergers
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用研究中心（CIDMA））；AWS Center for Quantum Computing（亚马逊量子计算中心）；University of Arizona（亚利桑那大学）
In General Relativity and many modified theories of gravity, isolated black holes (BHs) cannot source massless scalar fields. Einstein-Maxwell-dilaton (EMd) theory is an exception: through couplings both to electromagnetism and (non-minimally) to gravity, a massless scalar field can be generated by an electrically charged BH. In this work, we analytically model the dynamics of binaries comprised of such scalar-charged ("hairy") BHs. While BHs are not expected to have substantial electric charge within the Standard Model of particle physics, nearly-extremally charged BHs could occur in models o…
Charged Black-Hole Binary Evolution at Second Post-Newtonian Order
Università di Perugia（佩鲁贾大学）；Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（阿尔伯特·爱因斯坦研究所））；INAF - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
Charged black-hole binary radiation at second post-Newtonian order
Università di Perugia（佩鲁贾大学）；Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova（帕多瓦大学伽利略·伽利莱物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We discuss the conditions under which plane electromagnetic and gravitational waves can be amplified by a rotating black hole due to superradiant scattering. We show, in particular, that amplification can occur for low-frequency waves with an incidence angle parametrically close to 0 (or $π$) with respect to the black hole spin axis and with a parametrically small left (or right) polarization. This is the case of the radiation emitted by a spinning electric/magnetic dipole or gravitational quadrupole orbiting a black hole companion at large radius and co-rotating with the latter. This can yiel…
We discuss the problem of the third black hole parameter, an electric charge. While the mass and the spin of black holes are frequently considered in the majority of publications, the charge is often neglected and implicitly set identically to zero. However, both classical and relativistic processes can lead to a small non-zero charge of black holes. When dealing with neutral particles and photons, zero charge is a good approximation. On the other hand, even a small charge can significantly influence the motion of charged particles, in particular cosmic rays, in the vicinity of black holes. Th…
When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.
An important issue in the dynamics of neutron star binaries is whether tidal interaction can cause the individual stars to collapse into black holes during inspiral. To understand this issue better, we study the dynamics of a cluster of collisionless particles orbiting a non-rotating black hole, which is part of a widely separated circular binary. The companion body's electric- and magnetic-type tidal fields distort the black hole and perturb the cluster, eventually causing the cluster to collapse into the hole as the companion spirals in under the influence of gravitational radiation reaction…
Charged Simpson-Visser-AdS spacetime: QPOs and observational constraints
School of Mathematics and Statistics, Fuzhou University（福州大学数学与统计学院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Kimyo International University in Tashkent（塔什干化学国际大学）；Tashkent State Technical University（塔什干国立技术大学）；Department of Physics, Shanghai University（上海大学物理系）；Tashkent State Transport University（塔什干国立交通大学）；Karakalpak State University（卡拉卡尔帕克国立大学）
