Gravitational wave signatures from periodic orbits around a Schwarzschild-Bertotti-Robinson black hole
National Research University TIIAME（国立TIIAME大学）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology（浙江工业大学引力波物理联合中心）
Tursunali Xamidov, Sanjar Shaymatov, Qiang Wu, Tao Zhu
In this paper, we investigate periodic bound orbits and gravitational wave (GW) emission in the Schwarzschild-Bertotti-Robinson (Schwarzschild-BR) spacetime-an exact electrovacuum solution describing a static black hole (BH) immersed in a uniform magnetic field. We explore how the background magnetic field qualitatively alters the BH's gravitational dynamics, affecting timelike geodesics such as the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO). We then analyze periodic bound orbits using the frequency ratio ${ω_φ}/{ω_{r}}$, which characterizes the orbits by their azimuthal and radial motions. Based on the numerical kludge method we further compute the gravitational waveforms emitted from periodic orbits around a supermassive Schwarzschild-BR BH. We show that the background magnetic field significantly changes orbital frequencies, resonance conditions, zoom-whirl structures, and the resulting waveforms. Finally, we examine the frequency spectra in the mHz range and the detectability of these GW signals by computing the characteristic strain via a discrete Fourier transform on the time-domain waveforms, comparing the results with the sensitivity curves of space-based GW detectors such as LISA, Taiji, and TianQin. Our results show that intrinsically magnetic fields modify spacetime and leave observable imprints on extreme mass-ratio inspiral GWs, which may be tested by future observations.
In the present article we obtain, by separation of variables, an exact solution to the Dirac equation with anomalous momentum for an electrically neutral massless particle in a Bertotti-Robinson universe. We discuss the phenomenom of particle creation in this model.
Bertotti-Robinson spacetimes are topologically $AdS_2 \times S^2$ and described by a conformally flat metric. Together with the Coulomb electric potential, they provide a class of static, geodetically complete Einstein-Maxwell solutions. We show here that the Bertotti-Robinson metric together with Wu-Yang magnetic pole potentials give a class of static solutions of a system of non-minimally coupled Einstein-Yang-Mills equations that may be relevant for investigating vacuum polarization effects in a first order perturbative approach to quantum fields.
We consider the pure electric type power-law Lagrangian in nonlinear electrodynamics theory of dimensions $n+1$. Conformally flat form of Bertotti-Robinson type spacetimes are obtained in all these dimensions with the specific power $s=-\frac{1}{n-4},$which naturally excludes $n=4.$ This particular dimension is considered separately which is not of power-law form.
We present a solution for the Einstein-Maxwell (EM) equations which unifies both the magnetic Bertotti-Robinson (BR) and Melvin (ML) solutions as a single metric in the axially symmetric coordinates ${t,ρ,z,φ} $. Depending on the strength of magnetic field the spacetime manifold, unlike the cases of separate BR and ML spacetime, develops singularity on the symmetry axis ($ρ=0$). Our analysis shows, beside other things that there are regions inaccessible to all null geodesics.
Spherically symmetric classical model of an elementary particle or a black hole spacetime without central singularity had been constructed by O. B. Zaslavskii in PRD 70(2004)104017. In this model an extremal Reissner-Nordstr% öm (RN) black hole and a Bertotti-Robinson (BR) spacetime are glued at the horizon such that the inner/core spacetime is the regular BR while outside is the extremal RN. In this note we investigate the stability of such a particle / regular black hole against linear radial perturbations. The model turns out to be stable against such perturbations with a linear equation of…
The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The set of equations representing the Dirac equation in the Newman-Penrose formalism is decoupled into an axial and angular part. The axial equation, which is independent of mass, is solved exactly in terms of hypergeometric functions. The angular equation is considered both for massless (neutrino) and massive spin-(1/2) particles. For the neutrinos, it is shown that the angular equation admits an exact solution in terms of the confluent Heun equation. In the existence of mass, the angular equation does not allow an anal…
We discuss the problem of wormholes from the viewpoint of gluing together two Reissner--Nordström-type universes while putting between them a segment of the Nariai-type world (in both cases there are also present electromagnetic fields as well as the cosmological constant). Such a toy wormhole represents an example of one-way topological communication free from causal paradoxes, though involving a travel to next spacetime sheet since one has to cross at least a pair of horizons through which the spacetimes' junction occurs. We also consider the use of thin shells in these constructions. Such a…
Thermodynamics of Kerr-Newman-Bertotti-Robinson black holes
Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所、物理科学与技术学院）；School of Physics, & Center for High Energy Physics, Peking University（北京大学物理学院、高能物理中心）
We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordström spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sen…
A conformally flat accelerated charge metric is found in an arbitrary dimension $D$. It is a solution of the Einstein-Maxwell-null fluid with a cosmological constant in $D \ge 4$ dimensions. When the acceleration is zero our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.
Light bending around the Kerr-Bertotti-Robinson black hole using material medium approach
National Institute of Technology, Agartala（阿加塔拉国家技术学院）；The Institute of Mathematical Sciences（数学科学研究所）；Khazar University（汗扎尔大学）；Hemwati Nandan Bahuguna Garhwal University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Centre for Space Research, North-West University（西北大学空间研究中心）；Assam University（阿萨姆大学）
Optical and thermodynamic properties of Kerr-Bertotti-Robinson black holes
California State University, Fresno（弗雷斯诺加州州立大学）；University of Hradec Králové（赫拉德茨克拉洛韦大学）；Khazar University（卡扎尔大学）；Nazarbayev University（纳扎尔巴耶夫大学）；National Taiwan University（台湾大学）；Arizona State University（亚利桑那州立大学）；University of Helsinki（赫尔辛基大学）；Università di Camerino（卡梅里诺大学）；University at Albany-SUNY（奥尔巴尼纽约州立大学）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所-布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Center for Theoretical Physics, Khazar University（卡扎尔大学理论物理中心）
The Levi-Civita Bertotti Robinson (LBR) spacetime is investigated in various coordinate systems. By means of a general formalism for constructing coordinates in conformally flat spacetimes, coordinate transformations between the different coordinate systems are deduced. We discuss the motion of the reference frames in which the different coordinate systems are comoving. Furthermore we characterize the motion of the different reference frames by their normalized timelike Killing vector fields, i.e. by the four velocity fields of the reference particles. We also deduce the formulae in the differ…
Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；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）；Institute of Fundamental and Applied Research, National Research University TIIAME（TIIAME国立研究型大学基础与应用研究所）；Tashkent State Technical University（塔什干国立技术大学）
Thermodynamics of Kerr-Bertotti-Robinson black hole
University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Hangzhou Institute for Advanced Study (HIAS), University of Chinese Academy of Sciences (UCAS)（中国科学院大学杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；Ningbo University（宁波大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
We present a series of new solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling $γ$ and a cosmological constant $Λ$. For general $γ$ and $Λ$ we give various generalizations of the Bertotti-Robinson solutions supported by electric and magnetic fluxes, some of which presumably describe the near-horizon regions of black strings or black rings. Among them there is a solution which could apply to the horizon of a topological AdS black ring in gauged minimal supergravity. Others are horizonless and geodesically complete. We also construct extrema…
Conformal field theories corresponding to two-dimensional electrically charged black holes and to two-dimensional anti-de Sitter space with a covariantly constant electric field are simply constructed as $SL(2,R)/Z$ WZW coset models. The two-dimensional electrically charged black holes are related by Kaluza-Klein reduction to the 2+1-dimensional rotating black hole of Banados, Teitelboim and Zanelli, and our construction is correspondingly related to its realization as a WZW model. Four-dimensional spacetime solutions are obtained by tensoring these two-dimensional theories with $SU(2)/Z(m)$ c…
We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace the origin of the inconsistency between a charge and rotation, considering the BR-like spacetime as a result of the limiting transition of a non-extremal black hole to the extremal state. We also find that the quasilocal energy and angular momentum of such BR-like spacetimes calculated within the boundary $l=const$ ($l$ is the proper distance) are constants …
Geodesics and Shadows in the Kerr-Bertotti-Robinson Black Hole Spacetime
Beijing Normal University（北京师范大学）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学汤川研究所）；Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术学院、物理科学与技术学院）；School of Physics, Peking University, & Center for High Energy Physics（北京大学物理学院、高能物理中心）
Global structure and stability of Kerr-Bertotti-Robinson spacetime
University of Science and Technology of China（中国科学技术大学）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；Ningbo University（宁波大学）
We report on a series of new solutions to five-dimensional minimal supergravity. Our method applies to space-times with two commuting Killing symmetries and consists in combining dimensional reduction on two-spaces of constant curvature with reduction on a two-torus. The first gives rise to various generalized Bertotti-Robinson solutions supported by electric and magnetic fluxes, which presumably describe the near-horizon regions of black holes and black rings (strings). The second provides generating techniques based on U-duality of the corresponding three-dimensional sigma model. We identify…
Magnetic Modification of Black Hole Photospheres with Image Contraction, Efficiency Shifts and Redshift Boosts in Schwarzschild-Bertotti-Robinson Spacetime
Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学TIIAME基础与应用研究所）；School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
Shadows and Thin-Disk Images of Kerr-Newman Black Holes in a Bertotti-Robinson Magnetic Field
Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所、物理科学与技术学院）；School of Physics, and Center for High Energy Physics, Peking University（北京大学物理学院、高能物理中心）
We investigate conformal mechanics associated with the rotating Bertotti-Robinson (RBR) geometry found recently as the near-horizon limit of the extremal rotating Einstein-Maxwell-dilaton-axion black holes. The solution breaks the $SL(2,R)\times SO(3)$ symmetry of Bertotti-Robinson (BR) spacetime to $SL(2,R)\times U(1)$ and breaks supersymmetry in the sense of $N=4, d=4$ supergravity as well. However, it shares with BR such properties as confinement of timelike geodesics and discreteness of the energy of test fields on the geodesically complete manifold. Conformal mechanics governing the radia…
The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $Λ$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventi…
We construct new solutions of five-dimensional quadratic gravity as direct products of a constant curvature two-surface with a solution of three-dimensional new massive gravity with constant scalar curvature. These solutions could represent near-horizon limits of five-dimensional asymptotically flat black strings or black rings. A number of these non-asymptotically flat solutions are themselves black strings or rings. A by-product of our analysis is the construction of new solutions of four-dimensional quadratic gravity obtained by toroidal reduction of the five-dimensional solutions with flat…
Melvin--Bonnor and Bertotti--Robinson spacetimes with Baryonic charge
Universidad de Tarapacá（塔拉帕卡大学）；Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Universidad de La Serena（拉塞雷纳大学）；Centro de Estudios Científicos (CECs)（科学研究中心）；Universidad San Sebastián（圣塞巴斯蒂安大学）；Universidad de Concepción（康塞普西翁大学）
We present a new solution to dilaton-axion gravity which looks like a rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous Maxwell field and a linear axion and can be obtained as a near-horizon limit of extremal rotating dilaton-axion black holes. It has the isometry $SL(2,R)\times U(1)$ where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation, while $SL(2,R)$ corresponds to the $AdS_2$ sector which no longer factors out of the full spacetime. Alternatively our solution can be obtained from the D=5 vacuum counterpart to the dyonic BR with equal electric a…
From Bertotti--Robinson to Vacuum: New Exact Solutions in General Relativity via Harrison and Inversion Symmetries
Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Vicerrectoría de Investigación y Postgrado, Universidad de La Serena（拉塞雷纳大学研究与研究生院）；Sede Esmeralda, Universidad de Tarapacá（塔帕卡里大学埃斯梅尔达校区）；Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Departamento de Física, Universidad de Concepción（康塞普西翁大学物理系）
In two previous papers we have analyzed the C-metric in a background with a cosmological constant, namely the de Sitter (dS) C-metric, and the anti-de Sitter (AdS) C-metric, following the work of Kinnersley and Walker for the flat C-metric. These exact solutions describe a pair of accelerated black holes in the flat or cosmological constant background, with the acceleration A being provided by a strut in-between that pushes away the two black holes. In this paper we analyze the extremal limits of the C-metric in a background with generic cosmological constant. We follow a procedure first intro…
Critical Behavior of Photon Rings in Kerr-Bertotti-Robinson Spacetime
Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所，物理科学与技术学院）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学李政道研究所）；School of Physics, and Center for High Energy Physics, Peking University（北京大学物理学院，高能物理中心）
Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita--Bertotti--Robinson
Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile（智利南方大学物理与数学科学研究所）；Departamento de Ciencias, Facultad de Artes Liberales, UAI Physics Center, Universidad Adolfo Ibañez（阿道夫·伊巴涅斯大学自由艺术学院科学系、UAI物理中心）
We consider the problem of quantum field theory on the Bertotti-Robinson space-time, which arises naturally as the near horizon geometry of an extremal Reissner-Nordstrom black hole but can also arise in certain near-horizon limits of non-extremal Reissner Nordstrom space-time. The various vacuum states have been considered in the context of $AdS_{2}$ black holes by Spradlin and Strominger who showed that the Poincare vacuum, the Global vacuum and the Hartle-Hawking vacuum are all equivalent, while the Boulware vacuum and the Schwarzschild vacuum are equivalent. We verify this by explicitly co…
Non-Monotonic Enhancement of the Magnetic Penrose Process in Kerr-Bertotti-Robinson Spacetime and its Implication for Electron Acceleration
National University of Uzbekistan（乌兹别克斯坦国立大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（塔什干国立研究大学基础与应用研究所）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Department of Physics, School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院物理系）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Department of Physics, Hemvati Nandan Bahuguna Garhwal Central University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔中央大学物理系）
Kerr-Bertotti-Robinson 空间中磁 Penrose 过程的非单调增强效应，揭示了电子加速至 $10^{15}\,\mathrm{eV}$ 的潜力，并通过辐射损失降至 TeV 级。
