A Hamiltonian approach to black hole entropy is used to study Riemannian Kerr-AdS solutions in the general, parity-violating Poincaré gauge theory. Entropy and the asymptotic charges are entirely determined by the parity-even sector of the theory, whereas the parity-odd contributions vanish. Entropy is found to be proportional to the horizon area, and the first law of black hole thermodynamics is confirmed.
A Hamiltonian variational approach is used to study asymptotic charges and entropy of Kerr-AdS black holes in the general Poincaré gauge theory, with both even and odd parity modes. The results turn out to be the same as those found earlier in the sector of parity invariant Lagrangians.
We analyze the near horizon symmetry of the extremal Kerr black hole within the framework of Poincaré gauge theory (PG) for two important limiting cases: Riemannian and teleparallel solution. We show that the algebra of canonical generators is realized by Virasoro algebra, with central charge which depends on the black hole horizon radius . The conformal entropy of the black hole is obtained via Cardy formula.
Using a Hamiltonian approach, we introduce black hole entropy for Kerr-AdS spacetimes with torsion as the canonical charge on horizon. In spite of a completely different geometric setting with respect to GR, the resulting thermodynamic variables, energy, angular momentum and entropy, are shown to be proportional to the corresponding GR expressions. The validity of the first law is confirmed.
Light deviation around a rotating black hole is calculated using the Kerr metric for both small and large deviation angles. For small angles the Lindstedt-Poincaré method is employed to get well-behaved solutions, as well as Padé approximants. For large deviation angles numerical integration has been used.
We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the interior of the black hole. We then proceed to classify regular ambitoric $4$-orbifolds with some completeness assumptions. The tools developed also allow us to prove a partial classification of compact Riemannian $4$-manifolds which admit a Killing $2$-form.
The canonical approach to black hole entropy in Poincaré gauge theory without matter is extended to include Maxwell field as a matter source. The new formalism is used to calculate asymptotic charges and entropy of Kerr--Newmann--AdS black holes with torsion. The result implies that the first law, with a nontrivial contribution of the Maxwell field, takes the same form as in general relativity.
Black hole entropy of the Kerr-like family of spacetimes is introduced as the canonical charge on the horizon. Treating these spacetimes in the framework of Poincaré gauge theory either as Riemannian solutions or as solutions with torsion, it is shown that these geometrically different setups lead to the same black hole entropy.
We present firstly the equation of motion for the test scalar particle coupling to the Chern-Simons invariant in Kerr black hole spacetime by the short-wave approximation. We have analyzed the dynamical behaviors of the test coupled particles by applying techniques including Poincaré sections, fast Lyapunov exponent indicator, bifurcation diagram and basins of attraction. It is shown that there exists chaotic phenomenon in the motion of scalar particle interacted with the Chern-Simons invariant in a Kerr black hole spacetime. With the increase of the coupling strength, the motion of the couple…
A gravitational spin-orbit interaction in Poincaré gauge theory
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学 Kavli宇宙物理数学研究所）；Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学高等研究院）；Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)（韩国基础科学研究所宇宙理论物理中心）；Center for Geometry and Physics, Institute for Basic Science (IBS)（韩国基础科学研究所几何与物理中心）
General criteria for the existence of conformally flat Riemannian solutions in 3D Poincaré gauge theory without matter are formulated. Using these criteria, we show that the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Town\-send gravity, is also an exact vacuum solution of the Poincaré gauge theory. The related conserved charges, calculated from the Hamiltonian boundary term, are shown to satisfy the first law of black hole thermodynamics. The form of the boundary term is verified by using the covariant Hamiltonian approach.
In this paper, an exact solution of Kerr black hole surrounded by a cloud of strings in Rastall gravity is obtained by Newman-Janis algorithm without complexification, and the influence of the string parameter $a_0$ on the black hole thermodynamics is studied. Furthermore, according to this black hole solution, we investigate the effect of a cloud of strings on gravitational deflection of massive particles. For a receiver and a source at infinite distance from the lens object, we use an osculating Riemannian manifold method. While the distance is finite, we apply the generalized Jacobi metric …
The problem of spinning and spin deviation equations for particles as defined by their microscopic effect has led many authors to revisit non-Riemannian geometry for being described torsion and its relation with the spin of elementary particles. We obtain a new method to detect the existence of torsion by deriving the equations of spin deviations in different classes of non-Riemannian geometries, using a modified Bazanski method. We find that translational gauge potentials and rotational gauge potentials regulate the spin deviation equation in the presence of Poincare gauge field theory of gra…
The standard Black Holes (BHs) in General Relativity, as well as other ultra-compact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axi-symmetric spacetimes, non-planar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poinca…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincaré gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian piece…
Probing Quantum Gravity through Chaotic Orbits and Strong-Field Effects in Kerr Black Holes Embedded in Perfect Fluid Dark Matter
The Institute of Mathematical Sciences, C.I.T. Campus（泰米鲁纳德邦金奈塔拉马尼 CIT 校区的数学科学研究所）；Khazar University（阿塞拜疆巴库的哈萨尔大学）；University of Mazandaran（伊朗巴巴萨尔的马赞达兰大学）；Virtual University of Pakistan（巴基斯坦拉合尔的虚拟大学）；Hemwati Nandan Bahuguna Garhwal University（印度北阿坎德邦斯里纳加的赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Harbin Institute of Technology（中国哈尔滨的哈尔滨工业大学）；Zhejiang Normal University（中国金华的浙江师范大学）
The curvature scalar invariants of the Riemann tensor are important in General Relativity because they allow a manifestly coordinate invariant characterisation of certain geometrical properties of spacetimes such as, among others, curvature singularities, gravitomagnetism. We calculate explicit analytic expressions for the set of Zakhary-McIntosh curvature invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime as well as for the Kerr-Newman-(anti-)de Sitter black hole. These black hole metrics belong to the most general type D solution of the Einstein-Maxwell equatio…
We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase sp…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some ci…
We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal met…
We mainly focus on the effects of small changes of parameters on the dynamics of charged particles around the Kerr black hole surrounded by an external magnetic field, which can be considered as a tidal environment. The radial motions of charged particles on the equatorial plane are studied via an effective potential. It is found that the particle energies at the local maxima values of the effective potentials increase with an increase of the black hole spin and the particle angular momenta, but decrease with an increase of one of the inductive charge parameter and magnetic field parameter. Th…
