Dynamics of particles around a pseudo-Newtonian Kerr black hole with halos

The regular and chaotic dynamics of test particles in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is detailed.In particular,the dependence of dynamics on the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is studied.It is found that the small quadrupolar moment,in contrast with the spin angular momentum,does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles.In addition,chaos mainly occurs for small absolute values of the rotating parameters,and does not exist for the maximum counter-rotating case under some certain initial conditions and parameters.This means that the rotating parameters of the black hole weaken the chaotic properties.It is also found that the counter-rotating system is more unstable than the co-rotating one.Furthermore,chaos is absent for small absolute values of the quadrupoles,and the onset of chaos is easier for the prolate halos than for the oblate ones.     

Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo-Newtonian Potential

The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detailedly. An optimal fourth-order force gradient symplectic method, as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations, is used to calculate fast Lyapunov indicators. In this way, dynamical structures are described, and parameter domains for causing chaos are found.     

Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

Spherical Photon Orbits Around a Kerr Black Hole

Two circular photon orbits are known to exist in the equatorial plane of the Kerr black hole. In this paper, we investigate so-called spherical photon orbits—orbits with constant coordinate radii that are not confined to the equatorial plane. A one-parameter class of solutions is found, which includes the circular orbits as special cases. The properties of these spherical orbits are then analyzed, with the aim of classifying them by qualitative differences in their behavior. Finally, representative orbits from each class are plotted out, including a zero-angular momentum photon orbit and one with non-fixed azimuthal direction.     

High-Frequency Gravitational Waves in Electromagnetic Waveguides

The interaction between a very-high-frequency gravitational wave (VHFGW) and an electromagnetic wave (EMW) in a rectangular waveguide is discussed in the weak field limit. The background EMW is assumed to be initially in the TE₁₀ mode along the waveguide. It is then shown that a VHFGW, having the same frequency and direction of propagation of the EMW, induces through the waveguide a TE mode with a frequency doubled when compared to the original EMW frequency. In that respect, the GW acts similar to a non-linear medium, giving rise to a Second Harmonic Generation (SHG) effect.     

A Gravitational Wave Background from Primordial Black Hole Lattices in Matter Dominated Era

We use the wide-used Einstein Toolkit to solve the Einstein constraints and then simulate the expansion of primordial black hole lattices (PBHLs) with different value of $f_{\mathrm{PBH}}$ and $m_{\mathrm{PBH}}$. We find that $f_{\mathrm{PBH}}$ plays an important role during the evolution of PBHLs. Since the motion of primordial black holes (PBHs) caused by the expansion of PBHLs occurs at speeds close to that of light, we expect the emission of gravitational waves (GWs) during the expansion of PBHLs. We use both analytical estimates and numerical simulations to cross check the production of GWs in expanding PBHLs.     

Increase of the Number of Detectable Gravitational Waves Signals Due to Gravitational Lensing

This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.     

Parametrization of the Kerr Solution

From the Kerr solution of Ernst equation under Ehlers and unitary transformations, we build a parametrized Kerr solution depending on three parameters, namely the mass, the angular momentum of the source and an adimensional parameter m ₁. Varying m ₁ produces a topological deformation of the ergosphere.     

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.     

Letter: The Radial Infall of a Highly Relativistic Point Particle into a Kerr Black Hole Along the Symmetry Axis

In this Letter we consider the radial infall along the symmetry axis of an ultra-relativistic point particle into a rotating Kerr black hole. We use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and total energy radiated during this process. We discuss possible connections between these results and the black hole-black hole collision at the speed of light process.     

匀加速直线运动的Kerr黑洞的非热效应

研究了匀加速直线运动的Kerr黑洞周围时空中的自发辐射.得到了发生自发辐射的能量条件,它不仅依赖于黑洞的角动量和加速度,而且还与黑洞的变化有关 关键词： 动态Kerr黑洞 非热辐射     

Back-reaction of the Kerr black hole. A thermodynamical approach

A thermodynamical approach is used to solve the back-reaction problem of the Kerr black hole; the dressed mass, the dressed angular momentum, and the dressed entropy are calculated.     

Hawking radiation of scalar and Dirac quanta from a Kerr black hole

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.     

Letter: Slowly Rotating, Compact Fluid Sources Embedded in Kerr Empty Space-Time

Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to and including quadratic terms in an angular velocity parameter using Darmois junction conditions. The boundary behaviour of the metric tensor and partial derivatives is used to develop a series solution of Einstein's equation's for the rotating fluid. The boundary of the rotating source is expressed explicitly in terms of sinusoidal functions of the polar angle. As an example of the analysis the Schwarzschild interior solution is endowed with rotation and the equation of the fluid boundary is generated together with surface behaviour of the fluid density and angular velocity.     

Do Neutron Star Gravitational Waves Carry Superfluid Imprints?

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×10⁸ neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate.     

De Broglie Matter Waves from the Linearized Einstein Field Equations

We suggest a connection between matter waves and gravitational waves. We find solutions of the linearized Einstein field equations in the form of de Broglie waves. These therefore acquire a new geometrical meaning.