Gravitational radiation from a particle with zero orbital angular momentum plunging into a Kerr black hole

We have computed the energy ΔE, the momentum ΔP and the angular momentum ΔJ of gravitational radiation induced by a particle of mass μ and of zero orbital angular momentum plunging in the θ = π/2 plane into a Kerr black hole of mass M(?μ) and angular momentum Ma. It is found that ΔE for a = 0.99M is 4.45 × 10^-2 (μ²/M)c², which is 4.27 times larger than that for the a = 0 case.     

Gravitational radiation induced by a particle falling along the Z-axis into a Kerr black hole

We have computed the spectrum and the energy of gravitational radiation induced by a test particle of mass μ falling along the z-axis into a Kerr black hole of mass M(? μ) and angular momentum Ma(a < M). It is found that the total energy radiated is 0.0170 0.0170 μc²μM when α = 0.99M, which is 1.65 times larger than that when α = 0, i.e., the Schwarzschild black hole case.     

Gravitational radiation by a particle with nonzero orbital angular momentum falling into a Kerr black hole

We have computed the energy of the gravitational waves induced by a particle with nonzero orbital angular momentum μL_z plunging into a Kerr black hole in an equatorial plane. It is found that for the same |L_z| a corotating particle emits more energy than a counter-rotating one, which is due to the change of the frequency of the quasi-normal mode with the increase of the angular momentum of the black hole.     

Kerr-Newman黑洞的谐振子模型及量子面积谱

利用Kerr-Newman黑洞的质量M，电量Q，角动量J和它们各自的对偶量，π_M,π_Q,π_J,构成的六维相空间，通过规范变换，首先建立黑洞的简谐振子模型；再利用该模型进一步研究Kerr-Newman黑洞的量子面积谱. 关键词： 黑洞 规范变换 简谐振子模型 量子面积谱     

Angular momentum fluctuation energy in the cranking model

Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is $\text{E}{}_{\mathrm{<mtext>proj</mtext>}}\text{≈ E}{}_{\mathrm{<mtext>HFBC</mtext>}}\text{? (Δ}\text{J}\text{)}{}^2\text{/2}\text{J}{}_{\mathrm{<mtext>HFBC</mtext>}}$. The spin-dependent fluctuation $\text{Δ}\text{J}$ includes contributions from J_y and J_z as well as J_x. There are no correlations in the three angular momentum components. Projected energies are calculated for ^{168, 170}Yb and ¹⁷⁴Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement.     

Klein paradox in a kerr geometry

The crossing of the classical positive and negative energy states E⁺ and E^? introduced by Christodoulou-Ruffini and interpreted within the framework of a relativistic quantum field theory by Deruelle and Ruffini, leads to a Klein paradox. It has been shown by Euler and Heisenberg that when the transmission coefficient T² through the barrier between the E⁺ and E^? states is small it is proportional to the probability of pair creation. Numerical computations show that, in the case of a small Kerr black hole (GM/c² ??/muc), the probability of pair creation of particles of mass μ is maximum when $\text{E ～ ?Ω}$, where E is the energy of the created particles and Ω and M the angular velocity and the mass of the back hole.     

Hawking Radiation of Charged Particles from a Rotating Black String

Using Damour-Ruffini method, Hawking radiation of rotating black strings is studied. Under the condition that the total energy, total angular momentum and total charge are conservative, the transition probability from initial state (energy M+ω, charge Q+e and angular momentum J+m) to final state (energy M, charge Q and angular momentum J) for black strings is derived considering the reaction of radiation particles to spacetime. That is, the probability that black strings radiate particles with energy ω, charge e and angular momentum m is obtained. The real spectrum is not a strictly pure thermal spectrum. Our result is consistent with Parikh and Wilczek’s result. It satisfies the unitary principle of quantum mechanics. However, in our result there are not only the term that denotes effect of energy and charge of radiation particles but also the term that denotes effect of radiation particles angular momentum on rotating black strings angular momentum. We provide a new way for investigating radiation of black strings.     

Equivalence of Two Definitions of the Effective Mass of a Polaron

Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P ²/2M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.     

Angular Momentum and Positive Mass Theorem

Total angular momentum for asymptotically flat manifolds is defined. Positive mass theorem for initial (spin) data set (M, g _ij , p _ij ) with nonsymmetric p _ij is proved. As an application, we establish positive mass theorems involving total linear momentum and total angular momentum. This gives an answer to a problem of S. T. Yau in his Problem Section [Ya2] and a partial answer to his recent conjecture on the relationship among total energy, total linear momentum, total angular momentum and entropy of black hole. Received: 26 October 1998 / Accepted: 10 March 1999     

Gedanken experiments to destroy a black hole

It is widely believed that the complete gravitational collapse of a body always results in a black hole (i.e., “naked singularities” can never be produced) and that all black holes eventually “settled down” to Kerr-Newman solutions. An important feature of the Kerr-Newman black holes is that they satisfy relation m² ? a² + e² where m is the mass of the black hole, e is its charge, $\text{a =}\text{J}\text{m}$ is its angular momentum per unit mass and geometrized units G = c = 1 are used. (For m² <a² + e² the Kerr-Newman solutions describe naked singularities.) In this paper, we test the validity of the above conjectures on gravitational collapse by attempting to create a spacetime with m² <a² + e² starting with a Kerr-Newman black hole with m² = a² + e². Such a spacetime would either have to be a new black hole solution or a “naked singularity,” in violation of the above conjectures. In the first gedanken experiment we attempt to make the black hole capture a test particle having large charge and orbital angular momentum compared with energy. In the second gedanken experiment we attempt to drop into the black hole a spinning test body having large spin to mass ratio. In both cases we find that bodies which would cause violation of m² ? a² + e² will not be captured by the black hole, and, thus, we cannot obtain m² <a² + e², although we can come arbitrarily close in the sense that m² = a² + e² can be maintained in these processes.     

Preequilibrium GDR excitation and entrance channel angular momentum effects

The energy spectra of the γ-rays emitted in the ³⁵Cl + ⁹²Mo reaction at incident energy E = 260 MeV were measured in coincidence with the ejectiles produced in dissipative reaction events. The cumulative energy spectrum of the γ-rays coming from the decay of the ejectiles was calculated within the statistical model and its comparison to the experimental spectrum evidences an excess in the data for E _γ = 8 to 12 MeV. Such an excess, fitted with a Lorentz curve, is attributed to the preequilibrium GDR γ-decay of the intermediate dinuclear system. The centroid energy of the Lorentz curve corresponds to a dipole oscillation along the symmetry axis of the system and its width is found to be comparable to that of the ground state GDR low energy component of the deformed dinucleus. The small quantal dispersion Δ? = (10.3 ± 0.1)? of the entrance channel angular momentum, determined by analysing the dissipative fragment angular distribution in the framework of the Strutinsky model, is suggested to limit the broadening of the preequilibrium GDR width.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

Distribution of Energy-Momentum in a Schwarzschild-Quintessence Space-Time Geometry

An analysis of the energy-momentum localization for a four-dimensional Schwarzschild black hole surrounded by dark energy in the form of quintessence is presented in order to provide expressions for the distributions of energy and momentum. The calculations are performed by using the Landau–Lifshitz and the Weinberg energy-momentum complexes. It is shown that all the momenta vanish, while the expression for the energy depends on the mass M of the black hole, the state parameter w _q and the normalization factor c. The special case of $w_{q}=-\frac{2}{3}$ is studied and some limiting cases are examined.     

Effective Values of Komar Conserved Quantities and Their Applications

We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effective values of mass and angular momentum are then used to derive an identity (K_c^m=2STK_{\chi^{\mu}}=2ST) which relates the Komar conserved charge (K_c^mK_{\chi^{\mu}}) corresponding to the null Killing vector (χ ^μ ) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.     

M-dependence of collisional transfer of rotational energy in OCS mixtures

Collision-induced transitions between rotational levels of OCS in the ground vibrational state have been investigated by steady-state microwave double resonance, with the M sublevels separated by a Stark field. The (2 ← 1)_P-(1 ← 0)_S, (3 ← 2)_P-(1 ← 0)_S, and (4 ← 3)_P-(1 ← 0)_S systems have been studied for pure OCS and for mixtures with excess CH₃OH, He, and H₂. For four-level systems having dipolar connections (ΔJ = 1; ΔM = 0, ± 1; parity ± ? ?) between pump and signal levels, it is found for OCS and the OCS-CH₃OH mixture that the dipole-type ΔJ = 1 transitions always dominate the collisional transfer, but for the OCS-He and OCS-H₂ mixtures that ΔJ = 2 quadrupole-type transitions are dominant. For all four collision partners, significant ΔJ = 2 and ΔJ = 3 collisional transfer is observed in some systems, indicating the presence of high-order terms in the collisional interaction.     

Gravitational radiation from an extreme Kerr black hole

We analytically investigate gravitational radiation induced by a test particle falling into an extreme Kerr black hole. Assuming the radiation is dominated by the infinite sequence of quasi-normal modes which has the limiting frequencym/(2M), wherem is an azimuthal eigenvalue andM is the mass of the black hole. we find the radiated energy diverges logarithmically in time. Then we evaluate the back reaction to the black hole by appealing to the energy and angular momentum conservation laws. We find the radiation has a tendency to increase the ratio of the angular momentum to mass of the black hole, which is completely different from the non-extreme case, while the contribution of the test particle is to decrease it.     

A measurement of the ratio GE/GE of the proton form factors at very low momentum transfer

The ratioμG _EG_M of the proton form factors was determined by measuring the electron scattering cross section of the proton relative to that of¹²C. Data were taken atq ²=0.09, 0.16, 0.25, and 0.36 fm^?2, yielding a weighted mean ofμG _E/G_M=1.01±0.03.     

Observation of a spin 4 neutral meson with 2 GeV mass decaying in π° π°

The invariant mass spectrum of neutral meson states from π^?p interactions at 40 GeV/c incident momentum has been investigated in a high statistics experiment performed at the 70 GeV IHEP accelerator. To detect the high energy photons coming from the produced neutral states, a hodoscope spectrometer with a computer on-line was used. A clear structure on the mass spectrum of dipions produced in the reaction π^?p→π°π°n is observed at 2 GeV. The decay angular distributions show in this mass region the variation with mass typical of a state with a spin J = 4. The mass of the observed meson is found to be M = (2020±30)MeV and the estimate of the full width is (180±60) MeV.     

Instabilities of massive scalar perturbations of a rotating black hole

We study the stability of a massive scalar field in the exterior metric of a rotating Kerr black hole. An argument based on energy conservation shows, under some strong technical assumptions, that unstable normal modes exist. These unstable modes can be interpreted as wave packets in bound, superradiant orbits. A JWKB estimate of the fastest growth rate gives 10^?7M^?1exp(?1.84Mμ) in the case Mμ ? 1, where M is the mass of the hole and μ is the mass of the field. The existence of unstable normal modes has significant implications for quantum particle creation by rotating black holes, which we attempt to assess.