Ultra-spinning Chow’s black holes in six-dimensional gauged supergravity and their properties

By taking the ultra-spinning limit as a simple solution-generating trick, a novel class of ultra-spinning charged black hole solutions has been constructed from Chow’s rotating charged black hole with two equal-charge parameters in six-dimensional $$ \mathcal{N} $$ N = 4 gauged supergravity theory. We investigate their thermodynamical properties and then demonstrate that all thermodynamical quantities completely obey both the differential first law and the Bekenstein-Smarr mass formula. For the six-dimensional ultra-spinning Chow’s black hole with only one rotation parameter, we show that it does not always obey the reverse isoperimetric inequality, thus it can be either sub-entropic or super-entropic, depending upon the ranges of the mass parameter and especially the charge parameter. This property is obviously different from that of the six-dimensional singly-rotating Kerr-AdS super-entropic black hole, which always strictly violates the RII. For the six-dimensional doubly-rotating Chow’s black hole but ultra-spinning only along one spatial axis, we point out that it may also obey or violate the RII, and can be either super-entropic or sub-entropic in general.

Regular Bardeen Black Holes in Anti-de Sitter Spacetime versus Kerr Black Holes through Particle Dynamics

In this work, test particle dynamics around a static regular Bardeen black hole (BH) in Anti-de Sitter spacetime has been studied. It has been shown for neutral test particles that parameters of a regular Bardeen black hole in Anti-de Sitter spacetime can mimic the rotation parameter of the Kerr metric up to the value a≈0.9 providing the same innermost stable circular orbit (ISCO) radius. We have also explored the dynamics of magnetized particles with a magnetic dipole moment around a magnetically charged regular Bardeen black hole in Anti-de Sitter spacetime. As a realistic astrophysical scenario of the study, we have treated neutron stars orbiting a supermassive black hole (SMBH), in particular, the magnetar PSR J1745-2900 orbiting Sgr A* with the parameter β=10.2, as magnetized test particles. The magnetized particles dynamics shows that the parameter β, negative values of cosmological constant and magnetic charge parameter of the central BH cause a decrease in the ISCO radius. We have compared the effects of the magnetic charge of the Bardeen BH with the spin of rotating Kerr BH and shown that magnetic charge parameter can mimic the spin in the range a/M≃(0,0.7896) when Λ=0 at the range of its values g/M≃(0,0.648).

Nonlinear processes in the bunched electron beams of high-power klystrons and the limits of analytical and one-dimensional numerical models applicability for their analysis.

We present the results of a comparative theoretical analysis of the electron beam bunching in a single-stage klystron amplifier using analytical models, a one-dimensional disk program, and a two-dimensional program. Data on the influence of various one-dimensional and two-dimensional nonlinear effects on the efficiency of electron beam bunching at different values of the space charge parameter and the modulation amplitude are presented. The limits of applicability of analytical and one-dimensional numerical models for electron beam bunching analysis in high-power klystron amplifiers are found.

Nepheline solid solution compositions: stoichiometry revisited, reviewed, clarified and rationalised

Molecular formulae used to recalculate nepheline analyses generally have different numbers of oxygens (e.g. NaAlSiO4 (Ne), KAlSiO4, (Ks), CaAl2Si2O8 (An) and SiO2 (Q)). A 32 oxygen cell has 16 T cations and 8 cavity sites, but ideal nepheline stoichiometry is not necessarily followed. Ca end-member □CaCaAl2Si2O4 (CaNe) and excess silica end-member □SiSi2O4 (Q’) calculation requires inclusion of both vacancy species as cavity cation values. Q’ parameter calculations can involve different assumptions and four parameters are described: Qxs; QSi; Q(Si–Al); and Qcavity; these should have closely similar values for high-quality, stoichiometric analyses. Representative published compositions are recalculated to assess whether authors followed ideal nepheline stoichiometry. Phenocrysts from peralkaline rocks and nephelinites typically exhibit Al deficiencies reflected in negative Δ(Al – cavity cation) parameters (ΔAlcc), negative ‘normative’ corundum (Al2O3, Cn), and anomalously low or negative Qxs parameters; for such rock types Q(Si–Al) provides a better estimate of excess silica contents. A ΔT-site (cation charge) parameter (ΔTcharge), is closely coupled to ΔAlcc and end-member NaAlSiO4 has a ΔAlcc/ΔTcharge ratio of 1.4296; the derivation of this value is controlled by strict stuffed-tridymite, unit-cell constraints. Natural nephelines all contain excess silica with a mean ΔAlcc/ΔTcharge of ~1.134 reflecting their Si/Al ratio being > 1. Nepheline analyses with relatively low Al and Si and high Na (also Ca) contents are common; this might reflect the presence of small amounts (up to ~5%) of cancrinite as an alteration phase or perhaps even in solid solution. The compositions of alteration lamellae of Ca-rich cancrinite in altered nepheline phenocrysts in phonolites from the Marangudzi alkaline complex, Zimbabwe, are used to define diagnostic parameters for recognising such non-stoichiometry. These alteration lamellae formed hydrothermally from Ca-rich and K-poor fluids. An EXCEL file is provided to help researchers to standardise calculation of nepheline end-member molecular proportions.

Quasinormal Modes of Extended Gravity Black Holes

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

QUESTIONING THE RELEVANCE OF SOLUTION pH CALCULATION

A brief discussion on the unnecessary calculation of pH in solution was done, as the historical reasons for this need before the invention of commercial pH meter was widely diffused. An alternative approach for acid-base equilibrium evaluation was proposed, without approximation or need of application only for simple solutions. The central aspect for the new approach is the determination of equilibrium concentration of all chemical species in solution, including the strong acid or base concentration for adjusting of pH of solutions. Therefore, the proposed method allowed the calculation in a mixture, including several polyprotic systems. Two detailed examples were presented. The effective electrical charge parameter was formally defined.

Particle motion around generic black holes coupled to non-linear electrodynamics

We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.

A charged perfect fluid model with high compactness

A relativistic, static and spherically symmetrical stellar model is presented, constituted by a perfect charged fluid. This represents a generalization to the case of a perfect neutral fluid, whose construction is made through the solution to the Einstein-Maxwell equations proposing a form of gravitational potential $g_{tt}$ and the electric field. The choice of electric field implies that this model supports values of compactness$u=GM/c^2R\leq 0.5337972212$, values higher than the case without electric charge ($u\leq 0.3581350065$), being this feature of relevance to get to represent compact stars. In addition, density and pressure are positive functions, bounded and decreasing monotones, the electric field is a monotonously increasing function as well as satisfying the condition of causality so the model is physically acceptable. In a complementary way, the internal behavior of the hydrostatic functions and their values are obtained taking as a data the corresponding to a star of $1 M_\odot$,for different values of the charge parameter, obtaining an interval for the central density $\rho_c\approx (7.9545,2.7279) 10^{19}$ $ Kg/m^3$ characteristic of compact stars.

Effects of a brane world on gravitational time advancement

Solar System tests of a brane world, which is called DMPR model, were studied in recent works. The correction of DMPR model to the general relativity (GR) in the four-dimensional curved spacetime can be parametrized by a “tidal charge” parameter [Formula: see text]. The parameter [Formula: see text] in this model was obtained and improved as [Formula: see text] by the Earth–Mercury ranging. A new test of the DMPR model based on gravitational time advancement is proposed and investigated in this work. The advancement is a gravitational consequence on round-trip proper time duration of a photon. For ranging a distant spacecraft, it is shown that (1) the “tidal charge” parameter can make the advancement larger or smaller than the one of GR, depending on the sign of [Formula: see text]; (2) the superior conjunction (SC) and the inferior conjunction (IC) are all suitable for detecting the advancement; (3) the advancement can be complementary to the classical test of Shapiro time delay for detecting the brane world; and (4) the implementation of optical clocks and planetary laser ranging will provide more insights on the brane world model in the future.