Thermodynamic product formula for a Taub–NUT black hole

We derive various important thermodynamic relations of the inner and outer horizons in the background of the Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We compare these properties with the properties of the Reissner–Nordström black hole. We compute the area product, area sum, area subtraction, and area division of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From the area bound, we derive an entropy bound and an irreducible mass bound for both horizons. We further study the stability of such black holes by computing the specific heat for both horizons. It is shown that due to the negative specific heat, the black hole is thermodynamically unstable. All these calculations might be helpful in understanding the nature of the black hole entropy (both interior and exterior) at the microscopic level.     

Taub–NUT black holes in third order Lovelock gravity

We consider the existence of Taub–NUT solutions in third order Lovelock gravity with cosmological constant, and obtain the general form of these solutions in eight dimensions. We find that, as in the case of Gauss–Bonnet gravity and in contrast with the Taub–NUT solutions of Einstein gravity, the metric function depends on the specific form of the base factors on which one constructs the circle fibration. Thus, one may say that the independence of the NUT solutions on the geometry of the base space is not a robust feature of all generally covariant theories of gravity and is peculiar to Einstein gravity. We find that when Einstein gravity admits non-extremal NUT solutions with no curvature singularity at r=N$r=N$, then there exists a non-extremal NUT solution in third order Lovelock gravity. In 8-dimensional spacetime, this happens when the metric of the base space is chosen to be CP³${\mathbb{CP}}^3$. Indeed, third order Lovelock gravity does not admit non-extreme NUT solutions with any other base space. This is another property which is peculiar to Einstein gravity. We also find that the third order Lovelock gravity admits extremal NUT solution when the base space is T²×T²×T²$T^2\times T^2\times T^2$ or S²×T²×T²$S^2\times T^2\times T^2$. We have extended these observations to two conjectures about the existence of NUT solutions in Lovelock gravity in any even-dimensional spacetime.     

Cardy–Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

We derive a formula for the entropy for a multicomponent coupled fluid, which under special conditions reduces to the Cardy–Verlinde form relating the entropy of a closed FRW universe to its energy together with its Casimir energy. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and also modified gravity is included in terms of its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy–Verlinde formula corresponding to the 2d CFT entropy in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all known four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that, except from some special cases of Type II and Type IV singularities, the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter universe.     

Generalized Kerr–NUT–de Sitter metrics in all dimensions

We classify all spacetimes with a closed rank-2 conformal Killing–Yano tensor. They give a generalization of Kerr–NUT–de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness conditions of the Einstein metrics over compact Riemannian manifolds.     

A Lorentz-covariant interacting electron–photon system in one space dimension

Letters in Mathematical Physics - A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one...     

A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics

The Euler–Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler–Maclaurin summation formula and the Poisson summation formula as special cases. By making use of the modified formula, a possible numerical summation method is obtained and the remainder can be controlled. The modified formula is also generalized from one dimension to two dimensions. Approximate expressions of partition functions of a classical particle in square well in 1D and 2D and that of a quantum rotator are obtained with error estimation.     

Very special relativity in curved space–times

The generalization of Cohen and Glashow's very special relativity to curved space–times is considered. Gauging the SIM(2)$\mathit{SIM}(2)$ symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2)$\mathit{SIM}(2)$ invariant Lagrangians can always be constructed. For space–times with SIM(2)$\mathit{SIM}(2)$ holonomy, they describe chiral fermions propagating freely as massive particles.     

Relativistic spin-zero bosons in a Som–Raychaudhuri space–time

We investigate the Duffin–Kemmer–Petiau equation for spin-zero bosons in a (\(3+1\))-dimensional Som–Raychaudhuri space–time. We establish the covariant Duffin–Kemmer–Petiau equation in this curved space–time for the so-called oscillator and we include interaction with a scalar potential. We determine eigenfunctions and the corresponding eigenvalues for the oscillator with the Cornell potential. We investigate the effect of the space–time’s parameters, oscillator’s frequency and the Cornell potential’s parameters on the wave functions.     

On the origin of the phase–space diffusion limit in (dis)ordered protein aggregation

Derivation of a phase–space diffusion limit (D-L) allows to obtain a useful formula for a characteristic width of the macroion-channeling filter, controlling model (dis)ordered protein aggregations in a non-ideal aqueous solution. The channel’s width is estimated at the order of an inner half-width of the Stern-type double layer circumventing the growing object and depends in turn on an interplay of the local thermal and electrostatic conditions. The interfacial channeling effect manifests at the edge of biomolecular hydration-duration dependent (non)Markovianity of the system. The interface vs. solution aggregation late-time dynamics are discussed in such local (non)isothermal context with the aim to suggest their experimental assessment.     

A new limit for the noncommutative space–time parameter

The spectrum of the hydrogen atom in the framework of noncommutative quantum mechanics is studied and the related phenomenology is presented. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for this parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for this parameter.     

A Pfaffian formula for the monomer–dimer model on surface graphs

We consider the monomer–dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function, which generalises the one obtained by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) for graphs embedded in the disc. Our proof is based on an extension of a bijective method mentioned in Giuliani et al. (2016), together with the Pfaffian formula for the dimer partition function of Cimasoni–Reshetikhin (Commun Math Phys 275(1):187–208, 2007).     

A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat–Barthelemy–Vespignani (BBV) networks. First, we derived mean-field equations for rumor propagation based on the strength of the nodes in the propagation network. We then analyzed the stability of the model to determine whether a propagation threshold existed in the BBV networks. We also conducted numerical simulations of the BBV networks and found that rumors propagate more slowly in BBV networks than in unweighted networks. The numerical simulation results also demonstrated that as the forgetting rate increases, the rumor’s influence decreases in both BBV networks and unweighted networks. Finally, the simulation results confirmed that a threshold exists for rumor propagation in BBV networks, but that it was independent of the value of the stifling rate.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

Surface modification of bulk n-InAs (111)A etched in bromine–methanol

X-ray photoelectron spectroscopy, field emission scanning electron microscopy, Raman and photoluminescence spectroscopy were used to evaluate the surface properties of n-type InAs (111)A etched in a 1% Br–methanol solution. Etching completely removes the native oxides from the surface and enhances the photoluminescence response. The adsorption of bromine onto the InAs surface leads to the formation of In–Br_x and As–Br_x bonds (x = 1, 2, 3) as inferred from changes in the In 3d_3/2;5/2 and As 3d core level binding energies. The etch rate is found to decrease due to strong anisotropic effects and the high volatility of the bromine species. A 1 min Br–methanol etch was found to enhance the photoluminescence intensity by a factor of 3, probably due to a reduction in the surface state density upon de-oxidation of the surface. This is thought to be due to reductions in the surface state density. The presence of native oxides enhances both the surface accumulation layer and the surface state density.     

Multipole source-configuration of active sound absorption(ASA)in space sound field

In this paper,the energy formulas of Active Sound Absorption(ASA)in space sound field have been derived from the basic sound waveequation,and ASA including the relevant conditions of multipole secon-dary-source,such as monopole,dipole and tripole,etc.,has been dis-cussed.On the basis of the discussion,it has pointed out that dipole sec-ondary-configuration (DAA)is the simplest attenuator.The results of theexperiments done in anechoic chamber have shown that DAA has effectiveperformances which just provide the fundation and feasibility of practicaluse.     

Quantum fluctuations in planar domain wall space–times: A possible origin of primordial preferred direction

We study the gravitational effects of a planar domain wall on quantum fluctuations of a massless scalar field during inflation. By obtaining an exact solution of the scalar field equation in de-Sitter space, we show that the gravitational effects of the domain wall break the rotational invariance of the primordial power spectrum without affecting the translational invariance. The strength of rotational violation is determined by one dimensionless parameter β, which is a function of two physical parameters, the domain wall surface tension σ and cosmological constant Λ. In the limit of small β, the leading effect of rotational violation of the primordial power spectrum is scale-invariant.     

Microstructural evolution in Al–Mn–Cu–(Be) alloys

This study investigates the effects of alloying elements on the microstructural evolution of Al-rich Al–Mn–Cu–(Be) alloys during solidification, and subsequent heating and annealing. The samples were characterised using scanning electron microscopy, energy dispersive X-ray spectroscopy, synchrotron X-ray diffraction, time-of-flight secondary-ion mass spectroscopy, and differential scanning calorimetry. In the ternary Al₉₄Mn₃Cu₃ (at%) alloy, the phases formed during slower cooling (≈1?K?s^?1) can be predicted by the known Al–Mn–Cu phase diagram. The addition of Be prevented the formation of Al₆Mn, decreased the fraction of τ₁-Al₂₉Mn₆Cu₄, and increased the fraction of Al₄Mn. During faster cooling (≈1000?K?s^?1), Al₄Mn predominantly formed in the ternary alloy, whereas, in the quaternary alloys, the icosahedral quasicrystalline phase dominated. Further heating and annealing of the alloys caused an increase in the volume fractions of τ₁ in all alloys and Be₄Al (Mn,Cu) in quaternary alloys, while fractions of all other intermetallic phases decreased. Solidification with a moderate cooling rate (≈1000?K?s^?1) caused considerable strengthening, which was reduced by annealing for up to 25% in the quaternary alloys, while hardness remained almost the same in the ternary alloy.