Periods of generalized Fermat curves

Let $k,n\ge 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface S that admits a subgroup of conformal automorphisms $H\le \text{Aut}(S)$ isomorphic to ${\mathbb{Z}}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\stackrel{?}{\mathbb{C}}$ and has $n+1$ branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.     

Statistical Modeling of the Seismic Moments via Mathai Distribution

Mathai’s pathway model is playing an increasingly prominent role in statistical distributions. As a generalization of a great variety of distributions, the pathway model allows the studying of several non-linear dynamics of complex systems. Here, we construct a model, called the Pareto–Mathai distribution, using the fact that the earthquakes’ magnitudes of full catalogues are well-modeled by a Mathai distribution. The Pareto–Mathai distribution is used to study artificially induced microseisms in the mining industry. The fitting of a distribution for entire range of magnitudes allow us to calculate the completeness magnitude (Mc). Mathematical properties of the new distribution are studied. In addition, applying this model to data recorded at a Chilean mine, the magnitude Mc is estimated for several mine sectors and also the entire mine.     

Particle collisions near a three-dimensional warped AdS black hole

In this paper we consider the warped \(\hbox {AdS}_{3}\) black hole solution of topologically massive gravity with a negative cosmological constant, and we study the possibility that it acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon, which is known as the Bañnados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum \((L_c)\) of the particle decreases when the warping parameter(\(\nu \)) increases. Also, we show that despite the particle with \(L_c\) being able to exist for certain values of the conserved energy outside the horizon, it will never reach the event horizon; therefore, the black hole cannot act as a particle accelerator with arbitrarily high CM energy on the event horizon. However, such a particle could also exist inside the outer horizon, with the BSW process being possible on the inner horizon. On the other hand, for the extremal warped \(\hbox {AdS}_{3}\) black hole, the particle with \(L_c\) and energy E could exist outside the event horizon and, the CM energy blows up on the event horizon if its conserved energy fulfills the condition \(E^{2}>\frac{(\nu ^{2}+3)l^{2}}{3(\nu ^{2}-1)}\), with the BSW process being possible.     

Dirac quasinormal modes of two-dimensional charged dilatonic black holes

Following some recent unexpected hints of neutron production in high-voltage atmospheric discharges, we present a measurement of the neutron flux in plasma discharges in electrolytic cells. We use two different types of neutron detectors, polyallyl diglycol carbonate (PADC, aka CR-39) tracers and indium disks. At 95 % C.L. we provide an upper limit of 1.5 neutrons cm \(^{-2}\)  s \(^{-1}\) for the thermal neutron flux at \({\approx } 5\) cm from the center of the cell. Allowing for a higher energy neutron component, the largest allowed flux is 64 neutrons cm \(^{-2}\)  s \(^{-1}\) . This upper limit is two orders of magnitude smaller than the signal previously claimed in an electrolytic cell plasma discharge experiment. Furthermore the behavior of the CR-39 is discussed to point out possible sources of spurious signals.     

Hawking radiation and propagation of massive charged scalar field on a three-dimensional Gödel black hole

In this paper we consider the three-dimensional Gödel black hole as a background and we study the vector particle tunneling from this background in order to obtain the Hawking temperature. Then, we study the propagation of a massive charged scalar field and we find the quasinormal modes analytically, which turns out be unstable as a consequence of the existence of closed time-like curves. Also, we consider the flux at the horizon and at infinity, and we compute the reflection and transmission coefficients as well as the absorption cross section. Mainly, we show that massive charged scalar waves can be superradiantly amplified by the three-dimensional Gödel black hole and that the coefficients have an oscillatory behavior. Moreover, the absorption cross section is null at the high frequency limit and for certain values of the frequency.     

Fermionic greybody factors of two and five-dimensional dilatonic black holes

We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein–Gordon and Chandrasekhar–Dirac equation are used to probe the classical timelike naked singularity. We show that the classical singularity is felt even by our quantum probes. Next, we use loop quantization to resolve a singularity hidden beneath the horizon. The singularity is resolved in this case.     

Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

In this work we consider black hole solutions to Einstein's theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles, where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black holes and find that both first- and second-order phase transitions can occur in the canonical ensemble while, for the grand canonical ensemble, Hawking–Page and second-order phase transitions are allowed.     

Quasinormal modes of non-Abelian hyperscaling violating Lifshitz black holes

We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent \(z=2\) and hyperscaling violating exponent \(\tilde{\theta }>-2\). Also, we obtain numerically the quasinormal frequencies for different values of the dynamical exponent and the hyperscaling violating exponent by using the improved asymptotic iteration method.