Islands and Page curves in charged dilaton black holes

We study the Page curve for eternal Garfinkle–Horowitz–Strominger dilaton black holes in four dimensional asymptotically flat spacetime by using the island paradigm. The results demonstrate that without the island, the entanglement entropy of Hawking radiation is proportional to time and becomes divergent at late times. While taking account of the existence of the island outside the event horizon, the entanglement entropy stops growing at late times and eventually reaches a saturation value. This value is twice of the Bekenstein–Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the stringy coefficient n and charge Q on the Page time and the scrambling time respectively. For the non-extremal case, the influence of the coefficient n on them is small compared to the influence of the charge Q. However, for the extremal case, the Page time and the scrambling time become divergent or near vanishing. This implies the island paradigm needs further investigation.

Analog Particle Production Model for General Classes of Taub-NUT Black Holes

We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e., a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the particle and energy spectra is thermal at late times and that particle production is suppressed by the NUT parameter. We also compute the radiation spectrum in the rotating, electrically charged (Kerr–Newman) Taub-NUT scenario, and the extremal case, showing, explicitly, how these parameters affect the outgoing particle and energy fluxes.

Islands in linear dilaton black holes

We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

Extremal p-Adic L-Functions

In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations to automorphic forms on arbitrary groups. In the classical setting of GL2 over Q, this allows for us to construct the p-adic L-function in the so far uncovered extremal case, which arises under the unlikely hypothesis that p-th Hecke polynomial has a double root. Although Tate’s conjecture implies that this case should never take place for GL2/Q, the obvious generalization does exist in nature for Hilbert cusp forms over totally real number fields of even degree, and this article proposes a method that should adapt to this setting. We further study the admissibility and the interpolation properties of these extremal p-adic L-functionsLpext(f,s), and relate Lpext(f,s) to the two-variable p-adic L-function interpolating cyclotomic p-adic L-functions along a Coleman family.

Restriction formula and subadditivity property related to multiplier ideal sheaves

We give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

Deflection of light by a rotating black hole surrounded by “quintessence”

We present a detailed analysis of a rotating black hole surrounded by “quintessence.” This solution represents a fluid with a constant equation of state, [Formula: see text], which can for example describe an effective warm dark matter fluid around a black hole. We clarify the conditions for the existence of such a solution and study its structure by analyzing the existence of horizons as well as the extremal case. We show that the deflection angle produced by the black hole depends on the parameters [Formula: see text] which need to obey the condition [Formula: see text] because of the weak energy condition, where [Formula: see text] is an additional parameter describing the hair of the black hole. In this context, we found that for [Formula: see text] (consistent with warm dark matter) and [Formula: see text], the deviation angle is larger than that in the Kerr space–time for direct and retrograde orbits. We also derive an exact solution in the case of [Formula: see text].

Collision of particles near charged MSW black hole in 2 + 1 dimensions

Here, we explore the dynamics of particle near the horizon of charged Mandal–Sengupta–Wadia (MSW) black hole in 2 + 1 dimensions. We analyze angular momentum and potential energy for null and time-like geodesics. We also appraise the high center-of-mass energy of coming particles from rest at infinity near the horizon of the charged MSW black hole in 2 + 1 dimension for the extremal case. Finally, we study the ISCO and MBCO radii for this type of black hole.

The index of reducibility of powers of a standard parameter ideal

In this paper, we study the index of reducibility of powers of a standard parameter ideal. An explicit formula is proved for the extremal case. We apply the main result to compute Hilbert polynomials of socle ideals of standard parameter ideals.

Observing the contour profile of a Kerr–Sen black hole

In this paper, the shadow and the corresponding naked singularity cast by a Kerr–Sen black hole are studied. It is found that the shadow of a rotating black hole would be a dark zone surrounded by a deformed circle, and the shadow is distorted more away from a circle when the black hole approaches the extremal case. Besides, it is shown that the mean radius of the shadow decreases and distortion parameter increases with the increasing of charge, respectively. However, the mean radius and the distortion parameter vary complicatedly with the change of spin parameter. In the beginning, both observables decrease rapidly with the increasing of specific angular momentum, nevertheless, they increase slightly in the latter part. These results show that there would be a significant effect of the spin on the shadows, which would be of great importance for probing the nature of the black hole.

Cartesian product graphs and k-tuple total domination

A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S; the minimum size of a kTDS is denoted ?xk,t(G). We give a Vizing-like inequality for Cartesian product graphs, namely ?xk,t(G) ?xk,t(H)? 2k?xk,t(G_H) provided ?xk,t(G) ? 2k?(G) holds, where ? denotes the packing number. We also give bounds on ?xk,t(G_H) in terms of (open) packing numbers, and consider the extremal case of ?xk,t(Kn_Km), i.e., the rook?s graph, giving a constructive proof of a general formula for ?x2,t(Kn_Km).