In this work we determine that the Hawking temperature of black holes possesses a purely topological nature. We find a very simple but powerful formula, based on a topological invariant known as the Euler characteristic, which is able to provide the exact Hawking temperature of any twodimensional black hole -and in fact of any metric that can be dimensionally reduced to two dimensions -in any given coordinate system, introducing a covariant way to determine the temperature only using virtually trivial computations. We apply the topological temperature formula to several known black hole systems as well as to the Hawking emission of solitons of integrable equations.

We study the ultrafast Kerr effect and high-harmonic generation in type-II superconductors by formulating a new model for a time-varying electromagnetic pulse normally incident on a thin-film superconductor. It is found that type-II superconductors exhibit exceptionally large χ (3) due to the progressive destruction of Cooper pairs, and display high-harmonic generation at low incident intensities, and the highest nonlinear susceptibility of all known materials in the THz regime. Our theory opens up new avenues for accessible analytical and numerical studies of the ultrafast dynamics of superconductors.

The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution, is perhaps the most elegant and universal framework developed in theoretical physics, second only to the standard model of particle physics. In this Tutorial, we retrace the steps that led to the creation of such a remarkable framework, discuss its foundations, and present some of the classical examples of problems that can be solved using the path integral formalism, as a way to introduce the readers to the topic and help them get familiar with the formalism. Then, we focus our attention on the use of path integrals in optics and photonics and discuss in detail how they have been used in the past to approach several problems, ranging from the propagation of light in inhomogeneous media to parametric amplification and quantum nonlinear optics in arbitrary media. To complement this, we also briefly present the path integral Monte Carlo method, as a valuable computational resource for condensed matter physics, and discuss its potential applications and advantages if used in photonics.

Based on an investigation into the near-horizon geometrical description of black hole spacetimes (the so-called (r, t) sector), we find that the surface area of the event horizon of a black hole is mirrored in the area of a newly-defined surface, which naturally emerges from studying the intrinsic curvature of the (r, t) sector at the horizon. We define this new, abstract surface for a range of different black holes and show that, in each case, the surface encodes event horizon information, despite its derivation relying purely on the (r, t) sector of the metrical description. This is a very surprising finding as this sector is orthogonal to the sector explicitly describing the horizon geometry. Our results provide new evidence supporting the conjecture that black holes are, in some sense, fundamentally two-dimensional. As black hole entropy is known to be proportional to horizon area, a novel two-dimensional interpretation of this entropy may also be possible.

We consider the effect of orbital angular momentum (OAM) on localized waves in optical fibers using theory and numerical simulations, focusing on splash pulses and focus wave modes. For splash pulses, our results show that they may carry OAM only up to a certain maximal value. We also examine how one can optically excite these OAM-carrying modes, and discuss potential applications in communications, sensing, and signal filtering.

In this work, we present a new interpretation of the only static vacuum solution of Einstein’s field equations with planar symmetry, the Taub solution. This solution is a member of the AIII class of metrics, along with the type D Kasner solution. Various interpretations of these solutions have been put forward previously in the literature, however, some of these interpretations have suspect features and are not generally considered physical. Using a simple mathematical analysis, we show that a novel interpretation of the Taub solution is possible and that it naturally emerges from the radial, near-singularity limit of negative-mass Schwarzschild spacetime. A new, more transparent derivation is also given, showing that the type D Kasner metric can be interpreted as a region of spacetime deep within a positive-mass Schwarzschild black hole. The dual nature of this class of A-metrics is thereby demonstrated.

We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of integrability, we show that it is possible to associate a real spacetime metric tensor which defines a curved surface, perceived by the classical and quantum fluctuations propagating on the soliton. By defining proper scalar invariants of the associated Riemannian geometry, and introducing the conformal anomaly, we are able to determine the Hawking temperatures and entropies of the fundamental solitons of the nonlinear Schrödinger, KdV and sine-Gordon equations. The mechanism advanced here is simple, completely universal and can be applied to all integrable equations in two dimensions, and is easily applicable to a large class of black holes of any dimensionality, opening up totally new windows on the quantum mechanics of solitons and their deep connections with black hole physics. their energy and mass is radiated away. This outward flux of radiation can be measured at infinity with a characteristic temperature known as the Hawking temperature [4]. Since Hawking's seminal work other thermodynamical properties of black holes have been described in detail, perhaps most significantly the entropy, which in four dimensions turns out to be proportional to the black hole surface area, an observation due to Bekenstein which predates Hawking's work [5]. This result has had major implications for modern physics, and as its study requires a combination of general relativity, quantum field theory, thermodynamics and information theory, it is considered a promising route towards a deeper understanding of quantum gravity [6].Much literature has been devoted, experimentally and theoretically [7][8][9][10][11], to the possible detection of Hawking radiation in classical or semiclassical analogue systems (typically optical, hydrodynamical or based on quantum condensates), due to the considerable (and probably insurmountable) difficulty of detecting it in a real astrophysical setting. In light of Salam and Strathdee's conjecture about the equivalence between solitons and black holes, it is suggestive to imagine that the exact analogue of Hawking radiation can be directly seen in the physics of solitons. It is however important to establish a precise, unambiguous mathematical and physical connection between the two objects, something that we shall do in the present paper for the first time.In this paper, following Salam's steps, we push the analogy between black holes and solitons to a new level. We show that any soliton solution of a two-dimensional integrable nonlinear evolution equation potentially possesses a Hawking temperature which is determined solely by the geometrical properties of an internal surface connected to the specific soliton, called the integrable surface. The curvature of this surface is turned into Hawking radiation due to the existence of a quantum anomaly, well-known in two-dimens...

No abstract