Snellius meets Schwarzschild

Refraction of brachistochrones and time-like geodesics
snellHeinz-Jürgen Schmidt
The brachistochrone problem can be solved either by variational calculus or by a skillful application of the Snellius’ law of refraction. This suggests the question whether also other variational problems can be solved by an analogue of the refraction law. In this paper we investigate the physically interesting case of free fall in General Relativity that can be formulated as a variational problem w. r. t. proper time. We state and discuss the corresponding refraction law for a special class of spacetime metrics including the Schwarzschild metric…

What Is a Black Hole?

Erik Curiel
Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields.

The Hawking temperature, the uncertainty principle and quantum black holes


A static black hole. The horizon (H ) is at a distance RS from the singularity (S).

Jorge Pinochet
In 1974, Stephen Hawking theoretically discovered that black holes emit thermal radiation and have a characteristic temperature, known as the Hawking temperature. The aim of this paper is to present a simple heuristic derivation of the Hawking temperature, based on the Heisenberg uncertainty principle. The result obtained coincides exactly with Hawking’s original finding. In parallel, this work seeks to clarify the physical meaning of Hawking’s discovery. This article may be useful as pedagogical material in a high school physics course or in an introductory undergraduate physics course.


The End of Spacetime

Nima Arkani-Hamed is a theoretical physicist with broad interests in high-energy physics and cosmology. He was educated at Toronto and Berkeley, held a postdoctoral fellowship at SLAC National Accelerator Laboratory, and was a professor of physics at Berkeley and Harvard before joining the Institute for Advanced Study in 2008. He was an inaugural recipient of the Fundamental Physics Prize in 2012, and was one of six physicists featured in the documentary “Particle Fever” in 2014.


Gravitational Waves: A New Astronomy

Luc Blanchet
Contemporary astronomy is undergoing a revolution, perhaps even more important than that which took place with the advent of radioastronomy in the 1960s, and then the opening of the sky to observations in the other electromagnetic wavelengths. The gravitational wave detectors of the LIGO/Virgo collaboration have observed since 2015 the signals emitted during the collision and merger of binary systems of massive black holes at a large astronomical distance. This major discovery opens the way to the new astronomy of gravitational waves, drastically different from the traditional astronomy based on electromagnetic waves. More recently, in 2017, the detection of gravitational waves emitted by the inspiral and merger of a binary system of neutron stars has been followed by electromagnetic signals observed by the γ and X satellites, and by optical telescopes. A harvest of discoveries has been possible thanks to the multi-messenger astronomy, which combines the information from the gravitational wave with that from electromagnetic waves. Another important aspect of the new gravitational astronomy concerns fundamental physics, with the tests of general relativity and alternative theories of gravitation, as well as the standard model of cosmology.