Pi from the sky

A null test of general relativity from a population of gravitational wave observations
Carl-Johan Haster
Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant π. Allowing π to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of π=3.115+0.048−0.088, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable π test robust against simulated beyond-GR effects.
Read more at https://arxiv.org/abs/2005.05472

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Hawking for beginners

A dimensional analysis activity to perform in the classroom
Jorge Pinochet
In this paper we present a simple dimensional analysis exercise that allows us to derive the equation for the Hawking temperature of a black hole. The exercise is intended for high school students, and it is developed from a chapter of Stephen Hawking’s bestseller A Brief History of Time.
Read more at https://arxiv.org/pdf/2004.11850.pdf

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Exploring Gravitational Lensing

Einstein’s derivation of the lensing equation, solution, and amplification in AEA 62-275 (Albert Einstein Archives, The Hebrew University of Jerusalem, Israel)

Tilman Sauer, Tobias Schütz
In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein’s manuscripts.
Read more https://arxiv.org/pdf/1905.07174.pdf

The black hole fifty years after: Genesis of the name

Ann Ewing’s article in 1964 where the term Black Hole is published for the first time

Carlos A. R. Herdeiro, José P. S. Lemos
Black holes are extreme spacetime deformations where even light is imprisoned. There is an extensive astrophysical evidence for the real and abundant existence of these prisons of matter and light in the Universe. Mathematically, black holes are described by solutions of the field equations of the theory of general relativity, the first of which was published in 1916 by Karl Schwarzschild.
Another highly relevant solution, representing a rotating black hole, was found by Roy Kerr in 1963. It was only much after the publication of the Schwarzschild solution, however, that the term black hole was employed to describe these objects. Who invented it?
Conventional wisdom attributes the origin of the term to the prominent North American physicist John Wheeler who first adopted it in a general audience article published in 1968. This, however, is just one side of a story that begins two hundred years before in an Indian prison colloquially known as the Black Hole of Calcutta.
Robert Dicke, also a distinguished physicist and colleague of Wheeler at Princeton University, aware of the prison’s tragedy began, around 1960, to compare gravitationally completely collapsed stars to the black hole of Calcutta. The whole account thus suggests reconsidering who indeed coined the name black hole and commends acknowledging its definitive birth to a partnership between Wheeler and Dicke.
Read more at https://arxiv.org/pdf/1811.06587.pdf

Relativistic spring-mass system

Rodrigo Andrade e Silva, Andre G. S. Landulfo, George E. A. Matsas, Daniel A. T. Vanzella

The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative of it. It is usually assumed and galvanized in textbooks that the equation of motion of a relativistic harmonic oscillator is given by the same equation as the nonrelativistic one with the mass M at the tip multiplied by the relativistic factor 1/(1−v2/c2)1/2. Although the solution of such an equation may depict some physical systems, it does not describe, in general, one-dimensional relativistic spring-mass oscillators under the influence of elastic forces. In recognition to the importance of such a system to physics, we fill a gap in the literature and offer a full relativistic treatment for a system composed of a spring attached to an inertial wall, holding a mass M at the end.

Read more at https://arxiv.org/pdf/1810.13365.pdf

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…
Read more at https://arxiv.org/pdf/1809.00355.pdf

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.
Read more at https://arxiv.org/pdf/1808.01507.pdf

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.
Read more at https://arxiv.org/pdf/1808.05121.pdf