"Black holes ain't so black": An introduction to the great discoveries of Stephen Hawking

Between 1974 and 1975, Stephen Hawking revolutionized the world of physics by proposing that black holes have temperature, entropy, and evaporate gradually. The objective of this article is to offer a brief and updated introduction to these three remarkable results, employing only high school algebra and elementary physics. This article may be useful as pedagogical material in an introductory undergraduate physics course.Comment: 7 page

The Hawking temperature, the uncertainty principle and quantum black holes

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

Classical Tests of General Relativity Part I: Looking to the Past to Understand the Present

Einstein's theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as arousing substantial interest in topics related to gravitation. However, to understand present and future discoveries, it is convenient to look to the past, to the classical tests of GR, namely, the deflection of light by the Sun, the perihelion precession of Mercury, and the gravitational redshift of light. The objective of this work is to offer a non-technical introduction to the classical tests of GR. In this first part of the work, some basic concepts of relativity are introduced and the principle of equivalence is analysed. The second part of the article examines the classical tests.Comment: 9 pages, 6 figures. Physics Education 202

Three easy ways to the Hawking temperature

In this work, three heuristic derivations of the Hawking temperature are presented. The main characteristic of these derivations is their extreme simplicity, which makes them easily accessible to a wide and diverse audience.Comment: 5 pages, 1 figur

Graphic relation between amplitude and sound intensity level

We present a simple experiment that allows us to demonstrate graphically that the intensity of sound waves is proportional to the square of their amplitude, a result that is theoretically analysed in any introductory wave course but rarely demonstrated empirically. To achieve our goal, we use an audio signal generator that, when connected to a loudspeaker, produces sine waves that can be easily observed and measured using an oscilloscope. The measurements made with these instruments allow us to create a plot of amplitude versus sound intensity level, which verifies the mathematical relationship between amplitude and intensity mentioned above. Among the experimental errors, the plot obtained is in excellent agreement with what is theoretically expected.Comment: 6 pages, 5 figure

Einstein ring: Weighing a star with light

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon, known as gravitational lensing, has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known as Einstein ring. This model has recently allowed the measurement of the mass of a star, the white dwarf Stein 2051 B. The purpose of this work is to show an accessible and uptodate introduction to the effect of gravitational lensing, focused on the Einstein ring and the measurement of the mass of Stein 2051 B. The intended audience of this article are non-graduate students of physics and similar fields of study, and requires only basic knowledge of classical physics, modern physics, algebra and trigonometry.Comment: 10 pages, 5 figure

Five misconceptions about black holes

Given the great interest that black holes arouse among non-specialists, it is important to analyse misconceptions related to them. According to the author, the most common misconceptions are that: (1) black holes are formed from stellar collapse; (2) they are very massive; (3) they are very dense; (4) their gravity absorbs everything; and (5) they are black. The objective of this work is to analyse and correct these misconceptions. This article may be useful as pedagogical material in high school physics courses or in introductory courses in undergraduate physics.Comment: 8 page

Brown dwarfs and the minimum mass of stars

Stars form from large clouds of gas and dust that contract under their own gravity. The birth of a star occurred when a fusion reaction of hydrogen into helium has ignited in its core. The key variable that determines the formation of a star is mass. If the mass of the contracting cloud is below certain minimum value, instead of a star, a substelar object -- known as a brown dwarf -- will form. How much mass is required for a star to form? This article aims to answer this question by means of a simple heuristic argument. The found value is 0.016 solar masses, which is of the same order of magnitude as the accepted value 0.08 solar masses. This article may be useful as pedagogical material in an introductory undergraduate astronomy course.Comment: 9 pages, 2 figures. Physics Education 201

Classical Tests of General Relativity Part II: Looking to the Past to Understand the Present

The objective of this second part of the work is to present heuristic derivations of the three classical tests of general relativity. These derivations are based on the Einstein equivalence principle and use Newtonian physics as a theoretical framework. The results obtained are close to Einstein's original predictions. Historical and anecdotal aspects of the subject are also discussed.Comment: 9 pages, 6 figures. Physics Education 202

El limite de Chandrasekhar para principiantes / Chandrasekhar limit for beginners

In a brief article published in 1931 and expanded in 1935, the Indian astrophysicist Subrahmanyan Chandrasekhar shared an important astronomical discovery where he introduced what is now known as Chandrasekhar limit. This limit establishes the maximum mass that a white dwarf can reach, which is the stellar remnant that is generated when a low mass star has used up its nuclear fuel. The present work has a double purpose. The first is to present a heuristic derivation of the Chandrasekhar limit. The second is to clarify the genesis of the discovery of Chandrasekhar, as well as the conceptual aspects of the subject. The exhibition only uses high school algebra, as well as some general notions of classical physics and quantum theory.Comment: 14 pages, 2 figures, Text in Spanis