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What Are the Thermodynamics of Black Holes? A 5 Minute Introduction

Definition/Summary The four laws of black hole thermodynamics are as follows… The Zeroth Law Surface gravity [itex](\kappa)[/itex] is constant over a black holes event horizon. The First Law ‘This law deals with the mass (energy) change, dM when a black hole switches from one stationary state to another.’ The following (in natural units) applies- [tex]dM=\frac{\kappa}{8\pi}\,dA\,+\,\Omega\,dJ\,+\,\Phi\,dQ[/tex]…

What is Impedance? A 5 Minute Introduction

Definition/Summary The impedance of a load (a combination of components) in an AC current is a complex number [itex]Z\ =\ R+jX[/itex] where [itex]R[/itex] is the resistance of the load and [itex]X[/itex] is its reactance. It can also be written in polar form: [itex]Z\ =\ |Z|e^{j\phi}[/itex], or as the phasor [itex]|Z|\angle\phi[/itex]. Impedance is the AC equivalent…

What is Mass Inflation? A 5 Minute Introduction

Definition/Summary Abstract from Poisson and Israel’s 1990 paper, ‘Internal structure of black holes’- ‘The gravitational effects associated with the radiative tail produced by a gravitational collapse with rotation are investigated. It is shown that the infinite blueshift of the tail’s energy density occurring at the Cauchy horizon of the resulting black hole causes classically unbounded…

What is Potential Energy? A 5 Minute Introduction

Definition/Summary Potential energy is simply another name for (minus) the work done by a conservative force. Since the work-energy theorem states that change in energy minus work done is constant, that means that for a conservative force, energy plus potential energy is constant. For example, a object of mass [itex]m[/itex] moving a height [itex]h[/itex] and…

What is the Moment of Inertia? A 10 Minute Introduction

Definition/Summary The moment of Inertia is a property of rigid bodies. It relates rotational force (torque) to rotational acceleration in the same way that mass relates ordinary (linear) force to ordinary acceleration. Moment of Inertia has dimensions of distance squared times mass ([itex]ML^2)[/itex]. The moment of Inertia is always relative to a given axis. The…

What is a Linear Equation? A 5 Minute Introduction

Definition/Summary A first-order polynomial equation in one variable, its general form is [itex]Mx+B=0[/itex] where x is the variable. The quantities M, and B are constants and [itex]M\neq 0[/itex]. Equations [tex]Mx+B=0[/tex] Extended explanation Since [itex]M\neq 0[/itex] the solution is given by [tex]x=-B/M\;.[/tex] The variable x does not have to be a number. For example, x and…

What is a Fibre Bundle? A 5 Minute Introduction

Definition/Summary Intuitively speaking, a fibre bundle is space E which ‘locally looks like’ a product space B×F, but globally may have a different topological structure. Extended explanation Definition: A fibre bundle is the data group [itex](E, B,\pi, F)[/itex], where [itex]E, B[/itex], and [itex]F[/itex] are topological spaces called the total space, the base space, and the…

What is a Real Number? A 5 Minute Introduction

Definition/Summary The real numbers are the most commonly encountered number system, familiar to the layman via the number line, and as the number system lying behind decimal notation. Because real numbers have much nice arithmetic and geometric properties, they feature prominently in many fields of mathematics. Extended explanation This is a preliminary article. More information…

What is a Parabola? A 5 Minute Introduction

Definition/Summary A parabola has many definitions, a classical one being, “A Parabola is the locus of all points equidistant from a given point (called the focus) and a line (called the directrix)”. A parabola is a frequently encountered trajectory in kinematics and mechanical physics. Also, the plot of a Quadratic Equation in one variable is…

What is Lie algebra? A 5 Minute Introduction

Definition/Summary A Lie algebra (“Lee”) is a set of generators of a Lie group. It is a basis of the tangent space around a Lie group’s identity element, the space of differences between elements close to the identity element and the identity element itself. Lie algebras include a binary, bi-linear, anti-symmetric operation: commutation. The commutator…

What is a Tangent Line? A 5 Minute Introduction

Definition/Summary The tangent to a curve in a plane at a particular point has the same Gradient as the curve has at that point. More generally, the (n-1)-dimensional tangent hyperplane to an (n-1)-dimensional surface in n-dimensional space at a particular point has the same Gradient as the surface has at that point. So if [itex]A\,=\,(a_1,a_2,\cdots…

What are Virtual Particles? A 10 Minute Introduction

Definition/Summary Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) of interaction in quantum field theory. No virtual particle physically appears in the interaction: all possible virtual particles, and their antiparticles, occur equally and together in the mathematics and must be removed by integration over the values of their…

Where Did the Big Bang Happen?

According to standard cosmological models, which are based on general relativity and are found to agree well with observations, time and space did not exist before the Big Bang — or even at the time of the Big Bang, which is a point where the theory breaks down because various quantities (such as temperature and…

Could Redshifts Be Intrinsic Rather than Cosmological?

How do we know that the redshifts of galaxies and quasars are cosmological and not “intrinsic?” Evidence for the cosmological interpretation The purpose of this FAQ entry is to explain why nonstandard interpretations of redshifts are not viable, not to explain from scratch how standard cosmological models were arrived at. The following is only a…

How to Build a Definition for Heat

One of the most frustrating misconceptions in Thermodynamics centers on the actual definition of heat. Many science/engineering students often refer to a body as to be possessing heat, but as we shall see, to do so is completely nonsensical. We start by examining the first law and defining each of its terms. The first law…

Is the Universe a Black Hole?

In the early universe, the matter was gathered together at very high density, so why wasn’t it a black hole? The first thing to understand is that the Big Bang was not an explosion that happened at one place in a preexisting, empty space. The Big Bang happened everywhere at once, so there is no…

Can We Tell Whether the Universe Is Rotating?

If you believe wholeheartedly in Mach’s principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing else for it to be rotating relative to. However, general relativity is not very Machian, and it offers a variety of ways in which an observer inside a…

Why Do People Say That 1 And .999 Are Equal?

Why do people say 1 and 0.999… are equal? Aren’t they two different numbers? No, they really are the same number, though this is often very counterintuitive to many beginning students. Here are some non-rigorous proofs that 1=0.999…: Proof #1 For any two unequal numbers, there is always another number in between them. (That is…

A Layman’s Guide to: Lies, Damned Lies and Pseudoscience

It seems nowadays that we are getting swamped with science. But not the science of the valid kind. Science where people follow the scientific method and are based on sound reasoning, good experimental evidence and makes check-able predictions. No, sadly, most of the so-called science are pseudoscience, evil heinous impostors that exploit the public’s curiosity…