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Theoretical physics digest Wiki
Welcome to the Theoretical physics digest Wiki! Scientific papers on theoretical physics are hard to understand. One reason is that the information that they rely on may be unavailable to the reader. Another is that 
Epicyclic Frequency
For a particle in a closed orbit, the epicyclic frequency is the frequency of radial motions due to a small perturbation in the orbit. For example, consider a planet orbiting a star in a circular 
Chirp Mass
The chirp mass is the effective mass of a binary system, in the context of the Quadrupole Gravitational Radiation emitted by it. For a binary system with component masses 
Relativistic Beaming
Consider a source that is emitting isotropically in its own rest frame (denoted by primes): where is a unit solid angle and is the luminosity. 
Tremaine Gunn Bound
The nature of dark matter is still unknown, but in this entry we will show that it cannot be made up of low mass Fermions. This is because the exclusion principle limits the number of 
Ferraro Isorotation Law
Let us consider a rotating blob of plasma. The rotation does not have to be uniform, but we do assume no change in the azimuthal direction, so the velocity field can be written in cylindrical 
Curvature Drift
Curvature drift is a mode of motion of charged particles in a curved magnetic field. In contrast to the motion of charged particles in a uniform magnetic field, where the charged particles gyrate around the 
Accretion Discs
Suppose we have a massive object enshrouded in a gas cloud. Due to gravity, some of the gas will fall straight onto the massive object, but most of the gas particles would just move on 
Faraday rotation
Consider an electromagnetic wave propagating in a magnetized plasma. For simplicity we assume the plasma is magnetized in the direction and that the wave is travelling along the same direction. Electromagnetic waves in the plasma 
Gravitational Lensing
Suppose a photon passes near a massive object of mass with impact parameter. We assume that the energy of the photon is much greater than the gravitational energy at closest approach where is the speed 
Quadrupole Gravitational Radiation
Gravitational radiation is an essential result of Einstein's theory of General Relativity. It is an inevitable consequence of time delay of the gravitational fields experienced by moving masses. While the exact waveform of gravitational 
Black Hole Thermodynamics
At the heart of black hole thermodynamics is the idea that black holes have entropy. This idea was proposed by Jacob Bekenstein and Stephen Hawking, and hence formula for the entropy of a black hole 
Main Sequence Stars
Most stars occupy a very small volume in luminosity  mass space. In this section we will derive the analytic relations between those variables. We will assume that stars are characterised by a mass, radius, density 
Magnetic Reconnection
In magnetic reconnection, opposite magnetic field lines embedded in a plasma approach each other and merge. As a result, the configuration of the magnetic field changes. The difference in magnetic energy goes into the acceleration 
Fermi Acceleration
Fermi acceleration is a process by which particle are accelerated to super thermal energies. Usually, the spectrum of thermal distribution (e.g. Maxwell  Boltzmann, Maxwell  Juttner and Planck) decays exponentially for energies in excess of 
Bardeen Petterson Effect
Let us consider an accretion disc around a spinning black hole. Suppose the angular momenta of the disc and black hole are misaligned. Due to Lense Thirring precession, the line of nodes of each annulus 
Mass  Radius Relations for Neutron Stars
This pages review theoretical bounds and estimates relating the mass to the radius of neutron stars. If the mass of a neutron star become too large (or, alternatively, the radius becomes too small) then the 
Synchrotron radiation
Charged particles accelerated by a magnetic field will radiate due to Larmour's formula. For nonrelativistic electrons the frequency of radiation is simply the gyration frequency: and the radiation is cyclotron which is weak 
Mean Motion Resonance
Let us consider the following solar system: a star of mass, orbited by a massless asteroid on a nearly circular orbit with semi major axis, and a planet of mass on a perfectly circular orbit 
Growth of Super Massive Black Holes
Black holes can be divided into two groups. The first is stellar mass black holes. These were created as a result of a stellar collapse, and therefore have a mass of a few solar masses 
Plasma Dispersion Relations
This page contains the derivation of dispersion relations for electromagnetic waves in collision  less plasmas. It essentially involves perturbation theory to the equations of magnetohydrodynamics. Faraday's law 
Compactness Problem in GRBs
The compactness problem is seemingly a contradiction that arises from GRB light curve data. On the one hand, a large portion of the energy is the form of non thermal, power law spectrum photons. One 
Mean number of Scatterings
The optical depth of a medium of typical size can be approximated by where is the mean free path of the medium and is given by where is the density of scatterers and is their 
Burgers Turbulence
Let us consider a fluid stirred so vigorously that the stirring action creates shocks. In order to get the power spectrum of the ensuing turbulence we examine the Fourier transform of the spatial profile of 
Tayler Instability
Let us consider a star of radius, differentially rotating with an average rotation frequency. Due to the differential rotation, any initial magnetic field will be stretched and become predominantly toroidal. Suppose that the toroidal magnetic
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