Basic ideas of general relativity

General Relativity (GR) is a classical field theory (whatever that means, could be something like Electrodynamics or something like Fluiddynamics) There is no gravitational force. Principle of Mach: The distribution of matter and energy defines the geometry of space-time Principle of Equivalence: Acceleration = homogenous (in time and space) gravitational field; Principle of Covariance: All coordinate systems are equal.

Classical limit of quantum mechanics

The semi-classical limit corresponds to $ h\rightarrow 0$, which can be seen to be equivalent to $ m\rightarrow\infty $ , the mass increasing so that it behaves classically. (from http://en.

Fluid Dynamics of Spacetime

Bibliography Christopher Eling (2008) : Hydrodynamics of spacetime and vacuum viscosity Christopher Eling et al. (2006) : Non-equilibrium Thermodynamics of Spacetime Ted Jacobson (1995) : Thermodynamics of Spacetime: The Einstein Equation of State

Gravitational Cherenkov Radiation

Cherenkov Radiation is a very interesting phenomenom. Recently I asked myself, if such a phenomenom allso exists for gravity in the sense, that if a particle moves faster than the speed of gravity in a medium, it should radiate gravitational cherenkov radiation.


The basic equations are: $$G_{\mu \nu} + \Lambda g_{\mu \nu}= \frac{8\pi G}{c^4} T_{\mu \nu}$$ with $$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu}R$$ and $$T_{\mu \nu} = g_{\mu \alpha} g_{\nu \beta} T^{\alpha \beta}$$ and $$T^{\alpha \beta} , = \left(\rho + \frac{p}{c^2}\right)u^{\alpha}u^{\beta} + p g^{\alpha \beta}$$

Hawking radiation

From calculations of quantum tunneling through the horizon of a metric (black hole, Rindler..) Hawking/Unruh temperature can be calculated! [ Ryan Kerner: Fermions Tunnelling from Black Holes] _ Using this method it is recently claimed that the so called Black hole information paradox can be solved:

Korteweg-de Vries equation

From []: In fact, a transformation due to Gardner provides an algorithm for computing an infinite number of conserved densities of the KdV equation, which are connected to those of the so-called modified KdV equation through the Miura transformation v_x+v^2=u (Tabor 1989, p.

Quantum entanglement

Before the measurement the positions of the photons in space are not defined, thus the distance between them also makes no sense and without distance one cannot really speak about the speed of information transfer.

Relativistic Boltzmann equation

[Google Scholar: relativistic Boltzmann equation] [Literature citing Cercignani: The relativistic Boltzmann equation: theory and applications] [G. Kaniadakis (2006): Towards a relativistic statistical theory] [Garcia-Perciante (2006): Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation] [Tsumura (2009): Second-order Relativistic Hydrodynamic Equations for Viscous Systems; how does the dissipation affect the internal energy?


Fortgeschrittenenpraktikum Teil A SS 2003 Meine Protokolle aus dem Fortgeschrittenenpraktikum Teil A im Sommersemester 2003 kann hier jeder downloaden der will. Die *.ps.gz-Files enthalten nur das Protokoll, die *.tar.gz-Files enthalten den gesamten Latex-Sourcecode, Bilder und Mathematica4-Notebooks.