| Mi 31 May
Einstein's field equations for general relativity
In a paper published in 1915, Einstein developed the field equations
that describe the fundamental interaction of gravitation as a result
of space-time being curved by mass and energy. In the talk, I will
explain the physical meaning of Einstein's equations. I start with
a brief explanation of the "principle of equivalence" and
how light bends in a gravitational field. We then describe the key
concepts in the equations as Ricci's curvature tensor Rμν,
the scalar curvature R, the metric tensor gμν,
the cosmological constant, and the stress-energy tensor Tμν.
I show in particular how from the principle of equivalence we can
arrive at the field equations of general relativity.
Literature: James B. Hartle, "Gravity: An Introduction to Einstein's General
Relativity" (Pearson Publisher 2003).
| Wed 31 May
Comparison of electromagnetic and gravitational waves
Similar to electromagnetic (EM) waves, which are a product of Maxwell's equations, gravitational waves are that of general relativity. When
Einstein's equations are linearized to first order
in the metric solution, they produce these beautiful gravitational waves. In this talk I present a comparative study of their nature. Beginning with the subtle similarities between the two radiations, I take you through some mathematics that will help visualizing their existence. Static and time-varying configurations are included,
thus describing the sources producing the waves. The talk concludes with a unique method to animate the two fields, thus giving a deeper insight into the nature and production of EM and gravitational radiation.
Literature: Richard Price, John Belcher, and David Nicholas,
"Comparison of electromagnetic and gravitational radiation:
What we learn about each from the other",
Am. J. Phys. 81 (8), 575-84 (2013);
J. D. Jackson, Classical Electrodynamics (Wiley & Sons 2007);
Seam Carroll, Spacetime and Geometry: An Introduction to General Relativity
| Wed 14 Jun
Force, torque and energy of a moving magnetic/electric dipole
in an external electromagnetic field
The modern theory of electromagnetism involves special relativity
and provides equations for how electric and magnetic sources and fields
from one inertial frame of reference to another. In particular, the
derivation of the correct relativistic expressions for the force, torque
and energy of a moving electric/magnetic dipole in an external
electromagnetic field faced a number of errors in the last decades.
Recently the correct expression for the force was achieved, leading
the way to deriving the torque
and energy of a moving dipole as measured in the laboratory frame.
I will present these equations. Also, I will apply them to
some physical problems and show, that they yield the correct solution
for an observer in the laboratory frame for the problems in question.
Alexander Kholmetskii, Oleg Missevitch, and T. Yarman,
"Electric/magnetic dipole in an electromagnetic field:
force, torque and energy", Eur. Phys. J. Plus 129 (2014) 215
David Babson et al., "Hidden momentum, field momentum, and
elctromagnetic impulse", Am. J. Phys. 77(9), 826 (2009)
| Wed 14 Jun
Simple model for the CO2 greenhouse effect
Greenhouse gases in earth's atmosphere provide favorable conditions
for terrestrial life, but global warming induced by human CO2 emissions
threatens these conditions. In this talk a method to estimate the
contribution of CO2 to the greenhouse effect based on basic physical
considerations, such as radiative heat transfer, will be presented. It
comprises approximations of the frequency dependence of the CO2 absorption
spectrum and the temperature profile of the atmosphere. The main result
will be an estimate for the climate sensitivity, which quantifies
the change in global mean temperature under a doubling of the CO2
concentration. While this analytical treatment is very instructive,
it neglects certain features of the climate system, like feedbacks,
so that the need for more comprehensive modelling will become clear.
D. J. Wilson and J. Gea-Banacloche, "Simple model to estimate the
contribution of atmospheric CO2 to Earth's greenhouse effect",
Am. J. Phys. 80(4) 306 (2012);
R. T. Pierrehumbert, Principles of Planetary Climate
(Cambridge University Press 2010);
D.G. Andrews, An Introduction to Atmospheric Physics
(Cambridge University Press 2010).
| Wed 21 Jun
The Planck mass and the Chandrasekhar limit
The Planck mass combines three different field of
physics, classical Newtonian mechanics, relativity and quantum mechanics.
But it only plays a role at energy scales far above what we can reach on
earth. The most extreme physical conditions we find in space. We will
examine a white dwarf, the last stage in the life of a low mass star.
Using knowledge from all three mentioned fields of physics, we derive the
upper mass limit of such an object, the so-called Chandrasekhar limit.
David Garfinkle, "The Planck mass and the Chandrasekhar limit",
Am. J. Phys. 77 (2009) 683.
| Wed 21 Jun
Yohana Herrero Alonso
Kepler orbits of dropped charges
The accretion of dust grains which gives place to planet formation is not perfectly understood. This granular matter is composed of particles like for example coal, which are characterized by losing part of their energy when they interact (collide). In this talk, a recent theory about the formation and development of planetesimals will be presented. In order to do that, we will go through the equations of motion for dropping charges in the absence of gravity and through the different aggregates that we can get by changing the particles' charge. In this way, we will learn how particles can be added to form huge aggregates in a similar way as the aggregation in the planets formation happens. Several plots related to Keplerian orbits of dropped charges will be shown, as well as some graphs where the variation in energy depending of the location in the orbit is shown.
Literature: Frank Spahn and Martin Seiß, "Granular matter: Charges dropped",
Nature Phys. 11(9), 709-10 (2015);
Victor Lee et al., "Direct Observation of Particle Interactions and Clustering in Charged Granular Streams", Nature Phys. 11(9), 733-37 (2015);
Brent K. Hoffmeister et al., "Orbital dynamics of two electrically charged conducting spheres", Am. J. Phys. 78(10), 1002-06 (2010).
| Wed 05 Jul
Friedmann cosmologies and Newtonian back-reaction
One pillar of cosmology is the study of the expansion / contraction of our
Universe. Knowledge of the expansion rate is crucial in order to understand the
origin and the fate of the Universe. Friedmann derived from Einstein's
general relativity theory his famous equations which permits us to express this
expansion rate in terms of global properties of the universe. We present a
classical way to derive the Friedmann equations, which further yields additional
interesting feedback mechanisms. These mechanisms are called Newtonian
back-reaction. Their absence in the conventional Friedmann equations started a
controversy in the community which is discussed.
T. Buchert, J. Ehlers "Averaging inhomogeneous Newtonian cosmologies",
Astron. Astrophys. 320, 1-7 (1997);
N Kaiser, "There is no Newtonian backreaction",
Mon. Not. Roy. Astron. Soc. 469, 744-48 (2017)
| Wed 12 Jul
Density patterns ("propellers") in Saturn's rings
The planet Saturn has a ring system which is composed
of water ice particles of various sizes. For the study of the Saturn
Rings the size distribution of the particles is very important. We can
count the number of kilometer-sized objects by counting the gaps in the
ring system. The number of smaller objects (centimeters to several meters)
can be measured photometrically. In order to measure meter to kilometer
sized objects, another method is required. In this talk I will show what
kind of stationary density patterns in the Saturn Rings caused by these
objects (moonlets) we should expect. The shape and the scale of the
structures will be derived and compared to recent observations by the
Cassini space craft.
Frank Spahn and Jürgen Schmidt,
"Saturn's bared mini-moons", Nature 440(7084), 614-15 (2006);
F. Spahn and M. Sremčević,
"Density patterns induced by small moonlets in Saturn's rings?",
Astron. Astrophys. 358, 368-72 (2000);
M. Sremčević, F. Spahn, W. J. Duschl,
"Density structures in perturbed thin cold discs",
Mon. Not. Roy. Astron. Soc. 337(3), 1139-52 (2002)
| Wed 19 Jul
Brownian yet non-Gaussian Diffusion
Classically, Brownian diffusion is associated with the thermally driven
random displacement of small particles suspended in a fluid, characterized
by the diffusion coefficient.
The displacements of each particle can be associated as a sum of
small steps of a random walk, which are identically and independently
The central limit theorem therefore implies a Gaussian displacement probability
distribution. However, single particle tracking experiments of molecules
in live cells revealed a transition from a Laplace distribution on short
time scales to a Gaussian distribution on longer time scales. For this
reason, we will introduce a simple minimal model for diffusing
diffusivities, based on a subordination concept, which yields us
analytical results in accordance with the experimental observations.
Aleksei V. Chechkin et al., "Brownian yet non-Gaussian diffusion:
from superstatistics to subordination of diffusing diffusivities",
Phys. Rev. X 7(2), 021002 (2017);
Thomas J. Lampo et al., "Cytoplasmic RNA-protein particles exhibit
non-Gaussian subdiffusive behavior",
Biophys. J. 112(3), 532-42 (2017).
| Wed 19 Jul
Quantum cosmology for pedestrians
Quantum Cosmology is an application of quantum theory to describe the
Universe. It only works for special models like an isotropic and
homogeneous Universe and, in our case, a closed Universe.
will using techniques from general relativity theory and quantum theory to
arrive at the Wheeler-DeWitt equation for a spherical Friedman Robertson
Walker universe (FRW). Then we consider the solution of the Wheeler-DeWitt
equation for the birth of a universe via quantum tunneling.
Literature: D. Atkatz, "Quantum cosmology for pedestrians",
Am. J. Phys. 62, 619-27 (1994).
| Wed 26 Jul
Modified Gravitational Theory as an Alternative to Dark
Energy and Dark Matter
In 1929, Edwin Hubble discovered that almost all
galaxies are moving away form us with a velocity that is directly
proportional to the distance. The 2011 Nobel prize celebrated the
observation that the Universe is in a
state of accelerated expansion. 'Dark Energy' was proposed to explain this
expansion of the Universe. Flat galactic rotation curves indicate the
presence of 'Dark Matter'.
In this talk, the
possibility that Einstein's theory of gravity does not correctly describe the
large-scale structure of the Universe will be considered and an
alternative gravity theory will be proposed as a possible resolution to
Literature: J. W. Moffat,
"Modified Gravitational Theory as an Alternative to Dark
Energy and Dark Matter", arXiv:astro-ph/0403266v5 (2004);
J. B. Hartle, "An Introduction to Einstein's General Relativity"