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 R_μν, the scalar curvature R, the metric tensor g_μν, the cosmological constant, and the stress-energy tensor T_μν. 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).

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 (Pearson 1970).

The modern theory of electromagnetism involves special relativity and provides equations for how electric and magnetic sources and fields are changed 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.
Literature: 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)

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.
Literature: 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).

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.
Literature: David Garfinkle, "The Planck mass and the Chandrasekhar limit", Am. J. Phys. 77 (2009) 683.

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).

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.
Literature: 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)

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.
Literature: 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)

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 distributed. 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.
Literature: 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).

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. We 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).

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 the problems.
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"