A related toy problem in Newtonian physics is the representation of the electrostatic potential of a spherical, charged object inside a box with unusual boundary conditions on the box. A brief description of a numerical solution to this problem has the same flavor as our approach to self-force problems in extreme-mass-ratio-inspiral.

We also have proof of principle with a detailed technical analysis of the self-force on a scalar charge in a circular orbit about a Schwarzschild black hole. This is published in PRD vol.77, 084008 (2008).

With collaborators Peter Diener and Wolfgang Tichy, we also have a full scale application of the effective source approach to self-force problems. This is published in PRD vol.80, 084021 (2009). We have two different 3+1 codes that evaluate the "regular" field associated with a point charge in a circular orbit about a black hole, calculate the self-force acting back on the charge and provide the waveforms. The analysis compares well with our 1+1 analysis described and with our earlier frequency domain analyses.

The original 1784 article (3.3MB) in the Philosophical Transactions of the Royal Society, by the Rev. John Michell (an amateur scientist), which first proposes the possible existence of what we call "black holes" today. It is interesting to note that there are no equations, and what should have been written as an equation is written out in sentences. The relevant precursor discussion to "black holes" is paragraph 16 on page 42."

The original 1798 article (5.2 MB) in the Philosophical Transaction of the Royal Society where Henry Cavendish, a good friend of the Rev. John Michell, describes his measurement of the force of gravity between two lead balls in his laboratory which allowed him to first deduce Newton's gravitational constant "G." Interestingly, Michell, had started this experiment, but died before it was concluded. Cavendish picked up where Michell finished, made substantial and important improvements in the experimental design and deserves the credit. Cavendish clearly credits Michell in the opening sentence. I find this article to be extremely readable, and it gives a perspective of science in 1798.

An earlier 1760 article (6.5 MB) by Michell identifies a relationship between fault lines in the Earth's crust and the presence of volcanoes. For this work, he is sometimes referred to as the "Father of Seismology."

A brief description of John Michell, Henry Cavendish, black holes and Newton's gravitational constant "G". This includes a "translation" of the relevant paragraph of Michell's 1784 paper. Here are photocopies of the cover of the relevant issue of The Philosophical Transactions, the Title Page of Michell's article, and the notable paragraph wherein the possibility of black holes is first proposed.

A computer generated mpg movie (5.5MB), from the Max Planck Institute shows the motion of stars within about 10 light-days of the center of our galaxy, the Milky Way. Using just Newtonian gravity and the motions of these stars, we can deduce that there is a jumbo sized black hole in the center of our galaxy. Its mass appears to be about a million times the mass of our own sun.