Homogeneous Wave Equation in Curved Spacetime
The electromagnetic wave equation is modified in two ways, the derivative is replaced with the covariant derivative and a new term that depends on the curvature appears.
where is the Ricci curvature tensor and the semicolon indicates covariant differentiation.
The generalization of the Lorenz gauge condition in curved spacetime is assumed:
Read more about this topic: Electromagnetic Wave Equation
Famous quotes containing the words homogeneous, wave, equation and/or curved:
“O my Brothers! love your Country. Our Country is our home, the home which God has given us, placing therein a numerous family which we love and are loved by, and with which we have a more intimate and quicker communion of feeling and thought than with others; a family which by its concentration upon a given spot, and by the homogeneous nature of its elements, is destined for a special kind of activity.”
—Giuseppe Mazzini (1805–1872)
“Great Powers of falling wave and wind and windy fire,
With your harmonious choir
Encircle her I love and sing her into peace,
That my old care may cease....”
—William Butler Yeats (1865–1939)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)
“Our life is a faint tracing on the surface of mystery, like the idle, curved tunnels of leaf miners on the face of a leaf. We must somehow take a wider view, look at the whole landscape, really see it, and describe what’s going on here. Then we can at least wail the right question into the swaddling band of darkness, or, if it comes to that, choir the proper praise.”
—Annie Dillard (b. 1945)