Thanks I'll check it out.pervect said:You could try reading "Exploring black holes" by Taylor. It might not be hopelessly advanced, I think it has some workbooks/projects. I don't own it, unfortunately, though sample chapters are availble at the aurhtor's (E.F. Taylor) website.
Nugatory said:How much special relativity do you know? There's no shortage of interesting spacetime problems ieven in the flat spacetime of SR, before you get take on the much more demanding curved spacetime of general relativity and black holes.
How much classical mechanics and E&M do you know? Have you been through a calculus-based course on classical mechanics? You'll get better and more targeted answers if you can tell us more.
You said "Spacetime/Black holes" and there's a lot of spacetime that isn't black holes. Many introductory presentations of special relativity assume constant relative velocities (and instantaneous accelerations if changes of direction are required, as in the twin paradox) because that simplifying assumption reduces the amount of calculus that is required. Thus, if you are feeling a bit overwhelmed by tensor methods but still want a chance to experiment with multi-variable calculus and differential equations, you might look for special relativity problems that naturally involve accelerations: Born rigid motion, Bell's spaceship paradox, Rindler coordinates, the relativistic rocket equation come to mind.pmrotman said:I have a very limited understanding of E&M, but some understanding of Classical Mechanics. I do understand special relativity and some of general relativity, and I'm fairly good at teaching myself new things within a reasonable scope (e.g. simple calc-based mechanics). The project doesn't need to be particularly advanced as it will be presented to other students of my caliber, but this is my area of interest and I would enjoy doing a lot of work for it. Any other questions?
Multivariable Calculus is a branch of mathematics that deals with functions of more than one variable. It involves studying the behavior of functions in multiple dimensions and is used in various fields such as physics, engineering, and economics.
Multivariable Calculus is crucial in understanding Spacetime and Black Holes as it involves working with functions that represent the curvature of space and time. It helps in analyzing the behavior of objects in a multidimensional space, which is essential in understanding the effects of gravity in Spacetime and the formation of Black Holes.
Multivariable Calculus is used to solve equations and make predictions about the behavior of objects in Spacetime and Black Holes. It is also used to calculate the curvature of space and time, which is crucial in understanding the effects of gravity and the formation of Black Holes.
Multivariable Calculus is used to model Black Holes by applying the principles of general relativity to calculate the curvature of space and time around the singularity of a Black Hole. It also helps in predicting the behavior of matter and light near a Black Hole's event horizon.
Multivariable Calculus is used in various real-life applications, such as predicting the motion of planets and satellites in Spacetime, understanding the formation of galaxies and stars, and studying the behavior of matter and radiation near Black Holes. It is also used in the development of technologies such as GPS, which relies on the principles of general relativity to function accurately.