# Homework Solutions (12) - Ph 236 Homework 9 Due: Monday,...

• Homework Help
• MinisterIronHamster3090
• 1

This preview shows page 1 out of 1 page.

Ph 236 – Homework 9Due: Monday, January 23, 20121. Higher symmetries.[12 points]In class we considered spacetimes with Killing fields with the standard commutation relations of rotation[Ji,Jj] =-ǫijkJk,(1)with two-dimensional orbitsS(P). Cases where the orbits are higher-dimensional tend to be either trivialdue to the high degree of symmetry, or very weird. Here we will consider a trivial example.Consider the vectors in standard Minkowski spacetime given byHi=12(Ji+iKi)(2)(see Notes XVI,§IIIA for definitions ofJiandKiin Minkowski).(a) Show that[Hi,Hj] =-ǫijkHk.(3)Thus the three fields described commute like rotations.(b) Show that at a generic pointP, the three vectorsH1(P),H2(P), andH3(P) are linearly independent.Conclude that the orbit has dimension higher than 2.(c) What symmetries do the Killing fieldsHicorrespond to? Construct an alternative (non-Minkowski)metric that has theHias Killing fields.2. Spherical polytropes.[24 points]Consider a star with a polytropic equation of state,
End of preview. Want to read the entire page?

Course Hero member to access this document

Term
Spring
Professor
Chirata
Tags
Work, Spacetime, Fundamental physics concepts, Ji
• • • 