# R sinr r c c s r r r sinhr r c c

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 8 1 MeV = 1.6×10- 13 J UW, ASTR 323, SP13, Eric Agol ©2013 - 1/3 7 Geometry in curved spaces: ______ curvature α + β +γ = π β α γ rc Distance between (r,θ) and (r+dr,θ+dθ) is ds: ds2 = dr 2 + rc2 sin(r / rc )dθ 2 5/21/13 ds UW, ASTR 323, SP13, Eric Agol ©2013 8 Geometry in curved spaces: ______ curvature Distance between (r,θ) and (r+dr,θ+dθ) is ds: α + β +γ = π ds2 = dr 2 + r 2dθ 2 ds r 5/21/13 UW, ASTR 323, SP13, Eric Agol ©2013 dθ r+dr 9 Geometry in curved spaces:_______curvature ds2 = dr 2 + rc2 sinh(r / rc )dθ 2 α β γ α + β +γ = π 5/21/13 UW, ASTR 323, SP13, Eric Agol ©2013 10 Curvature of the universe Posi8ve curvature Nega8ve curvature Zero curvature 5/21/13 κ: curvature constant κ = 1 α + β +γ = π + κA rc2 ds2 = dr 2 + Sκ (r )2 dθ 2 κ = - 1 ! r sin(r / r ) c #c # Sκ (r ) = " r # r sinh(r / r ) c #c \$ κ = +1 κ =0 κ = −1 κ = 0 UW, ASTR 323, SP13, Eric Agol ©2013...
View Full Document

## This document was uploaded on 04/05/2014.

Ask a homework question - tutors are online