Given the spacetime with metric ds² - (1+)²+ + ²) dt². dr² 1+1 + r² (do² + sin² Odo²) where L > 0 is a constant, consider radial null geodesics, i.e., 0 = $ = 0, starting at the origin so t(0) = 0, r(0) = 0. Let A be the parameter along the geodesics; given that such geodesics satisfy + = EL², the expressions for the actual geodesics are: a. (A) E sinh(A), f(A) = L cosh(A) b. r(A) Eλ, t(A) = Lλ = □ c. r(A) = EA, t(A) = L arctan (A) d. t(A) = ±r(A)

Given the spacetime with metric ds² - (1+)²+ + ²) dt². dr² 1+1 + r² (do² + sin² Odo²) where L > 0 is a constant, consider radial null geodesics, i.e., 0 = $ = 0, starting at the origin so t(0) = 0, r(0) = 0. Let A be the parameter along the geodesics; given that such geodesics satisfy + = EL², the expressions for the actual geodesics are: a. (A) E sinh(A), f(A) = L cosh(A) b. r(A) Eλ, t(A) = Lλ = □ c. r(A) = EA, t(A) = L arctan (A) d. t(A) = ±r(A)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

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