The solution for the Einstein equations in vacuum with cosmological constant A is given by 1 (1-7²) di² - (1-1/²³²) dr²

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The solution for the Einstein equations in vacuum with cosmological constant A is given by 1 (1-7²) di² - (1-1/²³²) dr²

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The Solution For The Einstein Equations In Vacuum With Cosmological Constant A Is Given By 1 1 7 Di 1 1 Dr 1
The Solution For The Einstein Equations In Vacuum With Cosmological Constant A Is Given By 1 1 7 Di 1 1 Dr 1 (325.76 KiB) Viewed 15 times
The solution for the Einstein equations in vacuum with cosmological constant A is given by 1 (1-7²) di² - (1-1/²³²) dr² r² (d0² + sin² 0do²). 3 ds² - a) Analyzing the possible values of A, determine under what conditions this space-time possesses an event horizon and furthermore calculate the radius of this horizon. b) Consider a geodesic in the equatorial plane, 0 = π/2. Demonstrate that (1-1-¹²) i E - = h = p² are conserved along the geodesics, where the derivative is with respect to some affine parameter of the geodesic.
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