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Physics
Special and General Relativity
Calculate Ricci Scalar & Cosm. Const of AdS-Schwarzschild Metric in d-Dimensions
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[QUOTE="shinobi20, post: 6589210, member: 505829"] [B]TL;DR Summary:[/B] How do you calculate the Ricci scalar and cosmological constant of an AdS-Schwarzschild black hole in ##d##-dimensions? I know some basic GR and encountered the Schwarzschild metric as well as the Riemann tensor. It is known that for maximally symmetric spaces there is a corresponding Riemann tensor and thus Ricci scalar. [B]Question.[/B] How do you calculate the Ricci scalar ##R## and cosmological constant ##\Lambda## of an AdS-Schwarzschild black hole metric in ##d##-dimensions? ##ds^2 = \frac{L^2_{\rm{AdS}}}{z^2} \left( -f(z) dt^2 + \frac{dz^2}{f(z)} + \sum_{i=1}^d dx_i^2 \right)## where ##L_{\rm{AdS}}## is the AdS radius. I'm reading the article [URL='https://arxiv.org/pdf/1409.3575.pdf']AdS CFT Duality User Guide by Makoto Natsuume[/URL] and I'm just wondering how to find those quantities since there is a factor of ##f(z)## already present as opposed to the pure AdS case. The Riemann tensor and Ricci scalar for the maximally symmetric spaces are listed in p.98 of the article. [/QUOTE]
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Calculate Ricci Scalar & Cosm. Const of AdS-Schwarzschild Metric in d-Dimensions
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