My question is from an AdS/CFT review: http://arxiv.org/abs/1112.5403

The AdS_5 metric in the article is written

$$ ds^2=\frac{l^2}{z^2}(-dt^2+dz^2+dx^2), $$ where I'm denoting collectively three dimensions by $dx^2$.

Then the article says Schwarz black hole solution with a horizon radius $z_h$ in this spacetime is

$$ ds^2=\frac{l^2}{z^2}\Big[-\big(1-\frac{z^4}{z_h^4}\big)dt^2+\frac{1}{1-\frac{z^4}{z_h^4}}dz^2+dx^2\Big]. $$

I'm observing some weird things here:

when the black hole radius $z_h$ approaches infinity, the Schwarz metric becomes AdS,

so an infinitely large AdS-Schwarz black hole is AdS???

  • $\begingroup$ How does this contradict the fact that the spacetime is asymptotically AdS? The Schwarzschild solution that you have written down is a singular solution in AdS_5 spacetime in the Fefferman-Graham form. What are the weird things that you are observing? $\endgroup$ – user106422 Sep 12 '16 at 21:37
  • $\begingroup$ The weird thing is in the limit $z_h$ goes to infinity, the black hole solution reduces to AdS metric. An infinitely large black is same as an AdS spacetime having no black hole? $\endgroup$ – JamieBondi Sep 16 '16 at 5:59

It is known that a Schwarz blackhole in asymptotic AdS space is an Einstein vacuum solution,which at spatial infinity tends to AdS space time.Also to a Kerr metric as a generalisation of Schwarz metric. .Further generalization can conform to electrovacuum Einstein solution represented by Einstein.Maxwell.dirac[emd] equation,as a starting point for quantum state of a vector potential in a compactified dimension,as a generalised dimensional reduction of field theories,in a geometric way.This conforms to a gauge field,affording a gravity interpretation in a gauge theory duality perspective,as a maximally extended Schwarz blackhole in asymptotic AdS space time,generalised by the Einstein.Maxwell Dirac metric. This can be extended to explain particles like electrons and to QGP confinement /deconfinement models[witten].....thus pointing to a heuristics for a unified metric,combined metric tensor,gauge field in an extended Hilbert space and in an AdS/CFT correspondence context. The generalized eigen function theory base of extended Hilbert space as a pair of super structure and a dense subspace,has an inclusion map as a homeomorphism for binary operations for computations that are consistent in large structure and substructure.This can study spectral theory combining eigenvector bound functions and continuum ones.The dense subspace is a topological vector space for a vector potential,analogous to a quantized energy field in compactified dimension,conforming to a QED vacuum,in a simplectic form,flowing from the compact space,as a generalised dimensional reduction of field theories,corresponding to an AdS_5 metric,but as a gauge U(1)field,having no requirement to conform to CY manifold,though analogous to string like theories.. The model explains quantization of energy field in compact space,allowing momenta of a discrete nature,which has a gravity interpretation in dual space time as an AdS space time,with a thermal state corresponding to maximally extended Schwarz blackhole in asymptotic AdS space time...Thermal state corresponding t blackhole on conformal boundary,in a cft/ads duality. The invariance of change in scale (gauge)allows introduction of a complex quantity to transform scale change as phase change.Radiation likened to blackhole[Hawking/Page].,with phase transitions at critical thermal state threshold. Prof.Suresh Kumar.S,formerly Chief Scientist CSIR


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.