Embedding AdS Black Holes in Ten and Eleven Dimensions

TL;DR

This paper develops explicit non-linear Kaluza-Klein ansätze to embed lower-dimensional gauged supergravity black hole solutions into ten and eleven-dimensional string and M-theory, facilitating their uplift and interpretation.

Contribution

It provides general embedding formulas that enable the uplift of charged AdS black holes with various horizon topologies into higher dimensions.

Findings

Black hole solutions embedded in 10 and 11 dimensions.

Charges interpreted as angular momenta of branes.

Black hole horizons coincide with brane worldvolumes.

Abstract

We construct the non-linear Kaluza-Klein ans\"atze describing the embeddings of the U(1)^3, U(1)^4 and U(1)^2 truncations of D=5, D=4 and D=7 gauged supergravities into the type IIB string and M-theory. These enable one to oxidise any associated lower dimensional solutions to D=10 or D=11. In particular, we use these general ans\"atze to embed the charged AdS_5, AdS_4 and AdS_7 black hole solutions in ten and eleven dimensions. The charges for the black holes with toroidal horizons may be interpreted as the angular momenta of D3-branes, M2-branes and M5-branes spinning in the tranverse dimensions, in their near-horizon decoupling limits. The horizons of the black holes coincide with the worldvolumes of the branes. The Kaluza-Klein ans\"atze also allow the black holes with spherical or hyperbolic horizons to be reinterpreted in D=10 or D=11.