# K-group identification of supergravity solutions

## TL;DR

This paper explores the classification of supergravity solutions related to Dp-branes in type IIB string theory, linking geometric structures with quantum gravity insights into black hole entropy.

## Contribution

It introduces a K-group classification method for supergravity solutions of Dp-branes, connecting algebraic geometry with string theory and quantum gravity.

## Key findings

- Classified Hilbert spaces of N Dp-branes as vector bundles using K-functor.
- Linked black p-brane metrics with ten-dimensional D3-brane metrics.
- Applied Rosenberg theorem to relate geometric and algebraic structures.

## Abstract

The problem with Bekenstein-Hawking entropy of black hole can be resolved with quantum gravity theory with Dp-branes as supergravity solutions of type IIB string theory. Dp-brane solutions of type IIB are a direct analog of the Schwarzschild charged hole, so called black p-branes. The coincidence of the black p-brane metrics and ten-dimensional metrics of N-parallel D3-branes was used from the viewpoint of the Azumaya structure on D-branes connected with deformation of the classical moduli space. Applying Rosenberg theorem we can classify Hilbert spaces of N coinciding Dp-branes as vector bundles through K-functor.