Speaker
Description
It is believed that black holes remain a clean laboratoryfor probing ideas about quantum gravity. Decades of work on these obscure objects have shown they behave could behave like ordinary thermodynamic systems with temperature and entropy, or to the extreme, even as elementary particles.
It remains a huge challenge to reconcile the large-scale properties with the underlying quantum description.
We find a new exact time-dependent instanton solution on a vacuum Kerr-like warped spacetime in conformal dilaton gravity. Remarkably, the metric solution results from a first-order PDE, allowing the connection with self-duality. The solution can be described by a conformal K\"ahlerian manifold with Euclidean signature and a K\"ahler potential. As such, the self-dual nature makes the comparison with the Yang-Mills instanton counterpart solution interesting.
The antipodal boundary condition on the hypersurface of a Klein bottle $\sim \mathbb{C}^1\times\mathbb{C}^1$ is applied to describe the Hawking particles. We used the Hopf fibration to get $S^2$ as the black hole horizon, where the centrix is not in a torus but in the Klein bottle. The twist fits very well with the antipodal identification of the point on the horizon. No "cut and past" is necessary, so the Hawing particles remain pure without instantaneous information transport.
A local observer passing the horizon will not notice a central singularity in suitable coordinates.
The black hole paradoxes are also revisited in our new black hole model.
A connection is made with the geomeric quantization of $\mathbb{C}^1\times\mathbb{C}^1\sim S^3$, by considering the symplectic 2-form.
The model can be easily extended to the non-vacuum situation by including a scalar field. Both the dilaton and the scalar field can be treated as quantum fields when approaching the Planck area.