Black hole and Planck length belong to the unquestioned dogmas of the recent day theoretical physics. Scientists should remain always critical and especially so on notion like black hole which do not allow any direct experimental testing and represents a singularity of existing theory where it fails. The galactic black-holes are only something behaving like black-hole in certain respects when seen from outside. Indeed, in TGD black-holes are not key objects and Planck length is replaced by CP2 size.
Black holes and string theory
In string theory black-holes are not primary objects. They emerge as a result of QFT approach decided to be long length scale limit of string theory. This is a democratic decision but I feel that scientific truths are not something to be decided;-).
Maybe in the genuine string theory without all this additional stuff added by hand and leading to the landscape catastrophe, one actually has only strings in 10-dimensional Minkowski space. String model would describe physics of 2-D space-time but this is of course not enough for our purposes. The rest of string theory is hallucinated in absence of sensory feedback during last decades in the carefully isolated think tanks of Harward and Princeton and mostly figments of imagination and wishful thinking.
Black holes and TGD
In TGD framework black-hole solutions do not allow a complete embedding to M4× CP2 but only down to some radius. Black-hole exterior as a model for the empty space is an important vacuum extremal whose deformations are what is interesting physically.
- Black-hole interior itself is replaced with space-time region with Euclidian signature of induced metric and representing line of generalized Feynman diagram. This region is separated from external world by wormhole throat defined as a light-like 3-surface at which the signature of the induced metric changes carries a state of moving fermions in parallel. This is basic building brick: physical fermions and bosons are composites of wormhole throats and contacts.
The replacement of black holes with lines of generalized Feynman diagrams is something genuinely new - a prediction - rather than just gluing objects of GRT world to new theory. CP2 size replaces Planck length and is about 104 times longer than Planck length.
- Gravitational constant and cosmological constant emerge as a parameters characterizing solutions of field equations, not as a fundamental length: Einstein's equations T= κG+Λg emerge as a consistency condition guaranteeing the reduction of field equations to algebraic conditions analogous to those for minimal surface equations in string model.
- Quantum criticality realized in terms of a 4-D generalization of 2-D conformal invariance (CI) having the CI of 3-D light like surfaces as intermediary (this 4-D CI is not the ordinary 4-D CI!) leads to the algebraization and implies Einstein's equations as a consistency condition.
Quantum criticality requires that Newton's constant G and cosmological constant Λ are quantized. One of the future challenges is to estimate their possible values.
The possibility of this quite different interpretation shows how shaky assumptions are taken as granted in recent day theoretical physics.