# Black holes in String theory

1. Sep 13, 2007

### kurt.physics

Does string theory make a connection between elementary particles (quarks) and black holes? The only way to tell one black hole from another is mass, force charges, and rate of spin and these are exactly the three characteristics that distinguish one elementary particle from another.

What does string theory have to say about black holes? Apparently, a "three-brane" can be wrapped around a collapsed three-dimensional sphere ("Black hole") which provides a shield that separates the universe from the cataclysmic effect of the singularity.

So my interpritation of this is that a brane is wrapped around the little thing in a black hole which shields us from the singularity.

Is this correct?

What does string theory say about the singularity itself?

What does string theory say about the singularity of the big bang? and yes, i do know about the theory when two branes are floating in the multiverse and the collide releasing large amounts of energy, thus creating the big bang. But what I want to know is what happened at the instant of creation, i.e. extrapolating back further that (i think its) 10-35 seconds?

Apparently, according to new scientist, that all the problems of black holes have been solved in 3 dimensions, but the mathematics in it are so rigorous that they couldn't finish it in 10-11 dimensions, is this true? if so, does anyone know where the paper is on it?

2. Sep 13, 2007

### hellfire

Cosmological models based on string theory differ from each other on the effective action used to describe the physics at low energies. This action does not describe a string as a fundamental object, but fields that arise as an effective description of the physics of the string at low energies. Depending on the type of effective action that is chosen the resulting classical equations of motion are different.

An important class of effective actions are those that give rise to the brane models, in which the space-time has more than 3 spatial dimensions. However, there are also other models restricted to 3 spatial dimensions like the pre-big-bang models. The effective action for pre-big-bang cosmology looks something like:

$$S_{eff} = \int d^4 x \sqrt{- \det g} \left\{ e^{-\phi} (R + \partial_{\mu} \phi \partial^{\mu} \phi) \right\}$$

This has some resemblance to the action of the Brans-Dicke theory of gravitation with the Brans-Dicke scalar being the dilaton field $$\phi$$.

After reducing the degrees of freedom for homogeneous and isotropic models, this action leads to classical equations of motion that are symmetric under a transformation of the scale factor into a(t) -> 1/a(t). This symmetry is known as scale-factor duality. Applying a temporal inversion (which is also a symmetry of the equations of motion) and the scale-factor duality together, it is possible to associate to a solution a(t) another solution a(t) -> 1/a(-t). This enlarges the classical space of solutions of general relativity, and reveals a new branch of classical evolution beyond the singularity called pre-big-bang.

It has been shown that the pre-big-bang branch may account for inflation, leaving, moreover, a specific signature in the cosmic microwave background. However, the action above does not permit a transition between the pre-big-bang branch and the branch of classical cosmology. This problem is known as "graceful exit". To make the transition possible the action has to be expanded allowing for a dilaton potential or higher derivative terms and quantum effects have to be taken into account. This can be done in different ways, one of them being a standard canonical quantization of the classical theory, leading to a Wheeler-DeWitt type of quantum cosmological evolution equation. The behavior near the singularity would be therefore a tunneling of the wavefunction of the universe from one branch to the other. You can read about this in Graceful exit in quantum string cosmology by Gasperini et. al.

One has to keep in mind that such a model of the quantum universe does leave lots of questions open, especially regarding the dynamics at high energies. But on the other hand this is a simple model that succeeds providing a reasonable consistent description of the early universe in the framework of string theory.

Last edited: Sep 13, 2007