## Friday, November 14, 2008

### GR-like theory without black holes?

When I was reading the preprints today, I got upset by this one:
Alexander Torres-Gomez, Kirill Krasnov
so I must get some relief. They claim nothing less than having a theory that passes the same classical tests as general relativity (sensitive to first post-Newtonian corrections) but doesn't have any black holes.

So you have to look what is their action. In one form, equation 5, it is the Einstein-Hilbert action plus an action for a scalar field chi. Clearly, for the configurations where the scalar field is constant, the theory is nothing else than general relativity and shares all of its solutions. Fine. So a reader is surely still interested how they can possibly lose the black hole solutions such as Schwarzschild.

They write the equations of motion for the Schwarzschild problem and obtain a generalized Schwarzschild solution with two integration constants, K and R. The Schwarzschild solution is clearly there for K=0 which means constant chi. In order for the reader to get confused, they subsequently use different letters r, chi, x for the radial coordinate while they define a function kappa of the integration constants, K and R.

But with an infinitesimal attention, you will still know that K=0 corresponds to kappa=1/2 and the Schwarzschild black hole solution is still there. How can it evaporate? Well, finally, they list four possible values of the parameter kappa, and they are:
• kappa > 1/2
• 0 < kappa < 1/2
• kappa = i delta
• kappa = 0
Suddenly, kappa=1/2 is gone (although they briefly mention kappa=1/2 in the paragraph dedicated to the second option, however without realizing what this special choice means). They conclude that the theory doesn't have black holes. Well, this is what I call a genuinely dumb conclusion.

The black hole solution is still there, of course, for kappa=1/2. The other solutions for kappa different from 1/2 are, indeed, different from black holes. But general relativity doesn't mean that all solutions must be black holes. Non-vacuum solutions, such as solutions with a variable scalar field chi (the same thing as kappa different from 1/2 solutions), are not black holes. They are morally similar to "stars". General relativity doesn't imply and has never implied that stars couldn't exist.

More generally, I view the expectation in 2008 that black holes will evaporate from physics of gravity to reveal a stunning lack of knowledge and intuition. The emergence of black hole horizons is an inevitable consequence of the equivalence principle. Even in Newton's theory, one could see that the escape velocity could hypothetically exceed the speed of light for a sufficiently massive object. It may happen in relativity, too. Whenever it does, light cannot escape the gravitational field and an event horizon develops.

Moreover, we know that the black holes always follow from the correct microscopic description of quantum gravity whose range of validity goes much further than to these trivial classical problems such as "do black hole exist?", namely string theory. I assure you that every single compactification in the proverbial landscape of 10^{500} semi-realistic choices - as well as any other compactification of string theory - implies the existence of black holes. You may be amazed by the unprecedented predictivity of string theory in this respect but that's how the world works. All these basic things are settled.

The existence of black hole solutions could have been open in 1917 and, at a more academic level, in the 1960s. But not today. Sorry, Alexander and Kirill, but your text is dumb beyond imagination.