## Friday, June 15, 2007

### Gr-qc papers on Friday

Let us look at the new gr-qc papers tonight:

Diaz-Polo and Fernandez-Borja solve a well-defined mathematical problem how to extract the precise dependence of entropy on the horizon area of a black hole in loop quantum gravity. Physics-wise, the paper is of course incorrect because the calculation of areas and entropies in loop quantum gravity is known to be physically absurd. Nevertheless, it is a well-defined and potentially interesting mathematical problem.

The spectrum of areas in LQG is semi-discrete but it is not quite equally spaced because the contributions to the areas are of the form $[j(j+1)]^{\frac 12}$ for $j$ being an integer or a half-integer. The resulting dependence of the entropy on the area is something in between a linear function and a stair-like function. The authors study the impact of this semi-discrete spectrum on the Hawking radiation.

Alekseev and Belinski ask whether two charged black holes can be in equilibrium. In Newtonian physics, the answer would be Yes: you just cancel gravity against a repulsive electric force. In general relativity, the answer is also Yes in the case of extremal black holes. That's why BPS objects of the same kind can co-exist more peacefully than Hamas and Fatah.

The authors claim that for non-extremal black holes, the answer is No. The answer would also be No for two naked singularities (super-extremal holes) but it can be Yes for a mixed pair. They get it by a complex analysis of solutions. I don't quite understand what's non-trivial about their result: if the two black holes have the same Q/M ratio, the no-force condition clearly means that they are both extremal. If they have different Q/M ratios, the no-force condition clearly means that one of them must be sub-extremal and the other must be super-extremal, am I wrong? The Q/M ratios must move in the opposite directions, I think.

Hogan proposes a very interesting refinement of the idea that a non-commutative geometry is behind holography in quantum gravity. Take two space-like separated events 1,2 (if I understand well) whose proper distance is $L_{12}$. He argues that the relative separation in two transverse directions $x,y$ satisfies
$[x,y] = -i l_{P} L_{12}$
which implies a new uncertainty principle
$\Delta x \Delta y \geq l_{P} L_{12} / 2.$
Note that the uncertainty grows as you keep on separating the events. The paper is at a comparable level of concreteness as Lenny's or Raphael's holographic papers. It also talks about LIGO and holographic noise implied by this paradigm and I think people should read it.

Brevik, Elizalde, Gorbunova, Timoškin promote a combination of FRW equations with a specific fluid with a certain non-linear equation of state as a useful model for various transitions in cosmology as well as quintessence. They want to explain the CMB anisotropy by considering viscosity in their fluid.

Larena and Perez determine what kind of FRW-like equations of classical general relativity with additional scalars are solvable. The answer depends on rationality of certain exponents while other relevant exponents may be written in terms of square roots.

Nacir and Mazzitelli arguably study Einstein's equations with a scalar field source in the quantum gravity regime. The action for the scalar field contains arbitrarily high derivatives but it also depends on an observer velocity given by a D-vector $u_\mu$ that picks a privileged reference frame. That implies that the dispersion relations also depend on infinitely many coefficients.

While I don't find such general Lorentz-breaking theories well motivated, that's not my worst problem with the paper. What's worse is that they only want to write Einstein's equations for expectation values of the stress energy tensor only but at the same moment, they want to be careful about the renormalization of the stress energy tensor operators. I don't understand the logic and motivation of this approximation.