Superstring theoryをめぐって(放談室)

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

/pdf/particle-creation-by-black-holes-1htfzwsw5k.pdf

Particle Creation by Black Holes

http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-003180.pdf

Black holes as mirrors: quantum information in random subsystems

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter ?. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra, a covariant tensor calculus is constructed and all the concepts such as metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a ?-deformed Einstein?Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in ?.

https://iopscience.iop.org/article/10.1088/0264-9381/22/17/011/pdf

A gravity theory on noncommutative spaces

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein–Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints ensure that it is not topological. We find that the choice of the gauge group and of the constraints is crucial in recovering a correct deformation of standard gravity. Using the Seiberg–Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve the constraints explicitly and exhibit the first-order noncommutative corrections to the Einstein–Hilbert action.

/pdf/noncommutative-deformation-of-four-dimensional-einstein-48hun5uusq.pdf

Noncommutative deformation of four-dimensional Einstein gravity

An Alternative for Moduli Stabilisation

Scherk-Schwarz breaking and intersecting branes

We study the distribution of graded degrees of freedom in classically stable oriented closed string vacua and use the Rankin-Selberg transform to link it to the finite one-loop vacuum energy. In particular, we find that the spectrum of physical excitations not only must enjoy asymptotic supersymmetry but actually, at very large mass, bosonic and fermionic states must follow a universal oscillating pattern, whose frequencies are related to the zeros of the Riemann ζ-function. Moreover, the convergence rate of the overall number of the graded degrees of freedom to the value of the vacuum energy is determined by the Riemann hypothesis. We discuss also attempts to obtain constraints in the case of tachyon-free open-string theories.

/pdf/vacuum-stability-string-density-of-states-and-the-riemann-2474zfiqcz.pdf

Vacuum stability, string density of states and the Riemann zeta function

We study the distribution of graded degrees of freedom in classically stable oriented closed string vacua and use the Rankin-Selberg transform to link it to the finite one-loop vacuum energy. In particular, we find that the spectrum of physical excitations not only must enjoy asymptotic supersymmetry but actually, at very large mass, bosonic and fermionic states must follow a universal oscillating pattern, whose frequencies are related to the zeros of the Riemann zeta-function. Moreover, the convergence rate of the overall number of the graded degrees of freedom to the value of the vacuum energy is determined by the Riemann hypothesis. We discuss also attempts to obtain constraints in the case of tachyon-free open-string theories.

/pdf/vacuum-stability-string-density-of-states-and-the-riemann-4numcbeqzc.pdf

Matteo A. Cardella

Papers

Noncommutative deformation of four-dimensional Einstein gravity

An Alternative for Moduli Stabilisation

Scherk-Schwarz breaking and intersecting branes

Vacuum stability, string density of states and the Riemann zeta function

Vacuum stability, string density of states and the Riemann zeta function