Sommerfeld's quantum condition of action and the spectra of Schwarzschild black hole

If the situation of quantum gravity nowadays is nearly the same as that of the quantum mechanics in it's early time of Bohr and Sommerfeld, then a first step study of the quantum gravity from Sommerfeld's quantum condition of action might be helpful. In this short paper the spectra of Schwarzschild black hole(SBH) in quasi-classical approach of quantum mechanics is given. We find the quantum of area, the quantum of entropy and the Hawking evaporation will cease as the black hole reaches its ground state.Comment: 7 pages, no figures, submitted to Classical and Quantum Gravit

E_{11}, ten forms and supergravity

We extend the previously given non-linear realisation of E_{11} for the decomposition appropriate to IIB supergravity to include the ten forms that were known to be present in the adjoint representation. We find precise agreement with the results on ten forms found by closing the IIB supersymmetry algebra.Comment: 14 page