We investigate continuously self-similar solutions of four-dimensional Einstein-Maxwell-dilaton theory supported by charged null fluids. We work under the assumption of spherical symmetry and the dilaton coupling parameter a is allowed to be arbitrary. First, it is proved that the only such vacuum solutions with a time-independent asymptotic value of the dilaton necessarily have vanishing electric field, and thus reduce to Roberts’ solution of the Einstein-dilaton system. Allowing for additional sources, we then obtain Vaidya-like families of self-similar solutions supported by charged null fluids. By continuously matching these solutions to flat spacetime along a null hypersurface one can study gravitational collapse analytically. Capitalizing on this idea, we compute the critical exponent defining the power-law behavior of the mass contained within the apparent horizon near the threshold of black hole formation. For the heterotic dilaton coupling $a=1$ the critical exponent takes the value 1/2 typically observed in similar analytic studies, but more generally it is given by $\gamma = a^2(1+a^2)^{−1}$. The analysis is complemented by an assessment of the classical energy conditions. Finally, and on a different note, we report on a novel dyonic black hole spacetime, which is a time-dependent vacuum solution of this theory. In this case, the presence of constant electric and magnetic charges naturally breaks self-similarity.

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Black Holes,Spacetime Singularities,Black Holes in String Theory

• Physical Sciences - Natural Sciences