On the Possibility of Building a Black Hole for Electrons in the Laboratory

We point out in this work that if our recently proposed unified description of gravitation and electromagnetism through a symmetric metric tensor is true, then building in the laboratory black holes for electrons with radii rE ≥ 0.5m in air and with much smaller radii in a vacuum should be possible. The possibility that spacetime is curved in the presence of an electromagnetic field, just like it is curved in the presence of a gravitational field, was recently studied [1] and experiments to test this conjecture were proposed [2]. If the ideas introduced in ref.[1] are correct, then not only do we have a unified description of gravitation and electromagnetism through a symmetric metric tensor gμν , but also new physical phenomena such as the redshift and deflection of light in an electric and magnetic field, respectively [2]. When a negatively(positively) charged test particle moves in the viscinity of a positively(negatively) charged sphere of radius R and mass M , with an electric potential of V (R) on its surface, the line element is given by [2]