  This paper reexamines the physical roles of trapped and passing electrons in
electron Bernstein-Greene-Kruskal (BGK) solitary waves, also called the BGK
phase space electron holes (EH). It is shown that the charge density variation
in the vicinity of the solitary potential is a net balance of the negative
charge from trapped electrons and positive charge due to the decrease of the
passing electron density. A BGK EH consists of electron density enhancements as
well as a density depletion, instead of only the density depletion as
previously thought. The shielding of the positive core is not a thermal
screening by the ambient plasma, but achieved by trapped electrons oscillating
inside the potential energy trough. The total charge of a BGK EH is therefore
zero. Two separated EHs do not interact and the concept of negative mass is not
needed. These features are independent of the strength of the nonlinearity. BGK
EHs do not require thermal screening, and their size is thus not restricted to
be greater than the Debye length $\lambda_D$. Our analysis predicts that BGK
EHs smaller than $\lambda_D$ can exist. A width($\delta$)-amplitude($\psi$)
relation of an inequality form is obtained for BGK EHs in general. For
empty-centered EHs with potential amplitude $\gg 1$, we show that the
width-amplitude relation of the form $\delta\propto\sqrt{\psi}$ is common to
bell-shaped potentials. For $\psi\ll 1$, the width approaches zero faster than
$\sqrt{\psi}$.
