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Regular black strings solutions associated to a dynamicalFriedmann-Robertson-Walker braneworld are obtained as a particular case of aregular bulk metric, in the context of a variable brane tension. By analyzingthe 5D Kretschmann invariants, we show that the variable brane tension iscapable to remove bulk singularities, along some eras of the evolution of theUniverse. In particular, the black string time-dependent profile in the bulk isanalyzed in the context of the McVittie metric on an E\"otv\"os fluidbraneworld, wherein the fluid dynamical brane tension depends on the branetemperature. The whole bulk is shown to be regular for a Universe dominated bynon-relativistic matter or by relativistic matter/radiation, as thecosmological time elapses. In a particular case the associated black stringsare shown to have finite extension along the extra dimension, what prominentlymodify the higher-dimensional physical singularities. For a Universe dominatedby matter or radiation, we show that the brane singularities are removed alongthe extra dimension, as an effect of the variable brane tension, correspondingalso to the vanishing of the black string horizon. In this case there is aregular solution in the bulk. We show further that no additional physicalsingularity is introduced in the bulk when the Universe is dominated by acosmological constant.

Regular Bulk Solutions and Black Strings from Dynamical Braneworlds with Variable Tension