Set the `FrameMargins` to a small negative value,

    Manipulate[
       SphericalPlot3D[1, {theta, 0, Pi}, {phi, t, 2 Pi + t},
            Mesh -> {7, 7},
            MaxRecursion -> ControlActive[2, 5],
            PlotRange -> All,
            Boxed -> False,
            Axes -> None,
            SphericalRegion -> True,
            Method -> {"RotationControl" -> "Globe"},
            ImageSize -> {400, 400},
            Background -> Black],
       {{t, 0, Style["t", 10]}, 0, 2 Pi, 0.01},
       FrameMargins -> #
       ] & /@ {Automatic, None, -5}

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/DqAuD.png