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A classical computation of vector bremsstrahlung in ultrarelativisticgravitational-force collisions of massive point particles is presented in anarbitrary number d of extra dimensions. Our method adapts the post-linearformalism of General Relativity to the multidimensional case. The total emittedenergy, as well as its angular and frequency distribution and characteristicvalues, are discussed in detail.  For an electromagnetic mediation propagated in the bulk, the emitted energy$E_{em}$ of scattering with impact parameter b has magnitude $E_{em} \sim e^4e'^2 \gamma^{d+2}/(m^2 b^{3d+3})$, with dominant frequency $\omega_{em} \sim\gamma^2/b$. For the gravitational force the charge emits via vector field,propagated in the bulk, energy $E_{rad}\sim[G_D m' e]^2 \gamma^{d+2}/b^{3d+3}$for $d \geq 2$, with dominant frequency $\omega\sim\gamma^2/b$ and energy$E_{rad}\sim[G_5 m' e]^2\gamma^{3}\ln \gamma/b^{6}$ for $d=1$, with most of theenergy coming from a wide frequency region $\omega \in [\gamma/b),\gamma^2/b]$. For the UED model with extra space volume $V=(2\pi R)^d$ the emitted energyis $E_{UED}\sim (b^{d}/V)^2 E_{rad}$. Finally, for the ADD model, includingfour dimensions, the electromagnetic field living on 3-brane, loses on emissionthe energy $E_{ADD}\sim[G_D m'e]^2\gamma^{3}/(V b^{2d+3})$, with characteristicfrequency $\omega_{ADD}\sim\gamma/b$.  The contribution of the low frequency part of the radiation (soft photons) tothe total radiated energy is shown to be negligible for all values of d. Thedomain of validity of the classical result is discussed. The result is analyzedfrom the viewpoint of the deWitt - Brehme - Hobbs equation (and correspondingequations in higher dimensions).

Vector Bremsstrahlung by Ultrarelativistic Collisions in Higher Dimensions