[en] It is shown that four-dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: G_ab+ αGB_ab + δ⁵⁵_abαexp[-2χ/√α]GB₄ = 0 and the Pauli-Einstein equations G_ab - 3αP_ab/5 = 0, and the Bach-Einstein equations B_ab = 0. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.

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[en] Using two sequences of symmetric trace free tensors, called the 'null data', we give a complete characterization of the asymptotics of all asymptotically flat, stationary solutions with non-vanishing ADM mass to Einstein's vacuum field equations. We present necessary and sufficient growth estimates on the null data for the existence of such a solution.

[en] By using the fact that the Yang-Mills and the Einstein equations are the integrability conditions of simple linear systems, we give a local ''pre-integration'' of these equations. This local pre-integration is the analogue of the integration of the zero curvature condition dsub(μ)Asub(ν)-dsub(ν)Asub(μ)+[Asub(μ), Asub(ν)]=0 in the form Asub(μ)=Mdsub(μ)(M^-1). (orig.)

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[en] This paper deals with the analytical solutions of the field equations in the presence of radiating plane symmetric source. For this purpose we have solved the field equations as well as junction conditions by imposing the conformal flatness conditions. The effective adiabatic index (that determines the stability of the system) has been calculated for the present radiating source. It has been found that effective adiabatic index remains invariant throughout the matter distribution. To study the thermal behavior of the source, we have discussed the thermal profile of the source and found that in the absence of dissipation from the system the temperature of the system remains constant. (author)

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[en] An exact plane wave solution of the coupled supergravity field equations is given. It is non-trivial in the sense that it cannot be reduced to the parallel-plane wave solution of vacuum Einstein's equations by supersymmetry transformations. (author)