Exact solutions in multidimensional gravity with antisymmetric forms

Abstract

This short review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the product form. The sigma-model approach and exact solutions are reviewed. 1

On Observational Predictions from Multidimensional Gravity

“…5 we derive the post-Newtonian (PN) approximation of the above solutions in order to designate possible traces of extra dimensions and p-branes in the comparatively weak gravitational fields of the great majority of planetary and stellar systems, including binary pulsars. This section generalizes the results of previous papers [28,29]. For black holes, apart from the PN parameters which determine the motion of test bodies in their sufficiently far neighbourhood, there is one more potentially observable parameter, the Hawking temperature T H , which is obviously important for small (e.g., primordial) black holes rather than those of stellar or galactic mass range.…”

“…where h ω , u ω , c A and c A are integration constants; c A and c A are constrained by the orthogonality relations (29) (the vectors c and c are orthogonal to each individual vector Y s ∈ V); the function s(., .) has been defined in (16).…”

“…Other solutions to the equations of motion are known, connected with Toda chains and Lie algebras [35,36,37].…”

Multidimensional Cosmology, Constants and Transition to New Si Units

“…These solutions appear either in models with antisymmetric forms and scalar fields [23][24][25][26][27][28][29] or in models with multi-component anisotropic fluid (MCAF). Here we consider spherically-symmetric solutions with horizon in two models: i) with scalar field and fields of forms, ii) with multi-component anisotropic fluid (MCAF), when certain relations on fluid parameters are imposed.…”

p-Brane black holes as stability islands

“…There exist a large number of such solutions in arbitrary dimensions -see e.g. [2,[4][5][6][7][8][9] and references therein. They are important in connection with studies of processes at early stages of the Universe, counts of micro-states in BH thermodynamics and now especially due to new developments in M-theory [10] related to the AdS/CFT correspondence [11].…”