By Renata Kallosh, Emanuele Orazi
These lecture notes are devoted to the latest theoretical functions of Black gap recommendations in high-energy physics. the most motivation of this quantity is to give the most recent black gap backgrounds which are proper for gauge/gravity correspondence. best scientists within the box clarify powerful options for locating singular and cosmological strategies embedded in gauged supergravity, laying off mild on underlying homes and symmetries. ranging from a simple point, the mathematical constructions underlying black holes and cosmologies are printed, supporting the reader seize the relationship among theoretical ways and actual observations with insights into attainable destiny advancements from either a theoretical and experimental standpoint.
The subject matters lined during this quantity are in keeping with lectures introduced in the course of the “Theoretical Frontiers in Black Holes and Cosmology” college, held in Natal in June 2015.
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Phys. Lett. B 383, 39 (1996) 5. S. Ferrara, R. Kallosh, Supersymmetry and attractors. Phys. Rev. D 54, 1514 (1996) 6. S. Ferrara, R. Kallosh, Universality of supersymmetric attractors. Phys. Rev. D 54, 1525 (1996) 7. K. Gaillard, B. Zumino, Duality rotations for interacting fields. Nucl. Phys. B 193, 221 (1981) 8. E. Schrödinger, Contributions to Born’s new theory of the electromagnetic field. Proc. Roy. Soc. Lond. A150, 465–477 (1935) 9. W. A. Wheeler, Classical physics as geometry: gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space.
Ferrara, R. Kallosh, Supersymmetry and attractors. Phys. Rev. D 54, 1514 (1996) 6. S. Ferrara, R. Kallosh, Universality of supersymmetric attractors. Phys. Rev. D 54, 1525 (1996) 7. K. Gaillard, B. Zumino, Duality rotations for interacting fields. Nucl. Phys. B 193, 221 (1981) 8. E. Schrödinger, Contributions to Born’s new theory of the electromagnetic field. Proc. Roy. Soc. Lond. A150, 465–477 (1935) 9. W. A. Wheeler, Classical physics as geometry: gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space.
Using simple identities of Real Special Geometry we arrive to S[U, φ x ] = dρ e2U a I J d −U (e h I ) ± q I dρ d d −U (e h J ) ± q J ± (2eU Ze ) , dρ dρ (157) whose associated flow equations are d −U (e h I ) = ∓q I . dρ (158) These can be solved immediately, giving e−U h I = A I ∓ q I ρ, (159) 30 T. F. Ramírez for some integration constants A I . These are harmonic functions in the 4-dimensional spatial, transverse space. It is a well-known result that the static, timelike supersymmetric solutions of these theories can be constructed in terms of harmonic functions (which can have more poles that the ones we have obtained, which must be consistent with spherical symmetry) [49].