Circumambient and galactic-scale environments are intermittently present around black holes that reside in active galactic nuclei. As supermassive impart energy on their host galaxy, so the environment affects dynamics of solar-mass objects gravitational waves emitted from non-vacuum asymmetric binaries. Only recently an exact general-relativistic solution has been found describes a Schwarzschild hole immersed dark matter halo Hernquist type. We perform extensive analysis generic geodesics...

We investigate solutions of type II supergravity which have the product 1,3×M6 structure with non-compact M6 factor and preserve at least four supersymmetries. In particular, we consider various conifolds N = 1 supersymmetric `NS5-brane wrapped on a 2-sphere' solution recently discussed in hep-th/0008001. all these cases, explicitly construct complex structures, Kähler parallel (3,0)-forms corresponding M6. addition, verify that above preserve, respectively, eight supersymmetries underlying...

Kundt spacetimes are of great importance in general relativity 4 dimensions and have a number topical applications higher the context string theory. The degenerate many special unique mathematical properties, including their invariant curvature structure holonomy structure. We provide rigorous geometrical kinematical definition spacetime dimensions; essentially is defined as one admitting null vector that geodesic, expansion-free, shear-free twist-free. A said to be if preferred kinematic...

We investigate the geometry of moduli spaces $\mathscr{M}_{HE}^*(M^{2n})$ Hermitian-Einstein irreducible connections on a vector bundle $E$ over K\"ahler with torsion (KT) manifold $M^{2n}$ that admits holomorphic $\hat\nabla$-covariantly constant fields, where $\hat\nabla$ is connection skew-symmetric $H$. demonstrate such fields induce an action leaves both metric and complex structure invariant. Moreover, if additional condition satisfied, induced are convariantly respect to...

We show that the structure constants of k-Lie algebras, k > 3, with a positive definite metric are sum volume forms orthogonal k-planes. This generalizes result for = 3 in Papadopoulos (2008 Preprint arXiv:0804.2662) and Gauntlett Gutowski arXiv:0804.3078), confirms conjecture Figueroa-O'Farrill (2002 math/0211170).

We investigate the patching of double and exceptional field theories. In theory conditions imposed on spacetime after solving strong section condition imply that 3-form strength H is exact. A similar conclusion can be reached for form strengths theories some plausive assumptions are made relation between transition functions additional coordinates data strengths. illustrate issues arise, explore several alternative options which include introduction C-folds topological geometrisation condition.

We present a novel approach in constructing deviations of the Kerr spacetime whereas symmetries can be preserved. The method was applied trivially all known classical black-hole spacetimes tested, while providing possibility testing and inventing deformations quick innovative way. methodology is based on earlier work by Benenti Francaviglia (1979 Gen. Relativ. Gravit. 10 79) separability geodesic equations we exploited elegant properties Yano tensor order to provide an additional way getting...

We show that the holonomy of supercovariant connection IIB supergravity is contained in SL(32, ). also find reduces to a subgroup SL(32 − N) ⋉ (⊕N 32−N) for backgrounds with N Killing spinors. give necessary and sufficient conditions background admit A supersymmetric probe configuration can involve up 31 linearly independent planar branes preserves one supersymmetry.

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which used for invariant characterization 4-dimensional homogeneous spaces possess an basis.

We investigate the set of spacetime general coordinate transformations (G.C.T.) which leave line element a generic Bianchi Type Geometry, quasi-form invariant; i.e. preserve manifest spatial Homogeneity. find that these G.C.T.'s, induce special time-dependent automorphic changes, on scale factor matrix $\gamma_{\alpha\beta}(t)$ -along with corresponding changes lapse function $N(t)$ and shift vector $N^{\alpha}(t)$. These are dependent, form group are, in general, different from those...

We describe a simple method for generating new string solutions which the brane worldvolume is curved space. As starting point we use with NS-NS charges combined two-dimensional CFTs representing different parts of spacetime. illustrate our many examples, some are associated conformally invariant sigma models. Using U-duality, also obtain supergravity RR can be interpreted as D-branes non-trivial geometry. In particular, discuss case D5-brane wrapped on AdS3× S3 , solution interpolating...

We describe all supersymmetric solutions of the heterotic string which preserve eight supersymmetries and show that these are distinguished by holonomy, , connection, with skew-symmetric torsion. The principal bundles over a four-dimensional hyper-Kähler manifold equipped an anti-self-dual connection fibre group G has Lie algebra, or . Some have interpretation as 5-branes wrapped on transverse space any manifold. construct new for they characterized three integers continuous moduli. There is...

We find under some mild assumptions that the most general potential of 1-dimensional conformal systems with time independent couplings is expressed as $V=V_0+V_1$, where $V_0$ a homogeneous function respect to homothetic motion in configuration space and $V_1$ determined from an equation source potential. Such admit at $SL(2,\bR)$ symmetry which, depending on couplings, embedded Diff(R)$ three different ways. In one case, also Diff(S^1). Examples such models include those $V=\alpha x^2+\beta...

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We identify the fractions of supersymmetry preserved by most general warped flux AdS and flat backgrounds in both massive standard IIA supergravities. find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]} k$ for $n\leq 4$ $2^{[{n\over2}]+1} $4<n\leq 7$ supersymmetries, $k\in \bN_{>0}$. In addition we show that, suitably restricted fields $M^{10-n}$, killing spinors are given terms zero modes Dirac like operators on $M^{10-n}$. This generalizes Lichnerowicz theorem connections whose...

We prove a non-existence theorem for smooth AdS5 solutions with connected, compact without boundary internal space that preserve strictly 24 supersymmetries. In particular, we show D=11 supergravity does not admit such solutions, and all of IIB are locally isometric to the AdS_5 * S^5 maximally supersymmetric background. Furthermore, (massive) IIA also provided homogeneity conjecture massive is valid. context AdS/CFT these results imply if N=3 superconformal theories in 4-dimensions exist,...