We carry out in full generality and without fixing specific boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are respectively two and three charges which are generic functions over the codimension one null surface. The integrability of charges and their algebra depend on the state-dependence of symmetry generators which is a priori not specified. We establish the existence of infinitely many choices that render the surface charges integrable. We show that there is a choice, the “fundamental basis”, where the null boundary symmetry algebra is the Heisenberg⊕Diff(d − 2) algebra. We expect this result to be true for d > 3 when there is no Bondi news through the null surface.

We present an analytic solution of a charged black hole with hyperscaling violating factor in an Einstein-Maxwell-Dilaton model where the scalar potential is key to the existence of a solution. This solution provides a candidate gravitational description of theories with hyperscaling violation at both finite temperature and finite charge density. Using this background we explore certain features of these theories via AdS/CFT correspondence. Finally, we discuss embeddings based on the well-known sphere reductions of ten and eleven-dimensional supergravity.arXiv:1209.3946v3 [hep-th]

Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T ) and vanishing horizon area A h , but with finite A h /T ratio, the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS 3 . This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS 2 throat. We show that in the near EVH near horizon limit the pinching AdS 3 factor turns to a pinching BTZ black hole and that this near horizon limit is indeed a decoupling limit. We argue that the pinching AdS 3 or BTZ orbifold is resolved if the near horizon limit is accompanied by taking the 4d Newton constant G 4 to zero such that the Bekenstein-Hawking entropy S = A h /(4G 4 ) remains finite. We propose that in this limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of evidence in support of the EVH/CFT correspondence and comment on its connection to the Kerr/CFT proposal and speculations how the EVH/CFT may be used to study generic e.g. Schwarzchild-type black holes.

Expanding upon [arXiv:1404[arXiv: .4472, 1511.06079], we provide further detailed analysis of Bañados geometries, the most general solutions to the AdS 3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon and boundary structure, and geodesic motion on these geometries, as well as the two class of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate further the one-to-one relation between the coadjoint orbits of two copies of Virasoro group and Bañados geometries. We discuss that the information about the Bañados goemetries fall into two categories: "orbit invariant" information and "Virasoro hairs". The former are geometric quantities while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have some number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS 3 Einstein gravity.