Self-similar accretion in thin disks around near-extremal black holes

Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov-Thorne accretion thin disk model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO). We observe that, when the disk pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov-Thorne model of GRS 1915+105, the Shakura-Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disk solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins.Comment: 13 pages, 6 figures; v2 matches published version in MNRAS; v3: typos fixed, results unchange

Gravitational multipole moments from Noether charges

We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We show that our definition exactly matches Thorne's mass and current multipole moments in Einstein gravity, which are defined in terms of metric components. For radiative configurations, the total multipole charges -- including the contributions from the source and the radiation -- are given by surface charges at spatial infinity, while the source multipole moments are naturally identified by surface integrals in the near-zone or, alternatively, from a regularization of the Noether charges at null infinity. The conservation of total multipole charges is used to derive the variation of source multipole moments in the near-zone in terms of the flux of multipole charges at null infinity.Comment: v1: 22 pages + 13 pages of appendices, 1 figure; v2: published version in JHE

Mass of Kerr-Newman Black Holes in an external magnetic field

The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular momentum and electric charge.Comment: 21 pages; v2 matches published versio

Symplectic and Killing Symmetries of AdS3_3 Gravity: Holographic vs Boundary Gravitons

The set of solutions to the AdS$_3$ Einstein gravity with Brown-Henneaux boundary conditions is known to be a family of metrics labeled by two arbitrary periodic functions, respectively left and right-moving. It turns out that there exists an appropriate presymplectic form which vanishes on-shell. This promotes this set of metrics to a phase space in which the Brown-Henneaux asymptotic symmetries become symplectic symmetries in the bulk of spacetime. Moreover, any element in the phase space admits two global Killing vectors. We show that the conserved charges associated with these Killing vectors commute with the Virasoro symplectic symmetry algebra, extending the Virasoro symmetry algebra with two $U(1)$ generators. We discuss that any element in the phase space falls into the coadjoint orbits of the Virasoro algebras and that each orbit is labeled by the $U(1)$ Killing charges. Upon setting the right-moving function to zero and restricting the choice of orbits, one can take a near-horizon decoupling limit which preserves a chiral half of the symplectic symmetries. Here we show two distinct but equivalent ways in which the chiral Virasoro symplectic symmetries in the near-horizon geometry can be obtained as a limit of the bulk symplectic symmetries.Comment: 39 pages, v2: a reference added, the version to appear in JHE

Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity

We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions.Comment: 16 pages, ESI proceedings, v2: typos corrected, published versio

Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra

We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to $d$ dimensional Einstein gravity. Each element in the phase space is a geometry with $SL(2,\mathbb R)\times U(1)^{d-3}$ isometries which has vanishing $SL(2,\mathbb R)$ and constant $U(1)$ charges. We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries. In four spacetime dimensions, the phase space is unique and the symmetry algebra consists of the familiar Virasoro algebra, while in $d>4$ dimensions the symmetry algebra, the NHEG algebra, contains infinitely many Virasoro subalgebras. The nontrivial central term of the algebra is proportional to the black hole entropy. This phase space and in particular its symmetries might serve as a basis for a semiclassical description of extremal rotating black hole microstates.Comment: Published in PLB, 5 page

Wiggling Throat of Extremal Black Holes

We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861]. Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the $U(1)$ isometry directions. We show that this set of metrics is equipped with a consistent symplectic structure and hence defines a phase space. The phase space forms a representation of an infinite dimensional algebra of so-called symplectic symmetries. The symmetry algebra is an extension of the Virasoro algebra whose central extension is the black hole entropy. We motivate the choice of diffeomorphisms leading to the phase space and explicitly derive the symplectic structure, the algebra of symplectic symmetries and the corresponding conserved charges. We also discuss a formulation of these charges with a Liouville type stress-tensor on the torus defined by the $U(1)$ isometries and outline possible future directions.Comment: 56 pages, 3 figure

Inner Mechanics of 3d Black Holes

We investigate properties of the inner horizons of certain black holes in higher-derivative three-dimensional gravity theories. We focus on BTZ and Spacelike Warped Anti-de Sitter black holes, as well as on asymptotically Warped de-Sitter solutions exhibiting both a cosmological and a black hole horizon. We verify that a First Law is satisfied at the Inner horizon, in agreement with the proposal of \cite{Castro:2012av}. We then show that, in Topologically Massive Gravity, the product of the areas of the inner and outer horizons fails to be independent on the mass, and trace this to the diffeomorphism anomaly of the theory.Comment: 5 page