Ivan Booth

Extremality conditions for isolated and dynamical horizons

A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a parameter e which characterizes how close a horizon is to extremality and should be calculable in numerical simulations.

Black brane entropy and hydrodynamics: The boost-invariant case

The framework of slowly evolving horizons is generalized to the case of black branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The results are used to analyze the behavior of both event and apparent horizons in the gravity dual to boost-invariant flow. These considerations are motivated by the fact that at second order in the gradient expansion the hydrodynamic entropy current in the dual Yang-Mills theory appears to contain an ambiguity. This ambiguity, in the case of boost-invariant flow, is linked with a similar freedom on the gravity side. This leads to a phenomenological definition of the entropy of black branes. Some insights on fluid/gravity duality and the definition of entropy in a time-dependent setting are elucidated.

On the apparent horizon in fluid-gravity duality

This article develops a computational framework for determining the location of boundary-covariant apparent horizons in the geometry of conformal fluid-gravity duality in arbitrary dimensions. In particular, it is shown up to second order and conjectured to hold to all orders in the gradient expansion that there is a unique apparent horizon which is covariantly expressible in terms of fluid velocity, temperature, and boundary metric. This leads to the first explicit example of an entropy current defined by an apparent horizon and opens the possibility that in the near-equilibrium regime there is preferred foliation of apparent horizons for black holes in asymptotically anti-de Sitter spacetimes.

Spacetime near isolated and dynamical trapping horizons

to determine the near-horizon spacetime, while for the null case (an isolated horizon) more information is needed. In both cases spacetime is allowed to be of arbitrary dimension and the formalism accomodates both general relativity as well as more general eld equations. The formalism is demonstrated for two applications. First, spacetime is considered near an isolated horizon and the construction is both checked against the Kerr-Newman solution and compared to the well-known near-horizon limit for stationary extremal black hole spacetimes. Second, spacetime is examined in the vicinity of a slowly evolving horizon and it is demonstrated that there is always an event horizon candidate in this region. The geometry and other properties of this null surface match those of the slowly evolving horizon to leading order and in this approximation the candidate evolves in a locally determined way. This generalizes known results for Vaidya as well as certain spacetimes known from studies of the uid-gravity correspondence.

Supersymmetric isolated horizons

We construct a covariant phase space for rotating weakly isolated horizons in Einstein?Maxwell?Chern?Simons theory in all (odd) D ? 5 dimensions. In particular, we show that horizons on the corresponding phase space satisfy the zeroth and first laws of black-hole mechanics. We show that the existence of a Killing spinor on an isolated horizon in four dimensions (when the Chern?Simons term is dropped) and in five dimensions requires that the induced (normal) connection on the horizon has to vanish, and this in turn implies that the surface gravity and rotation 1-form are zero. This means that the gravitational component of the horizon angular momentum is zero, while the electromagnetic component (which is attributed to the bulk radiation field) is unconstrained. It follows that an isolated horizon is supersymmetric only if it is extremal and nonrotating. A remarkable property of these horizons is that the Killing spinor only has to exist on the horizon itself. It does not have to exist off the horizon. In addition, we find that the limit when the surface gravity of the horizon goes to zero provides a topological constraint. Specifically, the integral of the scalar curvature of the cross sections of the horizon has to be positive when the dominant energy condition is satisfied and the cosmological constant ? is zero or positive, and in particular rules out the torus topology for supersymmetric isolated horizons (unless ? < 0) if and only if the stress?energy tensor Tab is of the form such that Tab?anb = 0 for any two null vectors ? and n with normalization ?ana = ?1 on the horizon.

Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang?Mills etc) in D = 4 dimensions and cosmological constant in D ? 3 dimensions. In this paper, we present a further extension of the framework that includes black holes in higher dimensional Einstein?Gauss?Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by In this expression SD?2 is the (D ? 2)-dimensional cross section of the horizon with an area form and the Ricci scalar is the D-dimensional Newton constant and ? is the Gauss?Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.

Supersymmetric isolated horizons in ADS spacetime

Abstract We discuss various physical aspects of non-extremal, extremal and supersymmetric black holes in asymptotically anti-de Sitter (ADS) spacetimes. Specifically, we discuss how the isolated horizon (IH) framework leads to an ambiguity-free description of rotating black holes in these spacetimes. We then apply this framework to investigate the properties of supersymmetric isolated horizons (SIHs) in four-dimensional N = 2 gauged supergravity. Among other results we find that they are necessarily extremal, that rotating SIHs must have non-trivial electromagnetic fields, and that non-rotating SIHs necessarily have constant curvature horizon cross sections and a magnetic (though not electric) charge.

Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions and extensions to modified gravity

The thermodynamics of the Universe is restudied by requiring its compatibility with the holographic-style gravitational equations which govern the dynamics of both the cosmological apparent horizon and the entire Universe, and possible solutions are proposed to the existent confusions regarding the apparent-horizon temperature and the cosmic entropy evolution. We start from the generic Lambda Cold Dark Matter (

Insights from Melvin–Kerr–Newman spacetimes

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Proximity of black hole horizons: Lessons from Vaidya spacetime

CDM) cosmology of general relativity (GR) to establish a framework for the gravitational thermodynamics. The Cai-Kim Clausius equation for the isochoric process of an instantaneous apparent horizon indicates that, the Universe and its horizon entropies encode the \emph{positive heat out} thermodynamic sign convention, which encourages us to adjust the traditional positive-heat-in Gibbs equation into the positive-heat-out version