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The invariant four-volume ($\mathcal V$) of a complete four-dimensional black hole (the volume of the spacetime at and interior to the horizon) diverges. However, if one considers the black hole resulting from the gravitational collapse of an object and integrates only a finite time to the future of the collapse, the resultant volume is well-defined and finite. We show that for non-degenerate black holes, the volume in this case can be written as $\mathcal V \propto \ln|\lambda|$, where lambda is the affine generator of the horizon and we define our volume $\mathcal V^*$ to be the constant of proportionality. In spherical symmetry, this is the Euclidean volume divided by the surface gravity ($\kappa$). More generally, it turns out that $\mathcal V^*$ is the Parikh volume $({}^3 \mathcal V^*)$ divided by $\kappa$. This allows us to define an alternative local and invariant definition of the surface gravity of a stationary black hole. It also encourages us to find a generalization of the Parikh volume (which depends on the existence of an asymptotically timelike Killing vector) to any region of space or spacetime of arbitrary dimension, provided that this space or spacetime contains a Killing vector. We find some properties of this generalized ``Killing volume'' and rewrite our volume as a Killing volume for a particular Killing vector. We revisit the laws of black hole mechanics, considering them in terms of volumes rather than areas, by writing out our volume and the Parikh volume of Kerr-Newman black holes and then considering their variation with respect to the parameters $M$, $J$ and $Q$ to find a modified BH mechanics first law. We also use our new definition of $\kappa$ to develop an alternate demonstration of the BH mechanics third law. We note that the Parikh volume of a Kerr-Newman black hole is equal to $A r_+/3$, where $A$ is the horizon surface area and $r_+$ the value of the radius at the horizon, and we offer some interpretations of this relationship. We review some other relevant work by Parikh as well as some by Cveti\v{c} et al. and by Hayward. We point out some possible next steps to follow up on the work in this thesis. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-06-04 15:58:03.984

This thesis examines exact solutions to gauged and ungauged supergravity theories in space-time dimensions D⩾5 as well as various instabilities of such solutions. I begin by using two solution generating techniques for five dimensional minimal ungauged supergravity, the first of which exploits the existence of a Killing spinor to generate supersymmetric solutions, which are time-like fibrations over four dimensional hyper-Kähler base spaces. I use this technique to construct a supersymmetric solution with the Atiyah-Hitchin metric as the base space. This solution has three independent parameters and possesses mass, angular momentum, electric charge and magnetic charge. Via an analysis of a congruence of null geodesics, I determine that the solution contains a region with naked closed time-like curves. The centre of the space-time is a conically singular pseudo-horizon that repels geodesics, otherwise known as a repulson. The region exterior to the closed time-like curves is outwardly geodesically complete and possesses an asymptotic region free of pathologies provided the angular momentum is chosen appropriately. The second solution generating technique exploits a hidden G2 symmetry in five dimensional minimal supergravity. I use this hidden symmetry approach to construct the most general black string solution in five dimensions, which is endowed with mass, angular momentum, linear momentum, electric charge and magnetic charge. This general black string satisfies the first law of thermodynamics, with the Bekenstein-Hawking entropy being reproduced via a microstate counting in terms of free M-branes in the decoupling limit. Furthermore it reduces to all previously known black string solutions in its various limits. A phase diagram for extremal black strings is produced to draw conclusions about extremal black rings, in particular why supersymmetric black rings exhibit a lower bound on the electric charge. The same phase diagram further suggests the existence of a new class of supersymmetric black rings, which are completely disconnected from the previously known class. A particular limit of this general black string is the magnetically charged black string, whose thermodynamic phase behaviour and perturbative stability were previously studied but not very well understood. I construct magnetically charged topological solitons, which I then show play an important role in the phase structure of these black strings. Topological solitons in Einstein-Maxwell gravity, however, were previously believed to generically correspond to unstable "bubbles of nothing" which expand to destroy the space-time. I show that the addition of a topological magnetic charge changes the stability properties of these Kaluza-Klein bubbles and that there exist perturbatively stable, static, magnetically charged bubbles which are the local vacuum and the end-point of Hawking evaporation of magnetic black strings. In gauged supergravity theories, bubbles of nothing are stabilised by the positive energy theorem for asymptotically anti-de Sitter space-times. For orbifold anti-de Sitter space-times in odd dimensions, a local vacuum state of the theory is just such a bubble, known as the Eguchi-Hanson soliton. I study the phase behaviour of orbifold Schwarzschild-anti-de Sitter black holes, thermal orbifold anti-de Sitter space-times, and thermal Eguchi-Hanson solitons from a gravitational perspective; general agreement is found between this analysis and the previous analysis from the gauge theory perspective via the AdS/CFT correspondence. I show that the usual Hawking-Page phase structure is recovered and that the main effect of the soliton in the phase space is to widen the range of large black holes that are unstable to decay despite the positivity of their specific heat. Furthermore, using topological arguments I show that the soliton and orbifold AdS geometry correspond to a confinement phase in the boundary gauge theory while the black hole corresponds to a deconfinement phase. An important instability for rotating asymptotically anti-de Sitter black holes is the superradiant instability. Motivated by arguments that the physical end point of this instability should describe a clump of scalar field co-rotating with the black hole, I construct asymptotically anti-de Sitter black hole solutions with scalar hair. Perturbative results, i.e. low amplitude boson stars and small radius black holes with low amplitude scalar hair, are presented in odd dimensions relevant to gauged supergravity theories, namely D=5,7. These solutions are neither stationary nor axisymmetric, allowing them to evade the rigidity theorem; instead the space-time plus matter fields are invariant under only a single helical Killing vector. These hairy black holes are argued to be stable within their class of scalar field perturbations but are ultimately unstable to higher order perturbative modes.

This work investigates how black holes can be described in terms of different definitions of horizons. Global definitions in terms of event horizons and Killing horizons are contrasted with local definitions in terms of trapping horizons and dynamical horizons. The discussion is framed in the context of the laws of black hole thermodynamics.

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xii, 287 p.; also includes graphics. Includes bibliographical references (p. 279-287).

Two major aspects of particle creation by gravitational fields of black holes are studied; the neutrino emission from rotating black holes; and interactions between scalar particles emitted by a black hole. The neutrino emission is investigated under three topics. The asymmetry of the angular dependence of neutrino emission from rotating black holes is calculated first. A low frequency analytic approximation demonstrates the preferential emission of neutrinos (antineutrinos) antiparallel (parallel) to the direction of the black hole's angular momentum vector. Numerical calculations are performed which reveal the dependence of the neutrino emission on polar angle, neutrino energy, and black hole angular momentum and mass. Next we consider the production of a local matter excess by rotating black holes in a baryon symmetric universe. Black holes form at early cosmological times with their rotation axes aligned over the same scale size as the angular momentum in the universe. The evaporation of these black holes produces large scale neutrino currents, whose effectiveness in separating baryons from antibaryons during the hadron era of the early universe is estimated. The local baryon to photon ratio over a galactic size scale depends on the subsequent evolution of the resulting matter and antimatter regions, but is found to have an upper limit of 10 ⁻¹⁴. This is much less than the present observed value of about 10⁻⁹. We then study cosaological magnetic field generation by neutrinos from evaporating black holes. During the radiation era the neutrinos scatter off protons and alectrons, producing a net charge current. This current generates magnetic fields. If present in large enough numbers, rotating black holes could account for the present observed magnetic field in our galaxy. Finally we study the effects of interactions on the black hole evaporation process. Perturbation theory is used, to second order, to calculate the effects of a 2Ф⁴ self-interaction for a scalar field Ф in the 2 dimensional black hole spacetime. a mass renormalization was found to be insufficient to remove all divergences that occur in the calculations. However, the interaction appears to destroy the thermal character of the emission from a black hole evaporating in a vacuum. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. June 8, 2015. / We investigate the rewall paradox proposed by AMPS [1] by rst explaining the Information Paradox together with Hawking's derivation of the thermal radiation emitted from a evaporating black hole [28]. We then ask if one can apply arguments similar to that of Hawking and AMPS in the regime of uid mechanics, which was rst considered by Unruh [59]. We assume that a black hole, with a geometry conformal to the Schwarzschild metric, can be formed in a uid. The sonic hole or \dumb" hole, which is characterized by an acoustic event horizon, is the locus of points at which the background uid is traveling at the local speed of sound. Since sound disturbances are coupled to the background uid and travel at the speed of sound, the acoustic event horizon a ects sound disturbances in a manner analogous to how gravitational black holes a ect light [62]. Like a gravitational black hole, which evaporates by emitting Hawking radiation, we check if an acoustic black hole will emit in a similar kind of radiation in the form of phonons. This is done by constructing a massless scalar eld describing phonon propagation and treating the acoustic black hole just like a gravitational black hole. We apply the arguments put forth by Hawking and AMPS and see if there is any validity to an \acoustic rewall" as this would require certain physical phenomena emerging from sub-atomic scales.

This dissertation has two areas of interest with regard to the four dimensional Kerr black hole; the rst being its conformal nature in its near region and second it characteristic frequencies. With it now known that the scalar solution space of the four dimensional Kerr black hole has a two dimensional conformal symmetry in its near region, it was the rst focus of this dissertation to see if this conformal symmetry is unique to the near region scalar solution space or if it is also present in the spin-half solution space. The second focus of this dissertation was to explore techniques which can be used to calculate these quasinormal mode (characteristic) frequencies, such as the WKB(J) approximation which has been improved from third order to sixth order recently and applied to the perturbations of a Schwarzschild black hole. The additional correction terms show a signi cant increase of accuracy when comparing to numerical methods. This dissertation shall use the sixth order WKB(J) method to calculate the quasinormal mode frequencies for both the scalar and spin-half perturbations of a four dimensional Kerr black hole. An additional method used was the asymptotic iteration method, a relatively new technique being used to calculate the quasinormal mode frequencies of black holes that have been perturbed. Prior to this dissertation it had only been used on a variety of Schwarzschild black holes and their possible perturbations. For this dissertation the asymptotic iteration method has been used to calculate the quasinormal frequencies for both the scalar and spin-half perturbations of the four dimensional Kerr black hole. The quasinormal mode frequencies calculated using both the sixth order WKB(J) method and the asymptotic iteration method were compared to previously published values and each other. For the most part, they both compare favourably with the numerical values, with di erences that are near negligible. The di erences did become more apparent when the mode number (or angular momentum per unit mass increased), but less so when the angular number increased. The only factor that separates these two methods signi cantly, was that the computational time for the sixth order WKB(J) method is less than than that of the asymptotic iteration method.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 139-146).