42,898 research outputs found
Geodesic Geometry of Black Holes
No full textThe study of geodesics is of intrinsic significance in the study of the geometry of space-time. In this thesis null, space-like and
time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstrouml;m and Kerr black holes. These
space-times have been investigated with varying degrees of thoroughness in many articles and some books. However, there are some significant gaps in these treatments and the central aim of this thesis is to fill these gaps where necessary. Moreover, the following topics are covered for the first time.
1. In Chapter 4 a thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are
treated in a complete manner. This has been done by obtaining exact solutions and solving them numerically.
2. In Part II all solutions for geodesics for a
Reissner-Nordstrouml;m black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle.
3. In Chapter 14 all solutions for geodesics in the equatorial plane of a Kerr black hole have been given in complete detail, i.e. time-like, null and space-like geodesics.
4. The study of special types of non-equatorial geodesics for a Kerr black hole have been given in complete detail, i.e. time-like (Chapter 17), null (Chapter 15) and space-like (Chapter 16). This has been done in order to distinguish the qualitatively different types of solutions.
Calculation of the explicit formulas, which describe these geodesics, as well as numerically computed diagrams representing the geodesics have been incorporated in these studies. The following subjects have been also treated:
5. Solutions for the geodesics in Reissner-Nordstrouml;m black holes with |Q_*| gt;= M, which are black holes with one (|Q_*| = M) or no horizon (|Q_*|gt; M) (Chapter 8).
6. Solutions of geodesics in extreme and fast Kerr black holes, i.e. black holes with a = M (extreme) and a gt; M (fast). As in the case of |Q_*| gt; M, fast black holes have naked singularities (Chapter 14).
7. Some general observations about orbit types of the Kerr black holes regarding relationships between parameters such as angular momentum, energy, Carter constant and mass and angular momentum of black holes (Chapter 13).
8. Some corrections to errors found in the literature.
While it has not been possible to cover all different cases which occur for possible relations amongst the parameters specifying a
general black hole, interesting geodesics have, however, been studied and a more thorough presentation of the properties of geodesics has now been given
Braneworld black holes
No full textThe braneworld paradigm provides an interesting framework within which to explore the possibility that our Universe lives in a fundamentally higher dimensional space- time. In this thesis we investigate black holes in the Randall-Sundrum braneworld scenario. We begin with an overview of extra-dimensional physics, from the original proposal of Kaluza and Klein up to the modern braneworld picture of extra dimensions. A detailed description of braneworld gravity is given, with particular emphasis on its compatibility with experimental tests of gravity. We then move on to a discussion of static, spherically symmetric braneworld black hole solutions. Assuming an equation of state for the "Weyl term", which encodes the effects of the extra dimension, we are able to classify the general behaviour of these solutions. We then use the strong field limit approach to investigate the gravitational lensing properties of some candidate braneworld black hole solutions. It is found that braneworld black holes could have significantly different observational signatures to the Schwarzschild black hole of standard general relativity. Rotating braneworld black hole solutions are also discussed, and we attempt to generate rotating solutions from known static solutions using the Newman-Janis complexification "trick"
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Classical and thermodynamic stability of black holes
No full textWe consider the stability of black holes within both classical general relativity and
the semiclassical thermodynamic description. In particular, we study linearised perturbations and their contributions to the gravitational partition function. Exploring the connection between classical and thermodynamic stability, we find classical instabilities and new families of vacuum black holes.
We start by studying negative modes of black hole partition functions, which represent pathologies in the one-loop quantum corrections. In particular, we extend this study to charged black holes (Reissner-Nordstr¨om), using a method based on gauge-invariant perturbations, and to rotating black holes (Kerr-AdS), where a numerical technique is employed. In the both cases, we find a negative mode in the region where local thermodynamic stability fails, as expected.
We then present the first examples of linearised classical instabilities of vacuum
asymptotically flat black holes. We analyse numerically perturbations of Myers-Perry
solutions, both in the single spin and in the equal spins (odd D) cases. For sufficiently
high rotation, in the so-called ultraspinning regime, new negative modes of the partition function may arise whose threshold marks both the onset of a classical instability of the black hole (not just of the associated black branes) and the bifurcation to a new family of black hole solutions. In the case of singly-spinning solutions, we find the threshold stationary modes signalling the instabilities, confirming a conjecture by Emparan and Myers. In the case of solutions with equal spins, we are able to find perturbations that grow exponentially in time in D = 9 (we believe that this extends to higher odd D).
Furthermore, the new family of solutions bifurcating at the onset of the instability should have a single rotational symmetry, saturating the rigidity theorem
Einstein-Yang-Mills black holes in anti de-Sitter space
No full textIn this thesis we consider Einstein-Yang-Mills black holes in asymptotically anti-de Sitter space, in the presence of an su(N) gauge �eld. For a purely magnetic gauge �eld we de�ne a set of charges, namely the mass and N - 1 gauge invariant magnetic charges, and show that they characterize stable black holes.
We then go on to consider dyonic black holes which carry both electric and magnetic charge. We investigate spherically symmetric black holes and solitons, and �nd equations of motion for solutions with su(N) gauge �elds. These equations are solved numerically to �nd black hole and soliton solutions with su(2) and su(3) gauge groups.
We then turn to dyonic black holes with planar event horizons and investigate their suitability as gravitational analogues to high temperature superconductors under the AdS/CFT correspondence. We generalise a previously known ansatz for su(2) gauge groups to su(N), and show that there is a critical temperature above which non-abelian solutions do not exist. Below this critical temperature, we show that they are thermodynamically favoured over equivalent Reissner-Nordstr�om solutions, and have in�nite D.C. conductivity
Braneworld black holes and black strings
No full textThis thesis involves the study of strong and weak gravity phenomenology within the braneworld paradigm. We begin with a general overview of the hypothesised concept of extra spatial dimensions and explain why they are so interesting. Turning next to the topic of classical four-dimensional black holes, we discuss their formation via gravitational collapse and indicate some of the strong observational evidence of their existence. We then merge the two independent theories of extra dimensions and black holes together to form braneworld black holes. Focusing our attention on two distinct braneworld scenarios, we examine the effects produced from either strong or weak gravity. The prospect of obtaining experimental verification of the existence of additional spacelike dimensions in the upcoming ground-based accelerators, makes the theoretical research of braneworld gravity within this thesis even more enticing. We start with a non-perturbative approach to look for exact, spherically symmetric star or black hole solutions on a Randall-Sundrum brane from the perspective of the five-dimensional spacetime. By fixing the background, we explore the permissible braneworld trajectories within it that correspond to a braneworld observer, the solutions of the brane Tolmann-Oppenheimer-Volkoff equations. A variety of static gravitating matter sources on the brane are obtained in a range of different backgrounds. Our final aim is a consistent brane embedding in a Schwarzschild- Anti de Sitter spacetime as these solutions are potential candidates for brane stars or black holes. The weak and dominant energy conditions determine the physically sensible solutions which have the interpretation of braneworld stars. We then study time-dependent trajectories as a possible description of time-dependent braneworld black holes. This work is then generalised by relaxing the simplifying assumption of Z(_2)-symmetry, previously imposed around the brane. Non-Z(_2) symmetric spacetimes are applicable in processes which concern only one side of the brane, for example black hole recoil or the emission of Hawking radiation. We determine that a subset of the allowed brane trajectories in an asymmetric background are exactly the same as the Z(_2)-symmetric case. Next, we explore perturbative gravity in the Hofava-Witten model of heterotic M-theory. The study of scalar and gravitational fluctuations determines that the radion mode is coupled to the bulk scalar field, indicating only one single degree of freedom. Our analysis also determines the instability of a black string. We then compute the complete mass spectrum of the graviton mode. Using the five-dimensional gravitational physics, we determine what the gravitational interaction an observer on the braneworld would perceive. This analysis involves the computation of the Newtonian potential between two test masses on the visible brane, together with the four-dimensional tensor structure of the massless graviton propagator. Finally, as an application to the earlier work, we comment on work which is in progress: the study of possible brane black hole solutions in low energy heterotic M-theory
Quantum Aspects of Black Holes
No full textIn this thesis we study two quantum aspects of black holes, their entropy and the Hawking effect. First, we present a model for the statistical interpretation of black hole entropy and show that this entropy emerges as a result of missing information about the exact state of the matter from which the black hole was formed. We demonstrate that this idea can be applied to black holes made from both ultra-relativistic and nonrelativistic particles.
In the second part we focus our attention on several features of black hole evaporation. We discuss the dependence of the Hawking radiation on the vacuum definition of different observers. It becomes evident that in certain cases the choice of observer has an influence on the particle spectrum. In particular, we study the meaning of the Kruskal vacuum on the horizon. After that we determine the Hawking flux for nonstationary black holes. We find approximate coordinates which are regular on the time dependent horizon and calculate the particle density measured by an observer at infinity.
Finally, we derive the response of a particle detector in curved background. In our approach we use the Unruh detector to quantify the spectrum of radiation seen by general observers in Minkowski, Schwarzschild and Vaidya space-times. We find that an arbitrarily accelerated detector in flat space-time registers a particle flux with a temperature proportional to a time dependent acceleration parameter. A detector moving in Schwarzschild space-time will register a predominantly thermal spectrum with the exact temperature depending on the observer's trajectory. If the detector is located at constant distance from the black hole it measures a shifted temperature which diverges on the horizon. On the other hand, a detector in free fall towards the black hole does not register a thermal particle flux when it crosses the horizon. In this framework corrections to the temperature measured by a detector moving in Vaidya space-time are obtained as well. We argue that our result also clarifies the role of horizons in black hole radiation
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Black holes at accelerators
No full textIn theories with large extra dimensions and TeV-scale gravity, black holes are copiously produced in particle collisions at energies well above the Planck scale. I briefly review some recent work on the phenomenology of this process, with emphasis on theoretical uncertainties and possible strategies for measuring the number of extra dimensions
Black holes in the gravity/gauge theory correspondence
No full textThe AdS/CFT correspondence provides a microscopic description of black hole thermodynamics. In this thesis, I study the relation between the classical physics of black holes and this microscopic description. I first consider the gauge theory's holographic encoding of non-trivial global causal structure, by studying various probes of the black hole. I study the charged black hole, so that the thermal scale is separated from the horizon scale, to demonstrate which relates to the field theory scale size. I find that, when probing the horizon, both Wilson loops and the duals of static supergavity probes have a scale size determined by the horizon, but the field theory scale size is divergent for a time-dependent probe. I also use the bulk black hole geometry to study the physics of the boundary theory. If we consider a dynamical boundary, a braneworld cosmology is induced from the bulk. However, the presence of matter on the brane introduces unconventional quadratic terms in the FRW equations of this braneworld. I find that bulk black holes induce identical unconventional terms on a matterless brane, therefore providing an alternative description of the same cosmology. A new conjecture relating classical and thermodynamic stability of black branes has emerged from the AdS/CFT correspondence. I make progress in proving this for the case of Schwarzschild black holes in a finite cavity. I also extend the conjecture to the supergravity backgrounds of the direct product form Schwarzschild-AdS x Sphere, which are relevant to my study of the AdS/CFT correspondence
On black holes in string theory
No full textPhDThis thesis investigates black holes in string theory through string amplitudes and
through gauge-gravity duality. The research presented in this thesis supports the
claim that string theory is capable of a consistent quantum-mechanical description
of black holes and develops techniques which may prove useful in testing this claim
in new scenarios.
The thesis comprises two parts. Part I describes novel disk amplitudes which
derive the supergravity elds sourced by a D-brane with a travelling wave, and
Part II describes free particle structures arising in a matrix model which is related
through gauge-gravity duality to asymptotically anti-de Sitter black holes.
The disk amplitudes calculated in Part I provide a direct connection between
the microscopic worldsheet description of a D-brane with a travelling wave and
its macroscopic supergravity description. A D-brane carrying a travelling wave
can be mapped via string dualities to the two-charge D1-D5 black hole and this
research opens up the possibility to use these techniques to study the three-charge
D1-D5-P black hole.
Part II of the thesis identi es free particle descriptions of non-holomorphic operators
in a complex matrix model derived from dimensional reduction of N = 4
Super-Yang-Mills theory. This research generalizes the free particle description in
the half-BPS sector of this theory which was realized in supergravity and enabled
studies of the microscopics of singular geometries. The free particle descriptions
have been derived at zero gauge coupling; if these or similar structures are also
present at strong coupling this research could be used to study the microscopics
of non-extremal asymptotically anti-de Sitter black holes
Accretion Into and Emission from Black Holes
No full textAnalyses are given of various processes involving matter falling
into or coming out of black holes.
A significant amount of matter may fall into a black hole in a
galactic nucleus or in a binary system. There gas with relatively high
angular momentum is expected to form an accretion disk flowing into the
hole. In this thesis the conservation laws of rest mass, energy, and
angular momentum are used to calculate the radial structure of such a
disk. The averaged torque in the disk and flux of radiation from the
disk are expressed as explicit, algebraic functions of radius.
Matter may be created and come out of the gravitational field of
a black hole in a quantum-mechanical process recently discovered by
Hawking. In this thesis the emission rates of massless particles by
Hawking's process are computed numerically. The resulting power spectra
of neutrinos, photons, and gravitons emitted by a nonrotating hole are
given. For rotating holes, the rates of emission of energy and angular
momentum are calculated for various values of the rotation parameter.
The evolution of a rotating hole is followed as energy and angular
momentum are given up to the emitted particles. It is found that angular
momentum is lost considerably faster than energy, so that a black
hole spins down to a nearly nonrotating configuration before it loses a
large fraction of its mass. The implications are discussed for the lifetimes and possible present configurations of primordial black
holes (the only holes small enough for the emission to be significant
within the present age of the universe.
As an astrophysical application, a calculation is given of the
gamma-ray spectrum today from the emission by an assumed distribution
of primordial black holes during the history of the universe. Comparison
with the observed isotropic gamma-ray flux above about 100 MeV yields
an upper limit of approximately 10^4 pc^(-3) for the average number density
of holes around 5 x 10^(14)g. (This is the initial mass of a nonrotating
black hole that would just decay away in the age of the universe.) The
prospects are discussed for observing the final, explosive decay of an
individual primordial black hole. Such an observation could test the
combined predictions of general relativity and quantum mechanics and
also could provide information about inhomogeneities in the early universe
and about the nature of strong interactions at high temperatures.</p
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