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Register a new userGlobal aspects of accelerating and rotating black hole space-times
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The complete family of exact solutions representing accelerating and rotating black holes with possible electromagnetic charges and a NUT parameter is known in terms of a modified Plebanski-Demianski metric. This demonstrates the singularity and horizon structure of the sources but not that the complete space-time describes two causally separated black holes. To demonstrate this property, the metric is first cast in the Weyl-Lewis-Papapetrou form. After extending this up to the acceleration horizon, it is then transformed to the boost-rotation-symmetric form in which the global properties of the solution are manifest. The physical interpretation of these solutions is thus clarified.
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An exact solution of Einsteins equations which represents a pair of accelerating and rotating black holes (a generalised form of the spinning C-metric) is presented. The starting point is a form of the Plebanski-Demianski metric which, in addition to the usual parameters, explicitly includes parameters which describe the acceleration and angular velocity of the sources. This is transformed to a form which explicitly contains the known special cases for either rotating or accelerating black holes. Electromagnetic charges and a NUT parameter are included, the relation between the NUT parameter $l$ and the Plebanski-Demianski parameter $n$ is given, and the physical meaning of all parameters is clarified. The possibility of finding an accelerating NUT solution is also discussed.
Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect is both its similarity and simultaneous dissimilarity to classical black body radiation: A black holes spectrum certainly looks like that of a black/grey body, yet the number of emitted particles per unit time differs greatly. However it is precisely this emission rate that determines whether the resulting radiation field behaves classically or non-classically. It has been known nearly since the effects discovery that a black holes radiation is in this sense non-classical. However, this has been an utterly underappreciated property. In order to give a more readily quantifiable picture of this, we introduced the easily evaluated and interpreted notion of sparsity. Sadly, and much to relativists chagrin, astrophysical black holes (and their evaporation) tend to be observationally elusive entities. Luckily, Hawkings derivation lends itself to reformulations that survive outside its astrophysical origin - only three things are needed: a universal speed limit, a notion of a horizon, and lastly a sprinkle of quantum dynamics on top. With these ingredients at hand, the last thirty-odd years have seen a lot of work to transfer Hawking radiation into the laboratory, using a range of physical models. A large part of this thesis is aimed at providing electromagnetic analogues to prepare an analysis of our notion of sparsity in these analogues. For this, we developed extensively a purely algebraic/kinematical analogy based on covariant meta-material electrodynamics, but also an analytic/dynamical analogy based on stratified refractive indices. After introducing these analogue space-time models, we explain why the notion of sparsity is much more subtle and difficult to come by than in the original, astrophysical setting.
We study the evaporation of black holes in non-commutative space-times. We do this by calculating the correction to the detectors response function for a moving mirror in terms of the noncommutativity parameter $Theta$ and then extracting the number density as modified by this parameter. We find that allowing space and time to be non-commutative increases the decay rate of a black hole.
Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one of the critical tests for a model of quantum gravity. However, Hawkings original derivation used quantum field theory on a fixed background. Efforts have been made to include the spacetime fluctuations arising from the quantization of the dynamical degrees of freedom of gravity itself and study the effects on the Hawking particles. Using semi-classical analysis, we study the effects of quantum fluctuations of scalar field stress-tensors in asymptotic non-flat spherically symmetric black-hole space-times. Using two different approaches, we obtain a critical length-scale from the horizon at which gravitational interactions become large, i.e., when the back reaction to the metric due to the scalar field becomes significant. For 4-D Schwarzschild AdS (SAdS) and Schwarzschild de Sitter (SdS), the number of relevant modes for the back-reaction is finite only for a specific range of values of M/L (where M is the mass of the black-hole, and L is related to the modulus of the cosmological constant). For SAdS (SdS), the number of relevant modes is infinite for M/L $sim$ 1 (0.2 < M/L < $frac{1}{3sqrt{3}}$). We discuss the implications of these results for the late stages of black-hole evaporation.
In previous works we have studied spin-3/2 fields near 4-dimensional Schwarzschild black holes. The techniques we developed in that case have now been extended here to show that it is possible to determine the potential of spin-3/2 fields near $D$-dimensional black holes by exploiting the radial symmetry of the system. This removes the need to use the Newman-Penrose formalism, which is difficult to extend to $D$-dimensional space-times. In this paper we will derive a general $D$-dimensional gauge invariant effective potential for spin-3/2 fields near black hole systems. We then use this potential to determine the quasi-normal modes and absorption probabilities of spin-3/2 fields near a $D$-dimensional Schwarzschild black hole.
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