49 research outputs found

    Formation of Higher-dimensional Topological Black Holes

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    We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n+2)-dimensional collapsing space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions, and we prove that these can be matched to static Λ\Lambda-vacuum exterior space-times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Secondly, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizon-Chmaj-Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution.Comment: 16 pages, 3 figures; v2: typos corrected, matches final published versio

    Avoiding closed timelike curves with a collapsing rotating null dust shell

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    We present an idealised model of gravitational collapse, describing a collapsing rotating cylindrical shell of null dust in flat space, with the metric of a spinning cosmic string as the exterior. We find that the shell bounces before closed timelike curves can be formed. Our results also suggest slightly different definitions for the mass and angular momentum of the string.Comment: 6 pages; v2: references added; v3: remark added for final published versio

    Universality of Highly Damped Quasinormal Modes for Single Horizon Black Holes

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    It has been suggested that the highly damped quasinormal modes of black holes provide information about the microscopic quantum gravitational states underlying black hole entropy. This interpretation requires the form of the highly damped quasinormal mode frequency to be universally of the form: ωR=ln(l)kTBH\hbar\omega_R = \ln(l)kT_{BH}, where ll is an integer, and TBHT_{BH} is the black hole temperature. We summarize the results of an analysis of the highly damped quasinormal modes for a large class of single horizon, asymptotically flat black holes.Comment: 9 pages, 1 figure, submitted to the proceedings of Theory CANADA 1, which will be published in a special edition of the Canadian Journal of Physic

    The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes

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    We analyze in detail the highly damped quasinormal modes of DD-dimensional extremal Reissner-Nordstro¨\ddot{\rm{o}}m and Reissner-Nordstro¨\ddot{\rm{o}}m-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.Comment: 17 pages, 5 figure

    On The 5D Extra-Force according to Basini-Capozziello-Leon Formalism and five important features: Kar-Sinha Gravitational Bending of Light, Chung-Freese Superluminal Behaviour, Maartens-Clarkson Black Strings, Experimental measures of Extra Dimensions on board International Space Station(ISS) and the existence of the Particle ZZ due to a Higher Dimensional spacetime

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    We use the Conformal Metric as described in Kar-Sinha work on Gravitational Bending of Light in a 5D Spacetime to recompute the equations of the 5D Force in Basini-Capozziello-Leon Formalism and we arrive at a result that possesses some advantages. The equations of the Extra Force as proposed by Leon are now more elegant in Conformal Formalism and many algebraic terms can be simplified or even suppressed. Also we recompute the Kar-Sinha Gravitational Bending of Light affected by the presence of the Extra Dimension and analyze the Superluminal Chung-Freese Features of this Formalism describing the advantages of the Chung-Freese BraneWorld when compared to other Superluminal spacetime metrics(eg:Warp Drive) and we describe why the Extra Dimension is invisible and how the Extra Dimension could be made visible at least in theory.We also examine the Maartens-Clarkson Black Holes in 5D(Black Strings) coupled to massive Kaluza-Klein graviton modes predicted by Extra Dimensions theories and we study experimental detection of Extra Dimensions on-board LIGO and LISA Space Telescopes.We also propose the use of International Space Station(ISS) to measure the additional terms(resulting from the presence of Extra Dimensions) in the Kar-Sinha Gravitational Bending of Light in Outer Space to verify if we really lives in a Higher Dimensional Spacetime.Also we demonstrate that Particle ZZ can only exists if the 5D spacetime exists.Comment: Withdrawn: author no longer wishes to post work on arXi

    Area spectra versus entropy spectra in black holes in topologically massive gravity

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    We consider the area and entropy spectra of black holes in topologically massive gravity with gravitational Chern-Simons term. The examples we consider are the BTZ black hole and the warped AdS black hole. For the non-rotating BTZ black hole, the area and entropy spectra are equally spaced and independent of the coupling constant \v of the Chern-Simons term. For the rotating BTZ black hole case, the spectra of the inner and outer horizon areas are not equally spaced in general and dependent of the coupling constant \v. However the entropy spectrum is equally spaced and independent of the coupling constant \v. For the warped AdS black holes for >ˇ1\v >1 by using the quasinormal modes obtained without imposing the boundary condition at radial infinity we find again that the entropy spectrum is equally spaced and independent of the coupling constant \v, while the spectra of the inner and outer horizon areas are not equally spaced and dependent of the coupling constant \v. Our result implies that the entropy spectrum has a universal behavior regardless of the presence of the gravitational Chern-Simons term, and therefore it implies that the entropy is more `fundamental' than the horizon area.Comment: 16 page

    Area spectra of the rotating BTZ black hole from quasinormal modes

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    Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via Bohr-Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for the both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases

    Linking and causality in globally hyperbolic spacetimes

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    The linking number lklk is defined if link components are zero homologous. Our affine linking invariant alkalk generalizes lklk to the case of linked submanifolds with arbitrary homology classes. We apply alkalk to the study of causality in Lorentz manifolds. Let MmM^m be a spacelike Cauchy surface in a globally hyperbolic spacetime (Xm+1,g)(X^{m+1}, g). The spherical cotangent bundle STMST^*M is identified with the space NN of all null geodesics in (X,g).(X,g). Hence the set of null geodesics passing through a point xXx\in X gives an embedded (m1)(m-1)-sphere SxS_x in N=STMN=ST^*M called the sky of x.x. Low observed that if the link (Sx,Sy)(S_x, S_y) is nontrivial, then x,yXx,y\in X are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres SxS_x are isotopic to fibers of (STM)2m1Mm.(ST^*M)^{2m-1}\to M^m. They are nonzero homologous and lk(Sx,Sy)lk(S_x,S_y) is undefined when MM is closed, while alk(Sx,Sy)alk(S_x, S_y) is well defined. Moreover, alk(Sx,Sy)Zalk(S_x, S_y)\in Z if MM is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If (X,g)(X,g) is such that alkalk takes values in Z\Z and gg is conformal to gg' having all the timelike sectional curvatures nonnegative, then x,yXx, y\in X are causally related if and only if alk(Sx,Sy)0alk(S_x,S_y)\neq 0. We show that x,yx,y in nonrefocussing (X,g)(X, g) are causally unrelated iff (Sx,Sy)(S_x, S_y) can be deformed to a pair of Sm1S^{m-1}-fibers of STMMST^*M\to M by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then MM is compact. We show that the universal cover of MM is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

    Quasinormal Spectrum and Quantization of Charged Black Holes

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    Black-hole quasinormal modes have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We study {\it analytically} the asymptotic quasinormal spectrum of a {\it charged} scalar field in the (charged) Reissner-Nordstr\"om spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature TBHT_{BH}, and its electric potential Φ\Phi. We discuss the applicability of the results in the context of black-hole quantization. In particular, we show that according to Bohr's correspondence principle, the asymptotic resonance corresponds to a fundamental area unit ΔA=4ln2\Delta A=4\hbar\ln2.Comment: 4 page
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