Black hole critical phenomena without black holes

Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.     

Observing higher-dimensional black holes at the LHC

A new approach to spacetime proposing the existence of n compactified large extra dimensions predicts the creation of higher-dimensional black holes at the LHC of CERN. In case they form, signatures of such black holes at accelerators would be quite significant and black hole decay products would carry valuable information for particle physics and cosmology. In this study we first make a short theoretical introduction, then present the results of an analysis made on a Monte Carlo simulation modeling black hole production and decay at the LHC. This analysis includes the examination of the lepton case in black hole to Higgs decay channels, reconstruction of the black hole masses, a calculation of the Hawking temperature and a determination of the radiated jets/leptons multiplicity ratio.Received: 2 April 2004, Revised: 29 October 2004, Published online: 25 January 2005PACS: 04.70, 04.50, 14.80.-j Corresponding author: S. Sekmen     

Black holes and black hole thermodynamics without event horizons

We investigate whether black holes can be defined without using event horizons. In particular we focus on the thermodynamic properties of event horizons and the alternative, locally defined horizons. We discuss the assumptions and limitations of the proofs of the zeroth, first and second laws of black hole mechanics for both event horizons and trapping horizons. This leads to the possibility that black holes may be more usefully defined in terms of trapping horizons. We also review how Hawking radiation may be seen to arise from trapping horizons and discuss which horizon area should be associated with the gravitational entropy.     

Light’s bending angle due to black holes: from the photon sphere to infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray’s impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.     

Top quark production from black holes at the CERN LHC

LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this Letter we calculate the cross sections for top quark production from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, Higgs or supersymmetry) at the LHC may be an useful signature for black hole production.     

Thermodynamics of black holes

The thermodynamic approach is used to investigate the properties of black holes. The presence of surface gravitation makes it possible to introduce a coefficient of surface tension of black holes and capillary fluctuations of the horizon due to this surface tension; this makes it possible to find the temperature dependence of the surface entropy and the energy of the black holes. It is shown that there is a critical temperature at which a black hole explodes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–36, September, 1977.Some further matters will be discussed in a following paper in collaboration with Professor D. D. Ivanenko, t o whom the author is very grateful for fruitful discussions.     

Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

Geometrothermodynamics of black holes

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold’s and Ruppeiner’s thermodynamic metrics for black holes. For the Reissner–Nordström black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.     

Transition radiation at the boundary of a black body

Transition radiation from a charged particle intersecting the boundary with a black body has been examined. It has been shown that the radiation intensities for the cases when the relativistic particle enters the black body and leaves it are strongly different.     

On the topology of black holes

We establish from local hypotheses some results concerning the final state topology of black holes. We show that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple.Dedicated to Ted FrankelThis work has been partially supported by NSF grants DMS-8802877 and DMS-9006678     

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large $r$ go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the $N$ th order Lovelock $\Lambda $ -vacuum solutions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.