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Most of the quantum gravity theories support the idea that near the Planck scale, the standard Heisenberg uncertainty principle should be reformulated by the so-called Generalized Uncertainty Principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this manuscript, we consider the effects of the minimal length and maximal momentum as GUP on thermodynamics of the charged TeV-scale black holes and generalized our study to the universe with the extra dimensions based on the ADD model. In this framework, the effect of the electrical charge on thermodynamics of the black hole and existence of the black hole remnants as a potential candidate for the dark matter particles are discussed.

Hawking radiation is the evidence for the existence of black hole. What an observer can measure through Hawking radiation is the transmission probability. In the laboratory, miniature black holes can successfully be generated. The generated black holes are, most commonly, Myers-Perry black holes. In this paper, we will derive the rigorous bounds on the transmission probabilities for massless scalar fields of non-negative-angular-momentum modes emitted from a generated Myers-Perry black hole in six, seven, and eight dimensions. The results show that for low energy, the rigorous bounds increase with the increase in the energy of emitted particles. However, for high energy, the rigorous bounds decrease with the increase in the energy of emitted particles. When the black holes spin faster, the rigorous bounds decrease. For dimension dependence, the rigorous bounds also decrease with the increase in the number of extra dimensions. Furthermore, as comparison to the approximate transmission probability, the rigorous bound is proven to be useful.

We derive the Hawking temperature for both the Vaidya and the Reissner-Nordstrom-Vaidya black holes in two methods, the radial null geodesic method and the complex path method. Both black holes differ in some ways including the charge content and the number of horizons: the Vaidya black hole is charge-less and it has a single horizon while the Reissner-Nordstrom-Vaidya black hole is charged and it has two horizons. We obtain that the Hawking temperature for both black holes depends on their masses and on the radial change of their masses. Black hole with greater mass has a lesser Hawking temperature. We also obtain that there is a condition that should be fulfilled in order to guaranty positive values of the Hawking temperature. Some special cases for the Reissner-Nordstrom-Vaidya black hole are also discussed.

We classify the AdS black holes into extremal and non-extremal black holes by their asymptotic geometries near the horizons. We find that the extremality of the black holes are related to the Hawking temperature. In particular we study AdS black holes solutions of five dimensional Hilbert-Einstein action with a cosmological constant and a dilaton, which is minimally coupled to gravity. We consider type of solutions or black holes which are static and spherically symmetric. By completing the effective Lagrangian into square, or can be called the Hamiltonian method, we write the equation of motions in terms of BPS equations which are of first order differential equations. We find that trivial dilaton contribution gives non-extremal black hole solution while the non-trivial dilaton does not give black hole solution.

Extremal black holes of four dimensional N = 1 supergravity coupled to vector and chiral multiplets can be viewed as solitonic solutions of the theory. In this paper, we particularly study a static spherical symmetric black holes. In the asymptotic region the complex scalars are frozen which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. then, it turns out that the asymptotic geometries have a constant scalar curvature which in general are not Einstein. These spaces are boundaries of the black holes which could also correspond to the near horizon geometries if the value of the scalars in both regions coincides.

We solve numerically the Einstein-Euler system of equations for a perfect fluid with an ideal gas equation of state, moving radially toward a spherically symmetric black hole. In order to do so we use the 3+1 decomposition of space-time with the ADM formulation of general relativity. In particular we study the growth of the event horizon and verify the convergence of our code.

We review a generic recipe for deforming extremal black holes into non-extremal black holes, introduced in [1], which allows to construct general non-extremal black hole solutions from general supersymmetric solutions. We also relate the deformation procedure directly to the equations of motion, by means of the H-FGK formalism [2], providing additional support of the Ansatz.

The aim of these notes is to give a solid basis on the theory of gravitational waves generation using the black hole perturbation description. We present an analytical and numerical point of view. In these notes we present the derivation of the Newman-Penrose equations by means of the null tetrad formalism, with particular attention to the derivation of the scalar functionwhich will describe the gravitational wave, i.e, Ψ4. Next, we describe the case of a Schwarzschild background and show with great detail how to express the evolution equation in a way that can be dealt with in a numerical fashion. We show how to obtain the profiles of the gravitational waves and explain how to analyze several of their properties.

We review recent results about the modelling of radiating gravitational collapse to Schwarzschild-Tangherlini black holes. In particular, we prove that classes of five dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics can be matched to radiating exteriors given by the Bizo´n-Chmaj-Schmidt metric. We show that the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild-Tangherlini solution which is known to be stable

We summarise recent results about the gravitational collapse to black holes in higher dimensions. We construct (n + 2)-dimensional collapsing space-times, which include generalised Friedmann-Lemaitre-Robertson-Walker solutions, and we prove that these can be matched to static Λ-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.

Processes around astrophysical black holes are usually modeled with test (nongravitating) matter and fields. However, the very fact that the holes are "visible" implies that some matter has to be present there. Even if very thin, it can influence the metric, mainly in higher derivatives, which should in turn affect its own behaviour, as well as motion of further (test) satellites. In particular, the geodesic dynamics, integrable in the fields of isolated stationary black holes, should become chaotic. Here we consider exact static, axially and reflection- symmetric space-times of a Schwarzschild black hole surrounded by a thin disc or ring, and examine how the presence of the additional source affects the dynamics of free test particles using recurence analysis.

We calculate the thermal radiation from a thin accretion disk around a rotating black hole taken into account strong field effects. We compare the resulting spectrum in general relativity (GR), with the spectra obtained when modified theories of gravity are considered. The spectrum of Cygnus X-1 in the high-soft state is used to impose constraints on the free parameters in these theories.

In the present work we consider general relativity coupled to Maxwell’s electromagnetism and charged matter. Under the assumption of spherical symmetry, there is a particular class of solutions that correspond to regular charged black holes whose interior region is de Sitter, the exterior region is Reissner‐Nordström and there is a charged thin‐layer in‐between the two. The main physical and geometrical properties of such charged regular black holes are analyzed.

In this paper we study the evolution of a scalar field falling into a static black hole, for which we consider Eddington‐Finkelstein coordinates. For both the massless and massive cases, we find that dispersion depends upon the mean wave number k0 of the initial scalar field wave packet. In particular, we find total absorption for large values of k0 independently of the mass value of the scalar field.

The extreme limit of the double‐Reissner‐Nordstrom spacetime results in two particular solutions. The first one is the Majumdar‐Papapetrou solution which describes two charged non‐rotating extreme black holes in neutral equilibrium, the individual charges being equal to the respective masses. The second one is identified as the Bonnor solution whose constituents cannot be in equilibrium and are separated by a strut, their charges having opposite signs and exceeding the respective masses in absolute value.

We investigate analytically gravitational lensing by charged, stationary, axially symmetric Kerr‐Sen dilaton‐axion black hole in the weak deflection limit. Approximate solutions to the lightlike equations of motion are present up to and including third‐order terms in M/b, a/b and rα/b, where M is the black hole mass, a is the angular momentum, rα = Q2/M,Q being the charge and b is the impact parameter of the light ray. We compute the positions of the two weak field images up to post‐Newtonian order. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightly with the increase of the charge. The lensing observables are compared to these characteristics for particular cases as Schwarzschild and Kerr black holes as well as the Gibbons‐Maeda‐Garfinkle‐Horowitz‐Strominger black hole.

The Einstein equations admit the class of regular solutions asymptotically de Sitter at the origin (λδki as r→0) and at infinity (λδki as r→∞). In a certain range of mass M they describe a regular cosmological black holes with three horizons, a cosmological horizon rc, a black hole horizon rb

In this contribution we complexify five dimensional stationary solutions to obtain time‐dependent ones. In particular the analytic continuation of the Myers‐Perry black hole is obtained; remarkably, the corresponding time‐dependent solution represents a gravitational wave spacetime with boost and rotational symmetries. We also address the complexification of the Emparan‐Reall black ring solution, in this case a 5D inhomogeneous closed cosmology is obtained.

We study the scattering of light by two fixed extreme Reissner‐Nordstrom black holes. We identify the set of unstable periodic orbits of the fractal repeller that describes the chaotic escape dynamics of photons. The main quantities of chaos associated with the repeller are obtained from the analysis of the linear stability of these orbits. The escape rate obtained from the periodic orbit theory is compared with the one obtained from the evolution of statistical ensembles of photons. An analytic estimate of the escape rate in the proximity of a perturbed black hole is also provided.

We investigate the end state of gravitational collapse of Husain space‐time in higher dimensional space‐times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. Earlier work is generalized to higher dimensional space‐times to allow a study of the effect of number of dimensions on the possible final outcome of the collapse in terms of a black hole or a naked singularity. No restriction is adopted on the number of dimensions. These results might be important in the light of the recent proposal that there may exist extra dimensions in the universe.

Currently central black holes in collisionless self‐gravitating systems such as the bulges of galaxies are abundant. One of the most definite cases lies in the center of the milky way [3]. Simulations (e.g.[12]) have studied surrounding cusp profiles as produced by binary black hole mergers. However there seems to be no unified picture that places a black hole in a surrounding bulge and distant halo in a self‐consistent state. Moreover the time and nature of the growth of the black hole, together with the reason for the correlation between its mass and that of the distant galactic bulge, remain unidentified and unexplained. In this paper we study the problem analytically. We seek distribution functions that have a ‘memory’ of previous dynamical evolution. We justify these by fits to numerical simulations. One simple choice of distribution function is able to give a ‘zero flux’ [1] outer boundary region, followed by a 1/r inner shell that gives way to an 1/r2 cusp surrounding the black hole. The black hole...

Using the inverse scattering method we construct a six‐parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)2 rotational symmetry. It describes the superposition of two Myers‐Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C‐metric with an extra flat time direction. We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers‐Perry solution presented herein might be of interest in studying spin‐spin interactions in five dimensional general relativity.

In this contribution we shall discuss some analytic examples of non‐Abelian black holes in a specific N = 2 d = 4 supergravity theory. Some remarks will be made on a possible non‐Abelian version of the attractor mechanism, that works in the Abelian theories.

We study the stability of a family of static, spherically symmetric wormholes supported by a ghost scalar field. We find that these objects are unstable under perturbations, both in the linear regime using perturbation theory and in the nonlinear case which we analyze by numerical means. In particular, we show that an initial perturbation may lead to the collapse of the wormhole to a black hole. We also focus on the possibility that a test particle or a photon can travel from one of the universes to the other through the throat of the wormhole before it collapses. We obtain constraints for the initial position of the test particle or photon in the home universe and the chances it has to explore the other universe and go back to the home universe before being trapped by the black hole horizon.

We consider black hole solutions in extended and alternate gravity theories where the geometry of the black hole spacetimes are modified due to extra‐dimensional effects. We study the cosmological evolution of primordial black holes in a few such theories. We show that the the phenomenon of accretion of radiation in the radiation dominated era could under certain conditions counterbalance the effect of Hawking evaporation, and this leads to longer lifetime for the black holes in these models. Such black holes could survive till the present era and act as candidates for cold dark matter. We discuss the impact of modified geometry of the black holes on strong gravitational lensing by them, which could be a possible avenue for obtaining observational signatures of extra dimensions.

The collision of two back holes is one of the most violent events that can take place in our universe. General relativity predicts that during such a process gravitational waves will be emitted. A lot of effort has been done in the areas of detection, data analysis and numerical simulations. From the point of view of the numerical simulations, the study of emission of gravitational waves in a black‐hole binary, has been extremely productive in the last 3 years. In this paper we will summarize the basic ideas behind the numerical codes used to evolve those systems and we will present two astrophysical motivated examples and the predictions of the simulations: the large gravitational recoil of the final black hole and the energy distribution obtained from the collision of two black holes at ultra‐relativistic speeds.

Recently Alekseev and Belinski have presented a new exact solution of the Einstein‐Maxwell equation which describes two Reissner‐Nordstrom (RN) sources in reciprocal equilibrium (no struts nor strings); one source is a naked singularity, the other is a black hole.In this paper we use the Alekseev‐Belinki solution in the special case in which the charge of the black hole is zero—therefore we have a naked singularity near a neutral black hole. We give the plots of the electric force lines in both the cases in which the naked singularity has a mass comparable with the black hole and in which it is much smaller. The analysis of this latter case confirm the goodness of the Hanni‐Ruffini approximation.

A Fourfold Co‐necessity Principle (FCP) was introduced at FFP8, according to which our customary four dimensions, such as represented with (τ, Θ, φ, r), correspond to four covariant types of dimensions. The paper develops some of its estimated consequences, from the potential impact of minimal and maximal FCP sizes–beyond twofold space‐time minimal length–to the derived existence of four types of singularities rather than only Black and White Hole, bringing geometric explanation and related values for ΛCDM density parameters: 0.04492 to 0.04516 for baryonic Ωm, 0.21436 to 0.21727 for ΩCDM and 0.73757 to 0.74048 for ΩΛ.

In the context of the scenario with Large Extra Dimensions, we investigate the emission spectra for Hawking radiation on the brane from a variety of higher‐dimensional black holes: Schwarzschild, Kerr and Schwarzschild ‐ de Sitter. The energy emission spectra in each case are presented, and their dependence on the spin of the emitted particle, dimension of spacetime, angular momentum of the black hole and cosmological constant of spacetime is discussed.

In the present work we study strong field limit, quasi‐equatorial lensing by the charged, stationary, axially‐symmetric Kerr‐Sen dilaton‐axion black hole. The most outstanding effect is that the Kerr‐Sen black hole caustics drift away from the optical axis and shift in clockwise direction. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found and it is showed that they decrease with the metric parameter Q2 / M. The magnifying power of the lens is shown.

Arguing that black hole physics presents perhaps the most potent rationale for a quantum formulation of general relativity, the Loop Quantum Gravity approach to the problem of microcanonical black hole entropy is surveyed, emphasizing quantum corrections beyond the semiclassical Bekenstein‐Hawking area law, which can be precisely and unambiguously computed, for isolated, macroscopic, generic black holes in four dimensions. For non‐isolated, radiating black holes, a universal criterion of thermal stability is derived in terms of the mass and microcanonical entropy of the equilibrium configuration, assumed to be an isolated system. The bound is shown to saturate at a phase boundary separating thermally stable and unstable phases, with a transition between these that has symptoms of a first order phase transition.

At the conference EFYRA [1] we presented the reconstructed topology of the magnetic flux lines for the solar wind and for prominences, solution of the Lorentz equations of motion for the local Minkowski spacetime of a global Dimension Embedded in Unified Symmetry (DEUS) topology of the Universe. The second solution of same equations of motion will give us the massive stars wind topology, or the followed trajectories in the proximity of a black hole distorted spacetime, differentiated after the values of the integration constants.

The aim of this paper is to evaluate the energy distribution of a stringy black hole solution with the Papapetrou energy‐momentum complex. The space‐time under consideration describes the dual solution known as the magnetic black hole solution. The energy distribution depends on the mass M and charge Q of the magnetic black hole.

Weak Isolated Horizon (WIH) is the most general definition of a black hole horizon so far i.e. WIH is defined through the weakest possible set of boundary conditions imposed on a generic null surface. We will also show that the laws of black hole mechanics can be derived for these horizons. In addition, the definition enables us to put the extremal and non‐extremal black holes on the same phase‐space so that one can make sense of extremal limit.

In the framework of the Dimension Embedded in Unified Symmetry (DEUS) model described by five‐dimensional minimal energy hypersurfaces we observe that, when the considered black hole internal geometry, which is Riemannian, evolves to the asymptotic flat external spacetime (which can be seen as a local Euclidean spacetime), the energy contained in curvature is released as electromagnetic and gravitational radiation. The electromagnetic release on an external observer perception of a DEUS black hole is a jet‐like emission from the black hole polar regions, with a spectrum consistent with the observed SED for blazars. Also, considering the self‐similarity of the DEUS model, with the Friedmann‐Robertson‐Walker (FRW) metric of the Universe as another description of the a higher level DEUS object’s helicoidal hypersurface, the extragalactic background light (EBL) spectrum must be consistent with our spectrum. Through these fittings we are able to determine the age of the Universe at present time.

In the series of papers by Ida, Oda and Park, the complete description of Hawking radiation to the brane localized Standard model fields from mini black holes in the low energy gravity scenarios are obtained. In this proceedings, we briefly review what we have learned in those papers.

Binary black hole spacetimes with a helical Killing vector are discussed as an approximation for the early stage of a binary system. The Einstein equations are studied in a projection formalism for this case where they are equivalent to a three dimensional gravitational theory with an SL(2, C)/SO(1, 1) sigma model as the material source. 2 + 1 decompositions of the 3‐metric are used to establish the field equations on the orbit space of the Killing vector. The Killing horizons and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. It is shown that the spacetime cannot be asymptotically flat in the strong sense to have a smooth null infinity.

Entanglement entropy is calculated for an extension of Bombeli et al. black hole entropy flat model to maximally extended Schwarzschild spacetime in order to present an integrated model with thermofield‐dynamical description. Local analysis shows that entanglement entropy is strongly concentrated near the horizon.

We construct initial data for spacetimes containing a black hole whose horizon is in quasi‐equilibrium. We adopt an excision technique to deal with the black hole singularity, and prescribe inner boundary conditions derived from the Isolated Horizon formalism. The numerical implementation makes use of pseudo‐spectral methods.

Over the past year and a half, a number of groups have produced stable runs of a binary black hole system evolving through merger and ringdown. In [2][3], in particular, the tremendous speedup to the field was driven by special sets of gauge evolution equations, capable of handling several issues that have traditionally plagued black hole simulations: avoiding the singularity, guaranteeing a constraint satisfying solution at least in the exterior region, and advecting the holes through the numerical grid.Since several successful recipes have already been proposed, the goal of this study is to review them and analyze the consistency of the published results. A preliminary comparison of the waveform outcome of each different gauge prescription is presented.

We show that LISA should detect the ringdown radiation emitted by newly formed, oscillating massive black holes with large signal‐to‐noise ratio and measure the characteristic (quasi‐normal) frequencies of the oscillations with great accuracy throughout the observable Universe, providing accurate estimates of the black holes’ mass and angular momentum. Under reasonable assumptions LISA’s signal‐to‐noise ratio should be large enough to allow tests of the Kerr nature of astrophysical black holes, i.e. tests of the no‐hair theorem of general relativity.

We present a 3+1 decomposition of the boundary conditions to be satisfied by a black hole whose horizon is in quasi‐equilibrium, according to the characterization provided by the Isolated Horizon formalism. Such a decomposition can be useful in the study of black hole dynamics as a Cauchy problem. We illustrate these boundary conditions through the numerical construction of initial data for spacetimes containing a black hole.

Suppose General Relativity, provocatively governed by a dimensional coupling constant, is a spontaneously Induced theory. In which case, black hole configurations are naively expected to get gracefully modified. For example, the exterior Schwarzschild solution is fully recovered at the GR‐limit of such a theory. Serendipitously, however, due to a phase transition, which takes place exactly at the would have been horizon, it connects with a novel dark core characterized by a varying Newton constant (the word ‘dark’ is borrowed from cosmology, where the one and the same theory gives rise to dark matter superimposed by a rippled structure). Once the strict GR‐limit is relaxed, localized Einstein‐style gravitational corpuscles (practically massless particle configurations with a Newton constant varying core) make their appearance; they become point‐like at the GR‐limit.

We shall review the present status of uniqueness theorem for static black holes in higher dimensional sapcetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerayte and non‐degenerate components of the event horizon. Next issue will be devoted to self‐gravitating σ‐models in n‐dimensional spacetime. One can show that the Schwarzschild‐Thargerlini spacetime is the only maximally extended static asymptotic flat solution with non‐rotating regular event horizon with constant mapping. Using conformal energy condition one can show the uniqueness of a static electrically and magnetically charged black holes being the solution of Einstein (n − 2)‐gauge form field equation of motion. The staticity theorem for n‐dimensional charged black holes and the uniqueness of five‐dimensional stationary axisymmetric black hole with self‐gravitating σ‐model with be treated.

We describe the stationary accretion of dark energy around a black hole. Solution for a stationary spherically symmetric accretion of the relativistic perfect fluid with an arbitrary equation of state onto the Schwarzschild black hole is presented. This solution is a generalization of Michel solution and applicable to the problem of dark energy accretion. It is shown that accretion of phantom energy is accompanied with the gradual decrease of the black hole mass. Masses of all black holes tend to zero in the phantom energy universe approaching to the Big Rip.

We study the emission of gravitational waves by EMRIs in numerically produced spacetimes which are highly accurate solutions of Einstein equations and contain a black hole and a torus. In order to assess the maximal impact these tori could have on the produced waveforms, we consider them as compact, massive and close to the central black hole and try to determine whether LISA can detect their presence. Our results reinforce the confusion problem recently pointed out in [1].

We discuss recent results concerning the gravitational wave (GW) emission from matter accretion onto a Schwarzschild black hole. A numerical “hybrid” procedure is adopted in which the dynamics of the accreting matter is studied by solving, in axisymmetry (m = 0), the non‐linear general relativistic equations of fluid dynamics using a code based on high‐resolution‐shock‐capturing (HRSC) methods; the GW signal is correspondingly obtained as a solution of the inhomogeneous odd‐and even‐parity equations of linearized metric perturbations of Schwarzschild spacetime (i.e., Regge‐Wheeler and Zerilli‐Moncrief equations). Self‐gravity of the accreting matter and radiation‐reaction effects are neglected. Different configurations are considered: i) quadrupolar dust shells; ii) runaway unstable thick accretion disks and iii) oscillations of (stable) thick disks.

A generic set of initial data recently proposed by Hertog, Horowitz and Maeda, within the asymptotically anti deSitter, spherically symmetric, class of spacetimes in Einstein scalar field theory, has been argued will evolve toward a singularity that can not be contained within a black hole. We will argue that there is a logical loophole in the argument associated with the supposition that the end state needs to be a stationary spacetime. We then describe a physically reasonable possibility for the evolution of the data that would allow the singularity to be contained within a black hole.

Recently Holz & Wheeler (2002) have considered a very attractive possibility to detect retro‐MACHOs, i.e. retro‐images of the Sun by a Schwarzschild black hole. We analyze the case of a Kerr black hole with an arbitrary spin for some selected positions of a distant observer with respect to the equatorial plane of a Kerr black hole. We discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses and rotation parameters by analyzing these forms of mirages. In some sense, that is a manifestation of gravitational lens effect in the strong gravitational field near the black hole horizon and a generalization of the retro‐gravitational lens phenomenon. We also propose to use future radio interferometer Radioastron facilities to measure shapes of mirages (glories) and to evaluate the black hole spin as a function of the position angle of a distant observer.

The asymptotics of Quasinormal Modes for Schwarzschild‐de Sitter Black Holes is investigated in the large angular momentum limit by means of the analytic dilatation method. The case of Nariai space‐time is exactly treated.