Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in $D > 3$ dimensions, but they fail for the three dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here we provide an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces instead of the full spacetime. Our method is also applicable to black holes in generic dimensions but is most efficient in three, four, and five dimensions. We give four dimensional Kerr, five dimensional Myers-Perry and three dimensional warped-anti-de Sitter, and the three dimensional asymptotically flat black holes as examples.
The relation between event horizons and trapping horizons is investigated in a number of different situations with emphasis on their role in thermodynamics. A notion of constant change is introduced that in certain situations allows the location of the event horizon to be found locally. When the black hole is accreting matter the difference in area between the two different horizons can be many orders of magnitude larger than the Planck area. When the black hole is evaporating the difference is small on the Planck scale. A model is introduced that shows how trapping horizons can be expected to…
In four dimensions the topology of the event horizon of an asymptotically flat stationary black hole is uniquely determined to be the two-sphere $S^2$. We consider the topology of event horizons in higher dimensions. First, we reconsider Hawking's theorem and show that the integrated Ricci scalar curvature with respect to the induced metric on the event horizon is positive also in higher dimensions. Using this and Thurston's geometric types classification of three-manifolds, we find that the only possible geometric types of event horizons in five dimensions are $S^3$ and $S^2 \times S^1$. In s…
The solution of the 5D Kaluza-Klein's theory is obtained. This solution is a Lorentzian wormhole between two event horizons. It is shown that this solution can sew with (4D Reissner-Nordström's solution + Maxwell's electrical field) on the event horizon. Such construction is composite wormhole connecting two asymptotically flat region. From the viewpoint of infinite observer this wormhole is an electrical charge. According to J. Wheeler terminology this is "charge without charge".
We show that there exist five-dimensional multi-black hole solutions which have analytic event horizons when the space-time has non-trivial asymptotic structure, unlike the case of five-dimensional multi-black hole solutions in asymptotically flat space-time.
We consider the microcanonical ensemble of black holes in gravitational theories in asymptotically anti-de Sitter spacetime with a conformal field theory dual. We argue that typical quantum black hole states show no violations of general covariance on the horizon.
It is proved that coordinate transformations of the Schwarzschild metric to new static and stationary metrics do not eliminate the mode of a particle ''fall'' to the event horizon of a black hole. This mode is unacceptable for the quantum mechanics of stationary states.
The Friedmann equation in the Friedmann-Robertson-Walker(FRW) universe with any spatial curvature is derived from the first law of thermodynamics on the event horizon. The key idea is to redefine a Hawking temperature on the event horizon. Furthermore, we obtain the evolution equations of the universe including the quantum correction and explore the evolution of the universe in the $f(R)$ gravity. In addition, we also investigate the generalized second law of thermodynamics in Einstein gravity and the $f(R)$ gravity. This perspective also implies that the first law of thermodynamics on the eve…
It is shown that the event horizon of 4D black hole or $ds^2 = 0$ surfaces of multidimensional wormhole-like solutions reduce the amount of information necessary for determining the whole spacetime and hence satisfy the Holography principle. This leads to the fact that by matching two metrics on a $ds^2 = 0$ surface (an event horizon for 4D black holes) we can match only the metric components but not their derivatives. For example, this allows us to obtain a composite wormhole inserting a 5D wormhole-like flux tube between two Reissner-Nordström black holes and matching them on the event horiz…
Event horizons are (generically) not physically observable. In contrast, apparent horizons (and the closely related trapping horizons) are generically physically observable --- in the sense that they can be detected by observers working in finite-size regions of spacetime. Consequently event horizons are inappropriate tools for defining astrophysical black holes, or indeed for defining any notion of evolving}black hole, (evolving either due to accretion or Hawking radiation). The only situation in which an event horizon becomes physically observable is for the very highly idealized stationary …
We study the evolution of cosmological event horizons in anisotropic Kasner universes in the presence of a positive cosmological constant by analyzing null geodesics. At later times, the asymptotic form of cosmological horizons is the same spherical surface as the de Sitter horizon. At the early times, however, it has non-spherical shape with its eccentricity decreases with time. The horizon area increases with time respecting the second law of thermodynamics. The initial shape of the cosmological horizon takes the form of a needle or pancake surface depending on the nature of the background s…
We present numerical evidence for the existence of new black hole solutions in $d\geq 6$ spacetime dimensions. They approach asymptotically the Minkowski background and have an event horizon topology $S^2\times S^{d-4}$. These static solutions share the basic properties of the nonrotating black rings in five dimensions, in particular the presence of a conical singularity.
We consider a pointlike two-level system undergoing uniformly accelerated motion. We evaluate the transition probability for a finite time interval of this system coupled to a massless scalar field near a fluctuating event horizon. Horizon fluctuations are modeled using a random noise which generates light-cone fluctuations. We study the case of centered, stationary and Gaussian random processes. The transition probability of the system is obtained from the positive-frequency Wightman function calculated to one loop order in the noise averaging process. Our results show that the fluctuating ho…
It is argued that free QFT can be defined on the event horizon of a Schwarzschild-like spacetime and that this theory is unitarily and algebraically equivalent to QFT in the bulk (near the horizon). Under that unitary equivalence the bulk hidden SL(2,R) symmetry found in a previous work becomes manifest on the event horizon, it being induced by a group of horizon diffeomorphisms. The class of generators of that group can be enlarged to include a full Virasoro algebra of fields which are defined on the event horizon. These generators have a quantum representation in QFT on the event horizon and…
We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward …
Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modif…
In this work, we have described the Brans-Dicke theory of gravity and given a particular solution by choosing a power law form of scalar field $ϕ$ and constant $ω$. If we assume first law and entropy formula on apparent horizon then we recover Friedmann equations. Next, assuming first law of thermodynamics, the validity conditions of GSL on event horizon are presented. Also without use first law, if we impose the entropy relation on the horizon, then we also obtain the condition of validity of GSL on event horizon. The validity of GSL completely depends on the model of BD scalar field solution…
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 show how Hawking radiation can also be seen to arise from trapping horizons and discuss which horizon area should be ass…
The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.
Event horizons are the defining feature of classical black holes. They are the key ingredient of the information loss paradox which, as paradoxes in quantum foundations, is built on a combination of predictions of quantum theory and counterfactual classical features: neither horizon formation nor its crossing by a test body is observable. Furthermore, horizons are unnecessary for the production of Hawking-like radiation. We demonstrate that when this radiation is taken into account it prevents horizon crossing/formation in a large class of models. We conjecture that horizon avoidance is a gene…
The Event Horizon Telescope (EHT) is expected to soon produce polarimetric images of the supermassive black hole at the center of the neighboring galaxy M87. There are indications that this black hole is rapidly spinning. General relativity predicts that such a high-spin black hole has an emergent conformal symmetry near its event horizon. In this paper, we use this symmetry to analytically predict the polarized near-horizon emissions to be seen at the EHT and find a distinctive pattern of whorls aligned with the spin.
Increasing astronomical evidence indicates that the expansion of the universe is accelerating. By simply solving Einstein equations we show in this letter that a wide class of generic quintessence models leading to eternal acceleration is associated with spacetime static metrics which do not exhibit future event horizons, and therefore do not pose the same problems for string theory as asymptotic de Sitter space.
We investigate the validity of the generalized second law of gravitational thermodynamics on the apparent and event horizons in a non-flat FRW universe containing the interacting dark energy with dark matter. We show that for the dynamical apparent horizon, the generalized second law is always satisfied throughout the history of the universe for any spatial curvature and it is independent of the equation of state parameter of the interacting dark energy model. Whereas for the cosmological event horizon, the validity of the generalized second law depends on the equation of state parameter of th…
In this paper, with the Parikh-Wilczek tunnelling framework the positions of the event horizon of the Vaidya black hole and the Vaidya-Bonner black hole are calculated respectively. We find that the event horizon and the apparent horizon of these two black holes correspond respectively to the two turning points of the Hawking radiation tunnelling barrier. That is, the quantum ergosphere coincides with the tunnelling barrier. Our calculation also implies that the Hawking radiation comes from the apparent horizon.
Several recently found properties of the event horizon of black holes are discussed. One of them is the reflection of the incoming particles on the horizon. A particle approaching the black hole can bounce on the horizon back, into the outside world, which drastically reduces the absorption cross section in the infrared region. Another, though related phenomenon takes place for particles inside the horizon. A locked inside particle has, in fact, an opportunity to escape into the outside world. Thus, the confinement inside the horizon is not absolute. The escape from within the interior region …
That event horizons generate quantum correlations via the Hawking effect is well known. We argue, however, that the creation of entanglement can be modulated as desired, by appropriately illuminating the horizon. We adapt techniques from quantum information theory to quantify the entanglement produced during the Hawking process and show that, while ambient thermal noise (e.g., CMB radiation) degrades it, the use of squeezed inputs can boost the non-separability between the interior and exterior regions in a controlled manner. We further apply our ideas to analog event horizons concocted in the…
A simple classical consideration of black hole formation and evaporation times focusing solely on the frame of an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for the formation time of a black hole event horizon to not exceed its evaporation time. We explore this paradox quantitatively and examine possible cutoff scales and their relation to the Planck scale. Our analysis suggests several different possibilities, none of which can be resolved classically and all of which require new physics associated with even large…
We consider the computation of the entanglement entropy in curved backgrounds with event horizons. We use a Hamiltonian approach to the problem and perform numerical computations on a spherical lattice of spacing $a$. We study the cosmological case and make explicit computations for the Friedmann-Robertson-Walker universe. Our results for a massless, minimally coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which resembles the flat space formula, although here the horizon radius, $r_H$, is time-dependent.
By fully exploiting the existence of the unitarily inequivalent representations of quantum fields, we exhibit the entanglement between inner and outer particles, with respect to the event horizon of a black hole. We compute the entanglement entropy and we find that the nonunitarity of the mapping, between the vacua in the flat and the curved frames, makes the entanglement very robust.
Einstein's General theory of relativity is plagued by cosmological and blackhole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield non-singular cosmological and mini-blackhole solutions. In particular, the theory possesses a {\it mass-gap} determined by the scale of new physics. We will use this property to argue that it is possible to form a non-singular super-massive compact objects without having any event horizon in this class of theories.
We show that, in a gravitational theory [in any number of dimensions greater than 3] which admits BPS branes and AdS-Reissner-Nordstrom black holes with flat event horizons, the specific [dimensionless] temperature of such a black hole is bounded below by approximately 0.156875. This confirms the recent suggestion by Hartnoll and Tavanfar, to the effect that no such black hole can be arbitrarily cold, since from the AdS/CFT dual point of view the low-temperature degrees of freedom should not be concealed by the equivalent of an event horizon.
General Relativity allows for a cosmological constant ($Λ$) which has inspired models of cosmic Inflation and Dark Energy. We show instead that $r_Λ= \sqrt{3/Λ}$ corresponds to an event horizon: a causal boundary term in the action. Our Universe is expanding inside its Schwarzschild radius $r_S=\rL=2GM$, which could have originated from a uniform free falling cloud of mass $M$ that collapsed as a Black Hole (BH) 25 Gyrs ago. Such a BH Universe allows for large-scale structure formation without the need of Inflation or Dark Energy.
Event horizons for fermion quasiparticles naturally arise in moving textures in superconductors and Fermi superfluids. We discuss the example of a planar soliton moving in superfluid 3He-A, which is closely analogous to a charged rotating black hole. The moving soliton will radiate quasiparticles via the Hawking effect at a temperature of about 5 μK, and via vacuum polarization induced by the effective `electromagnetic field' and `ergoregion'. Superfluid 3He-A thus appears to be a useful system for experimental and theoretical simulations of quantum effects related to event horizons and ergore…
We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature that typical states in such an ensemble contain firewalls, or otherwise singular horizons. We argue this conclusion can be avoided with a proper definition of the interior operators.
Quantum mechanics imposes a fundamental bound on the minimum time required for the quantum systems to evolve between two states of interest. This bound introduces a limit on the speed of the dynamical evolution of the systems, known as the quantum speed limit. We show that black holes can drastically affect the speed limit of a two-level fermionic quantum system subjected to an open quantum dynamics. As we demonstrate, the quantum speed limit can enhance at the vicinity of a black hole's event horizon in the Schwarzschild spacetime.
It has been argued in the literature that if a universe is expanding with an accelerating rate indefinitely, it presents a challenge to string theories due to the existence of event horizons. We study the fate of a currently accelerating universe. We show that the universe will continue to accelerate indefinitely if the parameter $ω= p/ρ$ of the equation of state is a constant, no matter how many different types of energy (matter, radiation, quintessence, cosmological constant and etc) are contained in the universe. This type of universe will always exhibit an event horizon indicating that suc…
