Infinite Redshift Research Articles

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.

Black Holes as Frozen Stars: Regular Interior Geometry

AbstractThe authors have proposed a model geometry for the interior of a regular black hole (BH) mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution of the Einstein equations which is sourced by an exotic matter with maximally negative radial pressure. The frozen star geometry is previously presented in singular coordinates for which and vanish in the bulk and connect smoothly to the Schwarzschild exterior. Additionally, the geometry is mildly singular in the center of the star. Here, the authors present regular coordinates for the entirety of the frozen star. Each zero in the metric is replaced with a small, dimensionless parameter ε; in both and thus maintaining maximally negative radial pressure. The authors also regularize the geometry, energy density and pressure in the center of the star in a smooth way. The frozen star solution presented here is a completely regular solution of Einstein's equations whose compactness is arbitrarily close to that of a Schwarzschild BH. It obeys the null energy condition, the universally agreed‐upon energy condition, and it is free of any known pathology. As far as it is known, this is the first solution that obeys all of these constraints and, in addition, as will be shown in a future publication, can mimic all of the thermodynamic properties of a standard BH. Our initial analysis uses Schwarzschild‐like coordinates and applies the Killing equations to show that an infalling, point‐like object will move very slowly, effectively sticking to the surface of the star and never coming out. If one nevertheless follows the trajectory of the object into the interior of the star, it moves along an almost‐radial trajectory until it comes within a small distance from the star's center. Once there, if the object has any amount of angular momentum at all, it will be reflected outwards by a potential barrier onto a different almost‐radial trajectory. Finally, using Kruskal‐like coordinates, the causal structure of the regularized frozen star and discuss its limit, for which the geometry degenerates and becomes effectively two dimensional is considered.

An analytic model for gravitational collapse of spherical matter under mixed pressure

In this paper, we investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state for the matter near interface, where pressure constituted of the transverse component and the longitudinal one is proportional to energy density. We present analytic solutions for the equation of state and discuss parameter region to satisfy physical conditions such as the absence of the shell crossing singularity, the monotonic increase of the emergent infinite redshift surface and energy conditions. We finally show that adopting the definition presented in arXiv:2005.13233 the total energy in this time-dependent system is invariant under the given time evolution.

On Black Holes as Macroscopic Quantum Objects

The relative flow of the Schwarzschild vs. the proper time during the classical evolution of a collapsing shell in the Schwarzschild coordinates practically forces us to interpret black hole formation as a highly non-local quantum process in which a shell/anti-shell pair is created within the incipient horizon, thus canceling out the original collapsing shell exactly at the horizon. By studying quantum fields in the black hole background, we reveal similar non-local effects. Among other things, the outgoing member of the Hawking pair very quickly becomes entangled with the black hole geometry (and not its partner), which is in contrast with the usual assumption that the Hawking pair is maximally entangled according to the local geometry near the horizon. Also, an infalling wave affects the black hole geometry even before it crosses the horizon. Finally, we find that a particle takes a finite amount of time to tunnel in and out of the black hole horizon, and thus avoids infinite blue and redshift in processes happening exactly at the horizon. These findings strongly support the picture of a black hole as a macroscopic quantum object.

On the dynamic effect of infinite redshift surface: Lorentz factor analysis method

On the dynamic effect of infinite redshift surface: Lorentz factor analysis method

Infinite-redshift localized states of Dirac fermions under Einsteinian gravity

We present a set of localized states for an even number of Dirac fermions under Einsteinian gravity that have an infinite central redshift. Near the center of the localized state the components of the Dirac spinor and the spacetime metric all show simple power-law dependences on the radial distance; further out the fermionic wave function decays to zero and the spacetime becomes asymptotically flat. We show that this `central' solution of the equations of motion can be used to understand much of the structure observed by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] in their numerical solutions of the same problem at finite central redshift.

Unsettling Physics in the Quantum-Corrected Schwarzschild Black Hole

We study a quantum-corrected Schwarzschild black hole proposed recently in Loop Quantum Gravity. Prompted by the fact that corrections to the innermost stable circular orbit of Schwarzschild diverge, we investigate time-like and null radial geodesics. Massive particles moving radially outwards are confined, while photons make it to infinity with infinite redshift. This unsettling physics, which deviates radically from both Schwarzschild (near the horizon) and Minkowski (at infinity) is due to repulsion by the negative quantum energy density that makes the quasilocal mass vanish as one approaches spatial infinity.

Redshift/blueshift Inside the Schwarzschild Black Hole

We consider an observer who moves under the horizon of the Schwarzschild black hole and absorbs a photon. There are two different situations when (i) a photon comes from infinity, (ii) it is emitted by another observer under the horizon (say, by a surface of a collapsing star). We analyze the frequency change for absorption near the event horizon, in an intermediate region and near the singularity and compare the results for both scenarios. Near the singularity, in both scenarios infinite redshift (in the pure radial case) or infinite blueshift are possible, depending on angular momenta of a photon and an observer. The main difference between both scenarios manifests itself, if photons from the star surface are emitted near the horizon and received in the intermediate region or near the singularity by the observer with a nonzero angular momentum.

The geometric phase of a two-level atom under the Hawking effect in a Kerr black hole

We study the Hawking effect in terms of the geometric phase for a two-level atom coupled to vacuum fluctuations in the background of Kerr black hole in a gedanken experiment. Since the atom interacts with a bath of fluctuating massless scalar field, its geometric phase for the nonunitary evolution turns out to be affected by the spacetime curvature that backscatters the vacuum field modes. We examine the geometric phase for two kinds of vacua, i.e. the Unruh vacuum and the Candelas–Chrzanowski–Howard vacuum. We find that for both of these two cases, the geometric phase of the static atom locating outside the infinite redshift surface (or the stationary atom locating inside the ergosphere) exposes that the atom behaves as if it were immersed in a thermal radiation at the Hawking temperature from the Kerr black hole. Therefore, our results show that one in principle can reveal the Hawking effect in the Kerr black hole by analyzing the correction of the geometric phase as opposed to that in a flat spacetime.

Optical Coulomb blockade lifting in plasmonic nanoparticle dimers.

If two metal nanoparticles are ultimately approached, a tunneling current prevents both an infinite redshift of the bonding dipolar plasmon and an infinite increase of the electric field in the hot spot between the nanoparticles. We argue that a Coulomb blockade suppresses the tunneling current and sustains a redshift even for sub-nanometer approach up to moderate fields. Only for stronger optical fields, the Coulomb blockade is lifted and a charge transfer plasmon is formed. Numerical simulations show that such scenarios are well in reach with manageable nanoparticle dimensions, even at room temperature. Applications may include ultrafast, optically driven switches, photo detectors operating at 500 THz, or highly nonlinear devices.

Generalized no-hair theorems without horizons

The simplicity of black holes, as characterized by no-hair theorems, is one of the most important mathematical results in the framework of general relativity. Are these theorems unique to black hole spacetimes, or do they also constrain the geometry around regions of spacetime with arbitrarily large (although finite) redshift? This paper presents a systematic study of this question and illustrates that no-hair theorems are not restricted to spacetimes with event horizons but are instead characteristic of spacetimes with deep enough gravitational wells, extending Israel’s theorem to static spacetimes without event horizons that contain small deviations from spherical symmetry. Instead of a uniqueness result, we obtain a theorem that constrains the allowed deviations from the Schwarzschild metric and guarantees that these deviations decrease with the maximum redshift of the gravitational well in the external vacuum region. Israel’s theorem is recovered continuously in the limit of infinite redshift. This result provides a first extension of no-hair theorems to ultracompact stars, wormholes, and other exotic objects, and paves the way for the construction of similar results for stationary spacetimes describing rotating objects.

Orbiting naked singularities in large- $$\omega $$ ω Brans–Dicke gravity

Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the $$\omega \longrightarrow \infty $$ limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.

A rough end for smooth microstate geometries

Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an “evanescent ergosurface” of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorpo-rating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in AdS3 × S3 propagating along one of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum j, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to jsim sqrt{n_1{n}_5} where the density of microstates is maximal. We argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.

Building cosmological frozen stars

Janis–Newman–Winicour (JNW) solutions generalize Schwarzschild to include a massless scalar field. While they share the familiar infinite redshift feature of Schwarzschild, they suffer from the presence of naked singularities. Cosmological versions of JNW spacetimes were discovered some years ago, in the most general case, by Fonarev. Fonarev solutions are also plagued by naked singularities, but have the virtue, unlike e.g. Schwarzschild–deSitter, of being dynamical. Given that exact dynamical cosmological black hole solutions are scarce, Fonarev solutions merit further study. We show how Fonarev solutions can be obtained via generalized dimensional reduction from simpler static vacuum solutions. These results may lead towards constructions of actual dynamical cosmological black holes. In particular, we note that cosmological versions of extremal charged dilaton black holes are known. JNW spacetimes represent a different limiting case of the family of charged dilaton black holes, which have been important in the context of string theory, and better understanding their cosmological versions of JNW spacetimes thus provides a second data point towards finding cosmological versions of the entire family.

Instability of supersymmetric microstate geometries

We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.

Horizon structure of rotating Einstein–Born–Infeld black holes and shadow

We investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity ($\beta \rightarrow \infty$). We find that for a given $\beta$, mass $M$ and charge $Q$, there exist critical spinning parameter $a_{E}$ and $r_{H}^{E}$, which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and $a_{E}$ decreases and $r_{H}^{E}$ increases with increase in the Born-Infeld parameter $\beta$. While $a<a_{E}$ describe a non-extremal Einstein-Born-Infeld black hole with outer and inner horizons. Similarly, the effect of $\beta$ on infinite redshift surface and in turn on ergoregion is also included. It is well known that a black hole can cast a shadow as an optical appearance due to its strong gravitational field. We also investigate the shadow cast by the non-rotating ($a=0$) Einstein-Born-Infeld black hole and demonstrate that the null geodesic equations can be integrated that allows us to investigate the shadow cast by a black hole which is found to be a dark zone covered by a circle. Interestingly, the shadow of the Einstein-Born-Infeld black hole is slightly smaller than for the Reissner-Nordstrom black hole. F urther, the shadow is concentric circles whose radius decreases with increase in value of parameter $\beta$.

Semiclassical black holes expose forbidden charges and censor divergent densities

Classically, the black hole (BH) horizon is a rigid surface of infinite redshift; whereas the uncertainty principle dictates that the semiclassical (would-be) horizon cannot be fixed in space nor can it exhibit any divergences. We propose that this distinction underlies the BH information-loss paradox, the apparent absence of BH hair, the so-called trans-Planckian problem and the recent "firewall" controversy. We argue that the correct prescription is to first integrate out the fluctuations of the background geometry and only then evaluate matter observables. The basic idea is illustrated using a system of two strongly coupled harmonic oscillators, with the heavier oscillator representing the background. We then apply our proposal to matter fields near a BH horizon, initially treating the matter fields as classical and the background as semiclassical. In this case, the average value of the associated current does not vanish; so that it is possible, in principle, to measure the global charge of the BH. Then the matter is, in addition to the background, treated quantum mechanically. We show that the average energy density of matter as seen by an asymptotic observer is finite and proportional to the BH entropy, rather than divergent. We discuss the implications of our results for the various controversial issues concerning BH physics.

Comment on “Black Holes are Neither Particle Accelerators Nor Dark Matter Probes”

The Banados-Silk-West effect consists in the possibility to get infinite energy in the centre of mass frame of two particles colliding near the black hole horizon. According to S. T. McWilliams, Phys. Rev. Lett. 110 (2013) 011102, the energy at infinity of the outcome vanishes because of infinite redshift when the point of collision approaches the horizon. I show that this is not so.

Fully explorable horned particles hiding charge

The charge-hiding effect by a horned particle, which was studied for the case where the gravity/gauge-field system is self-consistently interacting with a charged light-like brane (LLB) as a matter source, is now studied for the case of a time-like brane. From the demand that no surfaces of infinite coordinate time redshift (horizons) appear in the problem, we are now led to a completely explorable horned particle space for a traveller that goes through the horned particle (as was the case for the LLB). Now, in addition to this, the horned region is fully visible to a static external observer. This requires negative surface energy density for the shell sitting at the throat. We study a gauge-field subsystem that is of a special nonlinear form containing a square root of the Maxwell term and that previously has been shown to produce a QCD-like confining gauge-field dynamics in flat spacetime. The condition of finite energy of the system or asymptotic flatness on one side of the horned particle implies that the charged object sitting at the throat expels all the flux it produces into the other side of the horned particle, which turns out to be of a ‘tube-like’ nature. An outside observer in the asymptotically flat universe detects, therefore, an apparently neutral object. The hiding of the electric flux behind the tube-like region of a horned particle is the only possible way that a truly charged particle can still be of finite energy, in a theory that in flat space it describes confinement. This points to the physical relevance of such solutions, even though there is the need of negative energy density at the throat of the horned particle, which can be of quantum-mechanical origin.

Geometry of modified Newtonian dynamics

Modified Newtonian dynamics is an empirical modification to Poisson's equation which has had success in accounting for the ``gravitational field'' $\ensuremath{\Phi}$ in a variety of astrophysical systems. The field $\ensuremath{\Phi}$ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ensuremath{\Phi}\ensuremath{\rightarrow}0$. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.