Apparent Horizon Research Articles

Effect of electric field on string-oriented perfect fluid collapse in f (R) gravity

This work investigates the nature of singularity formed from string-oriented charged perfect fluid collapse in theory of f (R) gravity. The spherically symmetric spacetime is assumed to be filled with a string-oriented charged perfect fluid. The gravitational collapse of the fluid is analyzed to understand the effects of electric field on the time and radii of apparent horizons and singularity formation. The presence of an electric field was discovered to increase the mass of the collapsing system, the radii of apparent horizon development, and the time gap between the event horizon and singularity. The term [Formula: see text] acts as an anti-gravity term. However, the presence of electric field accelerates the gravitational collapse.

Cosmic evolution and thermal stability of Barrow holographic dark energy in a nonflat Friedmann-Robertson-Walker Universe

We study the cosmological evolution of a nonflat Friedmann-Robertson-Walker Universe filled by pressureless dark matter and Barrow holographic dark energy (BHDE). The latter is a dark energy model based on the holographic principle with Barrow entropy instead of the standard Bekenstein-Hawking one. By assuming the apparent horizon of the Universe as IR cutoff, we explore both the cases where a mutual interaction between the dark components of the cosmos is absent/present. We analyze the behavior of various model parameters, such as the BHDE density parameter, the equation of state parameter, the deceleration parameter, the jerk parameter, and the square of sound speed. We also comment on the observational consistency of our predictions, showing that the interacting model turns out to be favored by recent experimental constraints from $\mathrm{Planck}+\mathrm{WP}+\mathrm{BAO}$, $\mathrm{SNIa}+\mathrm{CMB}+\mathrm{LSS}$ and Union2 SNIa joint analysis over the noninteracting one. The thermal stability of our framework is finally discussed by demanding the positivity of the heat capacities and compressibilities of the cosmic fluid.

Vaidya and Generalized Vaidya Solutions by Gravitational Decoupling

In this paper, we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution that can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and most well known when the mass function is the function only of space coordinate r. The second case is a Vaidya spacetime case when the mass function depends on time v. Finally, the third case represents the generalization of these two cases: the mass function is the function of both r and v. We also calculate the apparent horizon and singularity locations for all three cases.

The structure of the generalized Vaidya space–time containing the eternal naked singularity

In this paper, the structure of the generalized Vaidya space–time when the type-II of the matter field satisfies the equation of the state [Formula: see text] is investigated. Satisfying all energy conditions, we show that this space–time contains the “eternal” naked singularity. It means that once the singularity is formed it will never be covered with the apparent horizon. However. in the case of the apparent horizon formation the resulting object is a white hole. We also prove that this space–time contains only null naked singularity.

Quantum quench and time evolution of mutual information with hyperscaling violation

We studied the time evolution of the mutual information after a quantum quench in the strongly coupled field theories. We use a hyperscaling-violating background and generalize the results of Tanhayi (JHEP, 1603, 202 (2016). doi: 10.1007/JHEP03(2016)202) to subregions with unequal lengths. Precisely, we consider two different strips as the entangling regions and use a holographic prescription to obtain the corresponding mutual information due to a time-dependent coupling in the probe sector. In this setup, due to the formation of apparent horizons, the thermalization can happen and we show that in this process the mutual information remains positive; nevertheless, for three entangling regions the corresponding quantity is negative.

New time-dependent solutions of viable Horndeski gravity

We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in asymptotically FLRW spacetimes and contain apparent horizons and a finite radius singularity that evolve in time in peculiar ways apparently not encountered before in Einstein and “old” scalar-tensor gravity.

Evolution of black holes through a nonsingular cosmological bounce

We study the classical dynamics of black holes during a nonsingular cosmological bounce. Taking a simple model of a nonsingular bouncing cosmology driven by the combination of a ghost and ordinary scalar field, we use nonlinear evolutions of the Einstein equations to follow rotating and non-rotating black holes of different sizes through the bounce. The violation of the null energy condition allows for a shrinking black hole event horizon and we find that for sufficiently large black holes (relative to the minimum Hubble radius) the black hole apparent horizon can disappear during the contraction phase. Despite this, we show that most of the local cosmological evolution remains largely unaffected by the presence of the black hole. We find that, independently of the black hole's initial mass, the black hole's event horizon persists throughout the bounce, and the late time dynamics consists of an expanding universe with a black hole of mass comparable to its initial value.

Progress eras of the universe with spacetime dimensions

In this study, we examine on the expansion history of the universe from the inflationary era to the late-time phantom era in the framework of higher dimensional F(R) gravity. Following the unified first law of thermodynamics method, we find a general entropy expression of the gravity theory for the apparent horizon of the universe. Based on the assumption that the dark energy mystery is closely related to the dimensions of spacetime, we research the progress eras of the universe according to the opening of the space-time dimensionality. In a more general framework, we consider the space time manifold as n+1-dimensional spherically symmetric form and discuss the phases of the universe through the validity of entropy. During the inflation, we obtain a 10 dimensional spacetime model which is estimated by the string theory. However, while in the radiation era it is obtained 5 dimensional Kaluza-Klein spacetime, in the dust era 4 spacetime dimensions within the framework of entropy keep standing. At small curvatures of spacetime, a process occurs in which a metric deformation is observed with the negative value of the equation of the state (EoS) parameter, w<−13. This leads to the release of dark energy from the extra dimensions resulting in a 10 dimensional universe. Since the currently observable universe is in four dimensional spacetime form, this fact indicates that the universe needs to pass into a new phase. Hence, de Sitter phase w=−1 of the universe gives 10 dimensional spherically symmetrical spacetime, but here the deformation disappears. Therewithal, we find that 4 dimensional universe model emerges in the phantom region without disturbing the spherical and symmetrical structure of the universe. This means that the late-time accelerated expansion of the universe could be due to dark energy emanating from the extra dimensions.

Thermal effect in a causal diamond: Open quantum systems approach

A static observer with a finite lifetime has causal access to only a limited region of spacetime known as the causal diamond. The presence of an apparent horizon in the causal diamond, due to the observer's finite lifetime, is the origin of an Unruh-like thermal effect. Thus, even though the observer is static and the background is flat, the finite-lifetime observer experiences a thermal bath in the Minkowski vacuum. In this article, we provide an open quantum systems approach that yields a complete thermal characterization via the observer's steady-state density matrix, which is shown to be thermal with a temperature inversely proportional to its lifetime. This associated diamond temperature agrees with the established result derived from other methods. Moreover, our approach is particularly useful for designing entanglement harvesting protocols in the causal diamond. In addition, we introduce an insightful procedure that defines diamond coordinates using conformal transformations, and which leads to a more direct derivation of the thermal properties.

On dynamical stability and information loss of a collapsing string fluid in rainbow gravity

This work analyzes the dynamical variables and information transfer of a collapsing string fluid in the theory of Rainbow gravity (RG). Modifications are made to the field equations for the anisotropic string fluid in spherical geometry with the necessary rainbow functions. We have calculated the radius and time when effective horizons formed. This calculation helps to estimate the time of the observer reaching the apparent horizon. Moreover, we have computed the dynamical variables concerning the string fluid including mass density, pressure and the string tension. The behavior of the dynamical quantities is presented graphically. It is found that the rainbow parameter [Formula: see text] affects the dynamical variables. The results enable us to understand the physics of a collapsing fluid and the information transfer in the collapsing scenario.

General Thermodynamic Properties of FRW Universe and Heat Engine

In this work, the Friedmann–Robertson–Walker (FRW) Universe is considered a thermodynamic system, where the cosmological constant generates the thermodynamic pressure. Using a unified first law, we have determined the amount of energy dE crossing the apparent horizon. Since heat is one of the forms of thermal energy, so the heat flows δQ through the apparent horizon = amount of energy crossing the apparent horizon. Using the first law of thermodynamics, on the apparent horizon, we found TdS=A(ρ+p)Hr˜hdt+Aρdr˜h where T,S,A,H,r˜h,ρ,p are respectively the temperature, entropy, area, Hubble parameter, horizon radius, fluid density and pressure. Since the apparent horizon is dynamical, so we have assumed that dr˜h cannot be zero in general, i.e., the second term Aρdr˜h is non-zero on the apparent horizon. Using Friedmann equations with the unified first law, we have obtained the modified entropy-area relation on the apparent horizon. In addition, from the modified entropy-area relation, we have obtained modified Friedmann equations. From the original Friedmann equations and also from modified Friedmann equations, we have obtained the same entropy. We have derived the equations for the main thermodynamical quantise, such as temperature, volume, mass, specific heat capacity, thermal expansion, isothermal compressibility, critical temperature, critical volume, critical pressure and critical entropy. To determine the cooling/heating nature of the FRW Universe, we have obtained the coefficient of Joule–Thomson expansion. Next, we have discussed the heat engine phenomena of the thermodynamical FRW Universe. We have considered the Carnot cycle and obtained its completed work. In addition, we studied the work completed and the thermal efficiency of the new heat engine. Finally, we have obtained the thermal efficiency of the Rankine cycle.

Density and Positive Mass Theorems for Initial Data Sets with Boundary

We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for initial data sets with apparent horizon boundary in dimensions less than $8$ without a spin assumption.

Evolution of Brill waves with an adaptive pseudospectral method

As a first application of the new adaptive mesh functionality of the pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different one-parameter families of Brill wave initial data; two centered and four off-centered families. Of these the latter have not been treated before. Within each family, we tune the parameter towards the threshold of black hole formation. The results for centered data agree with earlier work. Our key results are first, that close to the threshold of collapse the global peak in the curvature appears on the symmetry axis but away from the origin, indicating that in the limit they will collapse around disjoint centers. This is confirmed in three of the six families by explicitly finding apparent horizons around these large curvature peaks. Second, we find evidence neither for strict discrete-self-similarity nor for universal power-law scaling of curvature quantities. Finally, as in Ledvinka and Khirnov's recent study, we find approximately universal strong curvature features. These features appear multiple times within individual spacetimes close to the threshold and are furthermore present within all six families.

Dynamics of charged string cloud collapse in rainbow gravity

This work will proceed to examine the dynamics of collapsing charged string cloud in a spherically symmetric rainbow metric. This is the framework that allows new stars and compact objects to emerge. The dynamical variables (mass density, string tension) and their physical existence as energy conditions are computed and visually depicted. We also calculated the duration and radius of development of the collapsing string cloud’s apparent horizons. The mass density, string tension, expected time and radius of apparent horizon creation are dependent on the Rainbow parameter [Formula: see text] At the center of the configuration [Formula: see text] the mass density, string tension and electric field intensity are at their maximum leading to the formation of a compact object (black hole). The fluid’s mass density and string tension are reduced by the electric field. Furthermore, the presence of an electric field delays the formation of a compact object (black hole).

Fate of quantum black holes

We study the quantum dynamics of the Lema\^{\i}tre-Tolman-Bondi space-times using a polymer quantization prescription based on loop quantum cosmology that incorporates fundamental discreteness. By solving an effective equation derived from this quantization, we find analytical solutions for the Oppenheimer-Snyder and thin-shell collapse models, and numerical solutions for a variety of asymptotically flat collapsing dust profiles. Our study (i) tracks the formation, evolution, and disappearance of dynamical horizons, (ii) shows that matter undergoes a nonsingular bounce that results in an outgoing shock wave, (iii) determines black hole lifetime to be proportional to the square of its mass, and (iv) provides a conformal diagram that substantially modifies the standard ``information loss'' picture by resolving the singularity and replacing the event horizon by transient apparent horizons.

Are astrophysical “black” holes leaky?

We continue a study by Adler and Ramazanoǧlu (AR) of “black” holes as modified by a scale invariant dark energy action. For the spherically symmetric Schwarzschild-like case, AR found that there is no event horizon; hence spacetime is not divided by the “black” hole into causally disconnected regions. We review the formalism for locating trapped surfaces and apparent horizons, and show that the modified “black” hole has no trapped surfaces. Thus, one suspects that it is “leaky,” and that there will be a “black hole wind” of particles streaming out from the location of the nominal horizon. This will have astrophysical consequences, for example, the wind may feed and stabilize star formation in the vicinity of the “black” hole. We initiate a study of the stationary axially-symmetric rotating “black” hole as modified by a scale invariant dark energy action, i.e. one that is Kerr-like. To set-up the axial case, we note that the conserving completion of the dark energy stress-energy tensor can be calculated algebraically by solving a [Formula: see text] matrix equation. Using Mathematica we calculate and simplify the modified system of Einstein equations for the axial case in quasi-isotropic coordinates, and give appropriate boundary conditions. Solution of these equations, which may require developing a special purpose numerical program, is rendered tricky by a residual general coordinate invariance of quasi-isotropic coordinates. This leads to the interesting mathematical question of representing a positive planar function as the gradient squared of a harmonic function.

Black holes and their horizons in semiclassical and modified theories of gravity

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

Boundary conditions for stationary black holes: Application to Kerr, Martínez-Troncoso-Zanelli, and hairy black holes

This work proposes a set of equations that can be used to numerically compute spacetimes containing a stationary black hole. The formalism is based on the $3+1$ decomposition of General Relativity with maximal slicing and spatial harmonic gauge. The presence of the black hole is enforced using the notion of apparent horizon in equilibrium. This setting leads to the main result of this paper: a set of boundary conditions describing the horizon and that must be used when solving the $3+1$ equations. Those conditions lead to a choice of coordinates that is regular even on the horizon itself. The whole procedure is validated with three different examples chosen to illustrate the great versatility of the method. First, the single rotating black holes are recovered up to very high values of the Kerr parameter. Second, nonrotating black holes coupled to a real scalar field, in the presence of a negative cosmological constant (the so-called Martinez-Troncoso-Zanelli black holes), are obtained. Last, black holes with complex scalar hairs are computed. Eventually, prospects for future work, in particular in contexts where stationarity is only approximate, are discussed.

Lagrangian formulation and implications of barotropic fluid cosmologies

In this paper, we investigate the behavior of cosmologies in homogeneous and isotropic background with a barotropic fluid. We solve the continuity equation and study several aspects of model including behavior of cosmological quantities like Hubble parameter, deceleration parameter, equation of state parameter along with statefinder diagnostic and validity of energy conditions. The [Formula: see text] plane is checked for identification of thawing and freezing regions. We derive the Lagrangian formulation with standard and non-standard kinetic terms for barotropic fluid model. It is demonstrated that the model possesses periodic potential in its Lagrangian description with standard kinetic terms. Using dynamical system analysis, we find the stability of solutions, too. We further explore the thermodynamic aspects at apparent horizon by investigating the validity of generalized second law of thermodynamics with equilibrium description. The model exhibits complete cosmological scenario for different values of model parameters and the inflationary scenario decays smoothly into radiation-dominated phase during its evolution. The model approaches to [Formula: see text] cold dark matter model during late times of its evolution.

Gravitational collapse involving electric charge in the decoupling limit of the dilatonic Gauss–Bonnet gravity

The paper discusses gravitational collapse of an electrically charged scalar field in the decoupling limit of the dilatonic Gauss–Bonnet gravity. The emerging spacetimes contained Schwarzschild black holes for sufficiently big scalar fields self-interaction strengths. Dependencies of the collapse characteristics on the dilatonic and Gauss–Bonnet parameters turned out to be similar in the case of black hole masses and radii as well as their time of formation in terms of retarded time. In the cases of masses and radii minima were observed, while in the remaining case a maximum existed. The electric charge of the emerging black holes possessed a maximum when measured versus the dilatonic coupling constant and was strictly decreasing with the Gauss–Bonnet coupling. The times of formation and charges of black holes decreased, while masses and radii increased with the self-interaction strengths of the dynamical fields. Values of the energy density, radial pressure, pressure anisotropy and the collapsing scalar fields were the biggest along the hypersurface of propagation of the scalar fields initial peaks. For big values of the Gauss–Bonnet coupling constant, an increase in their values was also observed in the vicinity of the central singularity within the whole range of advanced time. Non-zero values of the dilaton field outside the black hole event horizon may indicate a formation of a hairy black hole. The local temperature calculated along the apparent horizon was increasing for late times of the evolution and exhibited extrema in areas, where the dynamics of the gravity–matter system was observed.