Narrow Results

It is a consensus among researchers that the general solution of Einstein’s field equations is the Kerr–Newman solution. It describes the charge, mass and angular momentum of the Kerr–Newman Black Hole (KNBH). The study of this solution is still a topic of research in general relativity and theoretical astrophysics. Therefore, motivated by this fact we offer a benchmark artificial neural networking approximation for the dependency of the ergosphere and event horizon of KNBH on a mass, charge and angular momentum. To be more specific, in the first layer of the neural networking model, the mass, charge and angular momentum of KNBH are considered inputs, while in the last layer, ergosphere and event horizon radius are taken as targets. For the training of the model, 70% (140) of the data are chosen and 15% (30) each is distributed for validation and testing. For training, a Levenberg–Marquardt Algorithm (LMA) is used. To approximate event horizon radius and ergosphere, neural models, namely ANN-I and ANN-II, are developed, respectively. Mean squared error (MSE) and correlation coefficient (R) analysis are conducted to evaluate the performances of neural models. Owing to the training dataset we observed that the ANN-II model achieves a low MSE value (about ${10}^{-7}$), suggesting excellent accuracy in estimating the ergosphere of the KNBH. R values (9.99992E$-$1, 9.99999E$-$1) are consistently very close to 1, indicating a high correlation between predicted and actual values of the event horizon and ergosphere of the KNBH. This suggests that the models claim a strong predictive relationship with the real data. The present ANN-based results are thought to be useful in expanding the concept of processing large volumes of intricate data, finding patterns and accurately forecasting astrophysical events.

Hawking radiation on the apparent horizon of a Vaidya black hole is investigated using Parikh's tunneling method. When back-reaction of particles is neglected, precisely thermal spectrum can be obtained. Then the black hole thermodynamics can be built successfully on the apparent horizon. When a relativistic perturbation is given to the apparent horizon, similar calculation can also lead to a purely thermal spectrum, which is corresponding to a modified temperature from the former. The first law of thermodynamics can also be constructed successfully at a new supersurface which has a small deviation from the apparent horizon. When the event horizon is thought as such a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be built on the event horizon. It is concluded that the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.

We consider the relations between de Vaucouleurs–Ikeuchi diagram and generalized commutation relations among the coordinates and momenta. All physical objects in the Universe ranging from elementary particles to super-cluster of galaxies are confined within the Triangle of the de Vaucouleurs–Ikeuchi diagram on the matter density versus scale length plane. These three boundaries are characterized by the quantum uncertainty principle, gravitational event horizon, and cosmological constant. These are specified by the nonzero commutation relations [x_μ, p_ν], [x_μ, x_ν] (strictly [x_i, t]) and [p_μ, p_ν], respectively. The canonical commutation relation [x_i, p_j] are slightly modified, which preserves the self consistency as a whole.

We investigate the validity of the thermodynamical properties of the universe in a new parametric model of dark energy with the equation of state w = w₀ + w₁ · z(1 + z)/(1 + z²). In the spatially homogeneous and isotropic universe, assuming that the temperature and entropy in cosmology is as in a black hole, we examine the thermodynamical properties of the universe bounded by the apparent horizon and the event horizon respectively. By analysis, we find that the first and the second laws of thermodynamics are valid inside the apparent horizon, while they break down inside the event horizon.

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases.

Applying the generalized uncertainty relation to the calculation of the free energy and entropy of a black hole inside the brick wall, the entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon. This is compared with the entropy calculated via the original brick wall model. The entropy given by the original brick wall model comes from the outside of the brick wall seemingly. The inside result using generalized uncertainty relation is similar to the outside result using original uncertainty relation, and the divergence inside the brick wall disappears. It is apparent that the cutoff is something related to the quantum theory of gravity.

In this paper, we calculate exactly the solution of Klein–Gordon equation in anti-de Sitter space–time. Due to spherical symmetry, the angular wave functions are given by spherical harmonics. The radial wave functions are given by local Heun functions. We analyze the behavior of the radial wave function in regions near three possible event horizon positions $(r_0,r_1,r_2)$ and investigate the decay rate, Hawking radiation and Hawking temperature for these three cases. Comparing the results, we verify that if the decay rate and Hawking radiation are greater, then the closer the event horizon is to the singularity of the black hole. Finally, we analyze the special case of a small black hole limit.

Although it has been generally believed that classical general relativity is always correct for macroscopic length scales, certain predictions such as event horizons and closed time-like curves are inconsistent with ordinary quantum mechanics. It has recently been pointed out that the event horizon problem can be resolved if space-time undergoes a quantum phase transition as one approaches the surface where general relativity predicts that the redshift becomes infinite. Indeed a thought experiment involving a superfluid with a critical point makes such a suggestion appear plausible. Furthermore the behavior of space-time near an event horizon may resemble quantum phase transitions that have been observed in the laboratory. For example, the phenomenology of metamagnetic quantum critical points in heavy fermion materials resembles the behavior expected, both in terms of time standing still and the behavior of quantum correlation functions. Martensitic transformations accompanied by non-adiabatic changes in the electronic wave function are also interesting in this connection.

The entropy of a rotating and arbitrarily accelerating black hole whose metric changes slowly is calculated using the thin film brick-wall model. We obtain the entropy density at every point of the horizon surface and the total entropy of the black hole. The results show that the entropy of the nonstationary black hole is also proportional to the surface area of the black hole's event horizon as in the cases of stationary black holes.

What happens when Alice falls into a black hole? In spite of recent challenges by Almheiri et al. — the so-called "firewall" hypothesis —, the consensus on this question tends to remain "nothing special." Here I show that, besides the standard Hawking outgoing modes, Alice records at horizon-crossing a quasi-thermal spectrum of ingoing modes, whose temperature and intensity diverges as her Killing energy E goes to zero. I suggest that this effect can be thought of in terms a horizon-infinity duality, which relates the perception of near-horizon and asymptotic geodesic observers — the two faces of Hawking radiation.

The fusion of two black holes — a signature phenomenon of General Relativity — is usually regarded as a process so complex that nothing short of a supercomputer simulation can accurately capture it. In this essay, we explain how the event horizon of the merger can be found in an exact analytic way in the limit where one of the black holes is much smaller than the other. Remarkably, the ideas and techniques involved are elementary: the equivalence principle, null geodesics in the Schwarzschild solution, and the notion of event horizon itself. With these, one can identify features such as the line of caustics at which light rays enter the horizon, and find indications of universal critical behavior when the two black holes touch.

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 can be detected by a distant observer. Furthermore, horizons are unnecessary for the production of Hawking-like radiation. We demonstrate that when this radiation is taken into account, it can prevent horizon crossing/formation in a large class of models. We conjecture that horizon avoidance is a general feature of collapse. The nonexistence of event horizons dispels the paradox, but opens up important questions about thermodynamic properties of the resulting objects and correlations between different degrees of freedom.

How the supermassive black hole SgrA* in the Milky Way Center looks like for a distant observer? It depends on the black hole highlighting by the surrounding hot matter. The black hole shadow (the photon capture cross-section) would be viewed if there is a stationary luminous background. The black hole event horizon is invisible directly (per se). Nevertheless, a more compact (with respect to black hole shadow) projection of the black hole event horizon on the celestial sphere may be reconstructed by detecting the highly redshifted photons emitted by the nonstationary luminous matter plunging into the black hole and approaching the event horizon. It is appropriate to call this reconstructed projection of the event horizon on the celestial sphere for a distant observer as the “lensed event horizon image”, or simply the “event horizon image”. This event horizon image is placed on the celestial sphere within the position of black hole shadow. Amazingly, the event horizon image is a gravitationally lensed projection on the celestial sphere of the whole surface of the event horizon globe. As a result, the black holes may be viewed at once from both the front and back sides. The lensed event horizon image may be considered as a genuine silhouette of the black hole. For example, a dark northern hemisphere of the event horizon image is the simplest model for a black hole silhouette in the presence of a thin accretion disk.

In this work, the Kerr–Newman-NUT black hole solution in Rastall gravity is proposed and it turns out that the horizon is $𝜃$ dependence. Black hole dynamics such as the event horizons, ergosurface, zero angular momentum observer (ZAMO), thermodynamic properties, and the equatorial circular orbit around the black hole such as static radius limit, null equatorial circular orbit, and innermost stable circular orbit are investigated in this work. How the NUT and Rastall parameter affect the dynamic of the black hole is also shown.

This paper concerns the relationship between the nonmetricity 1-form and the change in entropy. Motion equations have been obtained for test bodies in a gravitational field created by a massive body with entropy varying over time. It has been shown that increasing entropy of the gravitational source will bring about an increase in the acceleration of the test body. Applied to the theory of gravitation with nonmetricity, black hole dynamics equations based on foundations laid by S. Hawking and J. Beckenstein, enabled identification of changes in black holes event horizon surface area as a putative source of nonmetricity field. The implication is that changes in event horizon area will affect test body motion. The latter property makes it possible to contemplate a completely new method for discovering short-lived microscopic black holes.

We consider the interacting scenario of pilgrim dark energy (with future event horizon) with cold dark matter in loop quantum cosmology. We explore various cosmological parameters (Hubble, equation of state and deceleration) and planes ($r-s$ and ${\omega }_{\mathrm{\Lambda }}$–${\omega }_{\mathrm{\Lambda }}^{\prime }$) in this framework. We also discuss the validity of generalized second law of thermodynamics and find that it remains valid in the early epoch as well as in late future epoch. Finally, it is remarked that all the above constraints of cosmological parameters show consistency with different observational data like Planck, WP, BAO, $H_0$, SNLS and nine-year WMAP.

This paper is concerned with the motion of relativistic strings in Schwarzschild space-time. In a general framework, we first analyze the basic equations for the motion of a $p$-dimensional extended object in a general enveloping space-time $(\mathcal{𝒩},\tilde{g})$, which is a given Lorentzian manifold, and then we investigate some important properties enjoyed by the equations for the motion of relativistic strings in Schwarzschild space-time. In particular, the equations are shown to form a totally linearly degenerate system of first-order hyperbolic equations in $(1+1)$ dimensions. Based on this observation and under suitable assumptions, we are able to prove the global existence of smooth solutions to the Cauchy problem for the equations of motion of relativistic strings (in Schwarzschild space-time) with sufficiently small arc length.

The Vector-Tensor (VT) theories of gravity are a class of alternative theories to General Relativity (GR) that are characterized by the presence of a dynamical vector field besides the metric. They are studied in attempts to understand spontaneous Lorentz violation, to generate massive gravitons, and as models of dark matter and dark energy. In this article, I outline how the nature of singularities and horizons in VT theories differ greatly from GR even under the same ordinary conditions. This is illustrated with Einstein-aether theory where vacuum black hole solutions have naked singularities and vacuum cosmological solutions have new singularities that are otherwise absent in GR. It would be interesting to explore these deviations using gravitational waves.

In this paper the mass of a universe, which began as a gravitationally closed, maximally spinning, Planck density quantum string is derived.

A universe beginning in such an initial state has been called a Super Spin Model universe. The total mass, M, of the Super Spin Model universe is shown to be a function of only four fundamental parameters ħ, c, G, e, such that: M = 4π²(ħc/G)^1/2 exp(ħc/e²).

The present paper primarily consists of a brief derivation of the above equation and a short synopsis of the Super Spin Model.

Although it has been generally believed that classical general relativity is always correct for macroscopic length scales, certain predictions such as event horizons and closed time-like curves are inconsistent with ordinary quantum mechanics. It has recently been pointed out that the event horizon problem can be resolved if space-time undergoes a quantum phase transition as one approaches the surface where general relativity predicts that the redshift becomes infinite. Indeed a thought experiment involving a superfluid with a critical point makes such a suggestion appear plausible. Furthermore the behavior of space-time near an event horizon may resemble quantum phase transitions that have been observed in the laboratory. For example, the phenomenology of meta-magnetic quantum critical points in heavy fermion materials resembles the behavior expected, both in terms of time standing still and the behavior of quantum correlation functions. Martensitic transformations accompanied by non-adiabatic changes in the electronic wave function are also interesting in this connection.