In this paper, we utilize the effective corrections of the $\barμ$-scheme in loop quantum black holes to obtain a 4-dimensional spherically symmetric metric with a cosmological constant. By imposing the areal gauge on the components of Ashtekar variables in the classical theory and applying the holonomy corrections, we derive the equations of motion, which can be solved to obtain the expression for the effective metric in the Painlevé-Gullstrand coordinates. Compared to the classical dS (AdS) spacetime, the LQG correction sets an upper bound on the cosmological constant as $Λ<\frac{3}{γ^2Δ}$. The thermodynamic properties of black holes have also been calculated. We interestingly found that for a small black hole, the temperature of the LQG black hole decreases as the mass decreases, which is quite different with the classical scenario. Moreover, our result shows that a logarithmic term appeared as the leading order correction to the Beikenstein-Hawking entropy. Furthermore, the LQG corrections also introduce an extra phase transition in the black hole's heat capacity at smaller radius.
Adopting a simple ansatz, we find exact solutions to the Einstein-Maxwell-dilaton equations, which stand for the multi-black hole configuration with maximal charge in a cosmological metric and dilaton field background driven by a cosmological term.
We construct the thermodynamic geometry of $2+1$ dimensional normal (exotic) BTZ black hole regarding to the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat spaces, the three dimensional thermodynamics parameters space including the cosmological constant as a fluctuating parameter will be curved. Some consequence of the fluctuation of cosmological constant will be investigated. We show that such fluctuation leads to a thermodynamics curvature which is correctly singular at …
The cosmological black holes are black holes living not in an asymptotically flat universe but in an expanding spacetime. They have a rich dynamics in particular for their mass and horizon. In this article we perform a natural step in investigating this new type of black hole: we consider the possibility of a \textit{charged} cosmological black hole. We derive the general equations of motion governing its dynamics and report a new analytic solution for the special case of the charged Lemaître-Tolman-Bondi equations of motion that describe a charged cosmological black hole. We then study variou…
Thermodynamics of the (2+1)-dimensional Black Hole with non linear Electrodynamics and without Cosmological Constant from the Generalized Uncertainly Principle
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states provide new representations of cosmological spaces that can be explored for the formulation of cosmological models in the context of loop quantum gravity. We show that their local geometry is described in an automorphism-invariant manner by one-node observables analogous to the one-body observables used in many-body quantum mechanics, and compute the density matr…
The loop quantum cosmological model from ADM Hamiltonian is studied in this paper. We consider the spatially flat homogeneous FRW model. It turns out that the modified Friedmann equation keeps the same form as the APS LQC model. However, the critical matter density for the bounce point is only a quarter of the previous APS model, i.e. $ρ_{cL}=\frac{ρ_c}{4}$. This is interesting because the lower critical bounce density means the quantum gravity effects will get involved earlier than the previous LQC model. Besides, the lower critical density also means the detection of quantum gravity effects …
A brief illustrative discussion of the shadows of black holes at local and cosmological distances is presented. Starting from definition of the term and discussion of recent observations, we then investigate shadows at large, cosmological distances. On a cosmological scale, the size of shadow observed by comoving observer is expected to be affected by cosmic expansion. Exact analytical solution for the shadow angular size of Schwarzschild black hole in de Sitter universe was found. Additionally, an approximate method was presented, based on using angular size redshift relation. This approach i…
Cosmic expansion is expected to influence on the size of black hole shadow observed by comoving observer. Except the simplest case of Schwarzschild black hole in de Sitter universe, analytical approach for calculation of shadow size in expanding universe is still not developed. In this paper we present approximate method based on using angular size redshift relation. This approach is appropriate for general case of any multicomponent universe (with matter, radiation and dark energy). In particular, we have shown that supermassive black holes at large cosmological distances in the universe with…
In the present work, we study the general surrounded Vaidya solution by the various cosmological fields and its nature describing the possibility of the formation of naked singularities or black holes. Motivated by the fact that real astrophysical black holes as non-stationary and non-isolated objects are living in non-empty backgrounds, we focus on the black hole subclasses of this general solution describing a dynamical evaporating-accreting black holes in the dynamical cosmological backgrounds of dust, radiation, quintessence, cosmological constant-like and phantom fields, the so called sur…
In this paper we study the Loop quantum effects on the \textit{Om} diagnostic and subsequently on the universe. We reconstruct the \textit{Om} diagnostic in the background of Loop quantum gravity and then study the behaviour of various Chaplygin gas dark energy models using the modified diagnostic in a comparative scenario. The trajectories discriminate the various dark energy models from each other both in the Einstein gravity as well as Loop quantum gravity. The Loop quantum effects are also clearly noticeable from the trajectories in past, present and future universe. We see that the Loop q…
We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime as a model for a Schwarzschild black hole embedded in a deSitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a non-zero finite value if the comoving observer approaches infinity.
We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution inside massive gravity by defining the Killing-vector in the direction of the Stückelberg function. We then consider the conditions which an observer in massive gravity has to obey in order to agree with the standard results of General Relativity.
We investigate the effect of the cosmological constant on the angular size of a black hole shadow. It is known that the accelerated expansion which is created by the cosmological constant changes the angular size of the black hole shadow for static observers. However, the shadow size must be calculated for the appropriate cosmological observes. We calculate the angular size of the shadow measured by cosmological comoving observers by projecting the shadow angle to this observer rest frame. We show that the shadow size tends to zero as the observer approaches the cosmological horizon. We estima…
Real black holes in the universe are located in the expanding accelerating background which are called the cosmological black holes. Hence, it is necessary to model these black holes in the cosmological background where the dark energy is the dominant energy. In this paper, we argue that most of the dynamical cosmological black holes can be modeled by point mass cosmological black holes. Considering the de Sitter background for the accelerating universe, we present the point mass cosmological background in the cosmological de Sitter space time. Our work also includes the point mass black holes…
