Note on the Charged Black Hole Solutions in a Static Quantum Inspired Spacetime: Massive Gravity as Background

In this paper, we explore the black hole solutions with rainbow deformed metric in the presence of exponential form of nonlinear electrodynamics with asymptotic Reissner-Nordstrom properties. We calculate the exact solution of metric function and explore the geometrical prop- erties in the background of massive gravity. From the obtained solution, the existence of the singularity is confirmed in proper limits. Using the solutions we also investigate the thermody- namic properties of the solutions by checking the validity of the first law of thermodynamics. Continuing the thermodynamic study, we investigate the conditions under which the system is thermally stable from the heat capacity and the Gibbs free energy. We also discuss the possible phase transition and the criticality of the system. It was found that the quantum gravitational effects of gravity’s rainbow render the thermodynamic system stable in the vicinity of the singu- larity. From the equation of state it was found that after diverging at the singularity, the system evolves asymptotically into pressure-less dust as one moves away from the central singularity.

Pure Gauss–Bonnet NUT black hole with and without non-central singularity

It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of 2-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss–Bonnet $$\Lambda $$ Λ -vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at $$r \ne 0$$ r ≠ 0 .

Gravitationally collapsing stars in f(R) gravity

The gravitational dynamics of a collapsing matter configuration which is simultaneously radiating heat flux is studied in f(R) gravity. Three particular functional forms in f(R) gravity are considered to show that it is possible to envisage boundary conditions such that the end state of the collapse has a weak singularity and that the matter configuration radiates away all of its mass before collapsing to reach the central singularity.

Anisotropic strange quintessence stars in f(R,G) gravity

This paper is devoted to formulate a new model of quintessence anisotropic compact stars in the modified [Formula: see text] gravity. Dynamical equations in modified theory consisting of anisotropic fluid along with quintessence field have been evaluated by adopting analytical solution of Krori–Barua. In order to determine the unknown constraints of Krori–Barua metric observational data of different stars, [Formula: see text]-[Formula: see text], [Formula: see text], [Formula: see text]-[Formula: see text] has been taken into account. To solve the dynamical equations Starobinsky-like model, [Formula: see text] of modified gravity has been used. The outcome of the results depicts that all the examined celestial bodies are free from central singularity and are physically stable. Different physical parameters, such as energy density, energy conditions, evolution of quintessence and compactness factor, have been reviewed in detail.

Gravitational collapse for the K-essence emergent Vaidya spacetime

In this paper, we study the gravitational collapse in the k-essence emergent gravity using a generalized Vaidya-type metric as a background. We also analyze the cosmic censorship hypothesis for this system. We show that the emergent gravity metric resembles closely to the new type of the generalized Vaidya metrics for null fluid collapse with the k-essence emergent mass function, where we consider the k-essence scalar field being a function solely of the advanced or the retarded time. This new type of k-essence emergent Vaidya metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the k-essence emergent Vaidya metric are the interesting outcomes of the present work.

On causal structure of 4D-Einstein–Gauss–Bonnet black hole

The recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in $$D\ge 5$$ D ≥ 5 , the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.

Cylindrically symmetric 2 + 1 gravity in terms of global variables: Quantum dynamics

We perform quantization of a model in which gravity is coupled to a circular dust shell in [Formula: see text] spacetime dimensions. Canonical analysis shows that momentum space of this model is [Formula: see text]-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.

Rotating and non-rotating AdS black holes in $$f(\mathcal{T})$$ gravity non-linear electrodynamics

We derive new exact charged d-dimensional black hole solutions for quadratic teleparallel equivalent gravity, $$f(\mathcal{T})=a_0+a_1\mathcal{T}+a_2\mathcal{T}^2$$f(T)=a0+a1T+a2T2, where $$\mathcal T$$T is the torsion scalar, in the case of non-linear electrodynamics. We give a specific form of electromagnetic function and find out the form of the unknown functions that characterize the vielbeins in presence of the electromagnetic field. It is possible to show that the black holes behave asymptotically as AdS solutions and contain, in addition to the monopole and quadrupole terms, other higher order terms whose source is the non-linear electrodynamics field. We calculate the electromagnetic Maxwell field and show that our d-dimensional black hole solutions coincide with the previous obtained one (Awad et al. in J High Energy Phys 13:1706.01773, 2017). The structure of the solutions show that there is a central singularity that is much mild in comparison with the respective one in general relativity. Finally, the thermodynamical properties of the solutions are investigated by calculating the entropy, the Hawking temperature, the heat capacity, and other physical quantities. The most important result of thermodynamics is that the entropy is not proportional to the area of the black hole. This inanition points out that we must have a constrain on the quadrupole term to get a positive entropy otherwise we get a negative value.

The “Planckonions”

We consider a spherically symmetric stellar configuration with a density profile [Formula: see text]. This configuration satisfies the Schwarzchild black hole condition [Formula: see text] for every [Formula: see text]. We refer to it as “Planckonion”. The interesting thing about the Planckonion is that it has an onion-like structure. The central sphere with radius of the Planck-length [Formula: see text] has one unit of the Planck-mass [Formula: see text]. Subsequent spherical shells of radial width [Formula: see text] contain exactly one unit of [Formula: see text]. We study this stellar configuration using Tolman–Oppenheimer–Volkoff equation and show that the equation is satisfied if pressure [Formula: see text]. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.