International Journal of Modern Physics D

It is congruous with the quantum nature of the world to view the spacetime geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the spacetime manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantization of Einstein–Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the “superspace” of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble “minisuperspace” approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability that they are black holes (BHs) rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the “horizon wave function (HWF),” the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum BHs.

It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black hole (BH) remnants of the order of the Planck mass. Usually, this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum length most readily leads to the idea of the BH remnants, here, we examine the behavior of the potential that follows from the Planck-length deformed QFT in the absence of the minimum length and show that it might also lead to the formation of the Planck mass BHs in some particular cases. The calculations are made for higher-dimensional case as well. Such BH remnants might be considered as a possible candidates for the dark-matter.

By combining analytical and numerical methods, we find that the solutions of the complete Hořava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the ${(\partial lnN)}^2$ term, which is the unique deviation from general relativity (GR) in the effective action, is small. At one side, the solution with the throat acquires a kind of deformed anti-de Sitter (AdS) asymptotia and at the other side, there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function $N$ diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.

We investigate spherically symmetric spacetime filled with global monopole and perfect fluid in $f(R)$-gravity. We consider field equations of $f(R)$-gravity in order to understand the global monopole and the perfect fluid curve to the spacetime. It has taken advantages of conformal symmetry properties of the spacetime to solve these equations. The obtained solutions are improved in case of phantom energy. It is shown that obtained $f(R)$ function is consistent with well-known models of the modified gravity. Also, it is examined whether the obtained solutions support a traversable wormhole geometry. Obtained results of the solutions have been concluded.

The energy density of the holographic dark energy (HDE) is based on the area law of entropy, and thus any modification of the area law leads to a modified holographic energy density. Inspired by the entropy expression associated with the apparent horizon of a Friedmann–Robertson–Walker (FRW) universe in DGP braneworld, we propose a new model for the HDE in the framework of DGP brane cosmology. We investigate the cosmological consequences of this new model and calculate the equation of state (EoS) parameter by choosing the Hubble radius, $L=H^{-1}$, as the system’s IR cutoff. Our study show that, due to the effects of the extra dimension (bulk), the identification of IR cutoff with Hubble radius, can reproduce the present acceleration of the universe expansion. This is in contrast to the ordinary HDE in standard cosmology which leads to the zero EoS parameter in the case of choosing the Hubble radius as system’s IR cutoff in the absence of interaction between dark matter (DM) and dark energy (DE).

We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore, we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.

A solution for $f(R,T)$ gravity of the type $f(R,T)=f_1(R)+f_2(T)$ for specific $f_2(T)$ functions is derived. It is shown that a slight modification to the Schwarzschild metric can be found for $f_2(T)=\alpha T^n+\beta$, where $n>0$, $\beta \ll 1$ and $\alpha$ is some constant. The effects of $f(R,T)$ gravity on gravitational lensing are calculated and the differences with general relativity are compared. Furthermore, it is shown that modified gravity can give a considerable contribution to gravitational lensing.

We study analytically the $d$-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results imply that holographic $d$-wave superconductor is indeed a type II one even for different Lifshitz scaling. This is the same as the conventional $d$-wave superconductors in the Ginzburg–Landau (GL) theory. Our results also indicates that the dynamical exponent $z$ cannot affect the droplet solutions, and the vortex lattice solutions receive its effects only in the radial part. This naively implies that it does not have direct influence on the shape of vortex lattice even after the higher-order corrections are taken into consideration (away from the phase transition point $B_c$). However, it has effects on the upper critical magnetic field $B_{c_2}$ through the fact that a larger $z$ results in a smaller $B_{c_2}$ and therefore influences the size (characterized by $r_0\equiv 1/\sqrt{B_{c_2}}$) of the vortex lattices. Furthermore, close comparisons between our results and those of the GL theory reveal the fact that the upper critical magnetic field $B_{c_2}$ is inversely proportional to the square of the superconducting coherence length $\xi$, regardless of the anisotropy between space and time.

Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.

We examine the motion of a charged particle in the vicinity of a weakly magnetized naked singularity. The escape velocity and energy of the particle moving around the naked singularity after being kicked by another particle or photon are investigated. Also at innermost stable circular orbit (ISCO) escape velocity and energy are examined. Effective potential and angular momentum of the particle are also discussed. We discuss the center-of-mass energy after collision between two particles having same mass and opposite charges moving along the same circular orbit in the opposite direction. It is investigated that under what conditions maximum energy can be produced as a result of collision.

Although equivalent to general relativity, teleparallel gravity (TG) is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the “vector torsion”. This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group $\mathrm{\text{SO}}(1,4)$. It is found that the current state of accelerated expansion of the universe corresponds to a late-time attractor that can be (i) a dark energy-dominated de Sitter solution (${\omega }_{\varphi }=-1$), (ii) a quintessence-type solution with ${\omega }_{\varphi }\ge -1$, or (iii) a phantom-type ${\omega }_{\varphi }<-1$ dark energy.

Shadows of black holes surrounded by an optically thin emitting medium have been extensively discussed in the literature. The Hioki–Maeda algorithm is a simple recipe to characterize the shape of these shadows and determine the parameters of the system. Here, we extend their idea to the case of a dressed black hole, namely a black hole surrounded by a geometrically thin and optically thick accretion disk. While the boundary of the shadow of black holes surrounded by an optically thin emitting medium corresponds to the apparent photon capture sphere, that of dressed black holes corresponds to the apparent image of the innermost stable circular orbit (ISCO). Even in this case, we can characterize the shape of the shadow and infer the black hole spin and viewing angle. The shape and the size of the shadow of a dressed black hole are strongly affected by the black hole spin and inclination angle. Despite that, it seems that we cannot extract any additional information from it. Here, we study the possibility of testing the Kerr metric. Even with the full knowledge of the boundary of the shadow, those of Kerr and non-Kerr black holes are very similar and it is eventually very difficult to distinguish the two cases.

Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies, we assume that the metric of momentum space determines the condition of on-shellness while the momentum space affine connection governs the form of the law of composition of momenta. We show that the possible choices of laws of composition of momenta are more numerous than the possible choices of affine connection on a momentum space. This motivates us to propose a new prescription for associating an affine connection to momentum composition, which we compare to the one most used in the recent literature. We find that the two prescriptions lead to the same picture of the so-called $\kappa$-momentum space, with de Sitter (dS) metric and $\kappa$-Poincaré connection. We then show that in the case of “proper dS momentum space”, with the dS metric and its Levi–Civita connection, the two prescriptions are inequivalent. Our novel prescription leads to a picture of proper dS momentum space which is DSR-relativistic and is characterized by a commutative law of composition of momenta, a possibility for which no explicit curved momentum space picture had been previously found. This momentum space can serve as laboratory for the exploration of the properties of DSR-relativistic theories which are not connected to group-manifold momentum spaces and Hopf algebras, and is a natural test case for the study of momentum spaces with commutative, and yet deformed, laws of composition of momenta.

We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle (GUP) which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical quantities, we obtain a deformed Friedmann equation which is very similar to that arising from loop quantum cosmology scenarios. The energy and entropy densities get maximum bounds about Planck temperature and a nonsingular universe then emerges in this setup.