General Relativity And Quantum Cosmology

The idea that, after their evaporation, Planck-mass black holes might tunnel into metastable white holes has recently been intensively studied. Those relics have been considered as a dark matter candidate. We show that the model is severely constrained and underline some possible detection paths. We also investigate, in a more general setting, the way the initial black hole mass spectrum would be distorted by both the bouncing effect and the Hawking evaporation.

Collapsing process is studied in special type of inhomogeneous spherically symmetric space-time model (known as IFRW model), having no time-like Killing vector field. The matter field for collapse dynamics is considered to be perfect fluid with anisotropic pressure. The main issue of the present investigation is to examine whether the end state of the collapse to be a naked singularity or a black hole. Finally, null geodesics is studied near the singularity.

Ghost-free bimetric theory describes two nonlinearly interacting spin-2 fields, one massive and one massless, thus extending general relativity. We confront bimetric theory with observations of Supernovae type 1a, Baryon Acoustic Oscillations and the Cosmic Microwave Background in a statistical analysis, utilising the recently proposed physical parametrisation. This directly constrains the physical parameters of the theory, such as the mass of the spin-2 field and its coupling to matter. We find that all models under consideration are in agreement with the data. Next, we compare these results to bounds from local tests of gravity. Our analysis reveals that all two- and three-parameter models are observationally consistent with both cosmological and local tests of gravity. The minimal bimetric model (only β 1 ) is ruled out by our combined analysis.

Recently, it was argued in [Phys. Rev. Lett. {\bf126}, 031102 (2021)] that the WCCC can serve as a constraint to high-order effective field theories. However, we find there exists a key error in their approximate black hole solution. After correcting it, their calculation cannot show the ability of WCCC to constrain the gravitational theories.

Recently, the inverse electrodynamics model (IEM) was introduced and applied to fined Reissner-Nordström black holes in the context of the general relativity coupled minimally with the nonlinear electrodynamics \cite{1}. The solution consists of both electric and magnetic fields as of the dyonic solutions. Here in this note, we show that the IEM model belongs to a more general class of nonlinear electrodynamics with T= T μ μ =0 . Here T ν μ is the energy-momentum tensor of the nonlinear electrodynamic Lagrangian. Naturally, such a dyonic RN black hole solution is the solution for this general class.

An integral kernel representation for the commutative ??-product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin'feld differential twist are established. A ??-Einstein field equation can be obtained, provided the matter-based twist's vector generators are fixed to self-consistent values during the variation in order to maintain ??-associativity. Variations not of this type are non-viable as classical field theories. ??-Gauge theory on such a spacetime can be developed using ??-Ehresmann connections. While the theory preserves Lorentz invariance and background independence, the standard ADM 3+1 decomposition of 4-diffs in general relativity breaks down, leading to different ??-constraints. No photon or graviton ghosts are found on ??-Minkowski spacetime. ??-Friedmann equations are derived and solved for ??-FLRW cosmologies. Big Bang Nucleosynthesis restricts expressions for the twist generators. Allowed generators can be constructed which account for dark matter as arising from a twist producing non-standard model matter field. The theory also provides a robust qualitative explanation for the matter-antimatter asymmetry of the observable Universe. Particle exchange quantum statistics encounters \emph{thresholded} modifications due to violations of the cluster decomposition principle on the nonlocality length scale ??10 3?? L P . Precision Hughes-Drever measurements of spacetime anisotropy appear as the most promising experimental route to test deformed general relativity.

Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for f(R) modified gravity for an appropriate choice of the function f(R) . Since such an f(R) could be determined from the noncommutative-geometry background, these gravitational theories make very similar predictions in the discussion of (a) dark matter and (b) traversable wormholes; they can therefore be taken as equally viable models.

In order to try explaining the present accelerated expansion of the universe, we consider the most complete noncommutativity, of a certain type, in a Friedmann-Robertson-Walker cosmological model, coupled to a perfect fluid. We use the ADM formalism in order to write the gravitational Hamiltonian of the model and the Schutz's formalism in order to write the perfect fluid Hamiltonian. The noncommutativity is introduced by four nontrivial Poisson brackets between all geometrical as well as matter variables of the model. Each nontrivial Poisson bracket is associated to a noncommutative parameter. We recover the description in terms of commutative variables by introducing four variables transformations that depend on the noncommutative parameters. Using those variables transformations, we rewrite the total noncommutative Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the scale factor dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. The solutions depend on six parameters: the four noncommutative parameters, a parameter associated with the fluid energy C , and the curvature parameter k . They also depend on the initial conditions of the model variables. We compare the noncommutative solutions to the corresponding commutative ones and determine how the former ones differ from the latter ones. The comparison shows that the noncommutative model is very useful for describing the accelerated expansion of the universe. We also obtain estimates for one of the noncommutative parameters.

Recently, the action growth rate of a variety of four-dimensional regular magnetic black holes in F frame is obtained in [1]. Here, we study the action growth rate of a four-dimensional regular electric black hole in P frame that is the Legendre transformation of F frame. We also investigate the action growth rates of the Wheeler-De Witt patch for such black hole configurations at the late time and examine the Lloyd bound on the rate of quantum computation. We show that although the form of the Lloyd bound formula remains unaltered, the energy modifies due to a non-vanishing trace of the energy-momentum tensor and some extra terms may appear in the total growth action. We also investigate the asymptotic behavior of complexity in two conjectures for static and rotating regular black holes.

This paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans-Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic pressure and massive scalar field. For this purpose, we formulate structure scalars by orthogonally splitting the Riemann tensor. We show that self-gravitating models collapsing homologously follow the simplest mode of evolution. Furthermore, we demonstrate the effect of scalar field on the complexity and evolution of non-dissipative as well as dissipative systems. The criteria under which the system deviates from the initial state of zero complexity is also discussed. It is concluded that complexity of the sphere increases in self-interacting Brans-Dicke gravity because the homologous model is not shear-free.