International Journal of Modern Physics D

In this methodological paper, we consider two problems an astronaut faces under the black hole horizon in the Schwarzschild metric. (1) How to maximize the survival proper time. (2) How to make a visible part of the outer universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the “river model.” Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point (1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point (2) requires maximizing the peculiar velocity of the observer. Both goals (1) and (2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology and its application for the problems studied in this paper can be used in advanced general relativity courses.

This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient $\rho$ when expanded as inverse powers of $r$ (where $r$ is the usual spherical radial coordinate, and $r\to \infty$ is null infinity, ${ℐ}$) has coefficient $-1$. (2) In the absence of gravitational radiation (a conformally flat ${ℐ}$), the group of asymptotic symmetries is trivial, with no room for supertranslations.

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.

A charged stellar model is presented by constructing a solution to the Einstein–Maxwell equations system in a spherically symmetrical static time-space. The rate of compactness for the model depends on two parameters $(w,\alpha )$, one of them $\alpha$ associated to the charge, which allows a value of compactness $u\le 0.520721786$ higher than the neutral case. The density and pressure are regular functions, positive and monotonically decreasing and the function of charge is positive regular and monotonically increasing, its shown that the model satisfies the condition of causality, the geometry is regular and as such the model is physically acceptable. Although the model can be applicable for a variety of stars, considering a star with mass $M=1M_{\odot }$ for $w=0.18008215$ the range of compactness is $u\in [0.21250263,0.25922408]$ and radius $R\in [5.7402,6.9480]\mathrm{\text{Km}}$, in this case the range of values for the central density is $[1.66819,3.30317]10^{18}\mathrm{\text{Kg}}/{\mathrm{\text{cm}}}^3$ greater than the value of the nuclear density and consistent with that expected for stars with this compactness rate.

The aim of this work is to analyze the modified form of holographic dark energy (DE) density suggested by Tsallis and Cirto within inhomogeneous models of the universe. This DE model is applied to IR cutoff equals the Hubble horizon. Some basic cosmological functions, such as the Hubble function, the deceleration function and the equation of state parameter, are reconstructed by choosing specific values of certain numerical parameters in this model. The stability of the model is studied by considering the square of sound speed and the strong, the weak and the dominant energy conditions (DEC). In addition, the variation of the diagnostic Omega, $Om$ and $L_m$ parameters with the redshift and space are studied. The obtained results show a close behavior to that of the cosmological constant DE universe so it can be compared well with the recent observations.

This study reports a reconstruction scheme of a Dark Energy (DE) model with higher-order derivative of Hubble parameter, which is a particular case of Nojiri–Odintsov holographic DE (HDE) [S. Nojiri and S. D. Odintsov, Gen. Relativ. Gravit. 38 (2006) 1285.] that unifies phantom inflation with the acceleration of the universe on late-time. The reconstruction has been carried out in the presence of bulk viscosity, where the bulk-viscous pressure has been taken as a function of Hubble parameter. Ranges of cosmic time $t$ have been derived for quintessence, cosmological constant and phantom behaviour of the equation-of-state (EoS) parameter. In the viscous scenario, the reconstruction has been carried out in an interacting and noninteracting situations and in both the cases stability against small perturbations has been observed. Finally, the slow roll parameters have been studied and a scope of exit from inflation has been observed. Also, the availability of quasi-exponential expansion has been demonstrated for interacting viscous scenario and a study through tensor-to-scalar ratio has ensured consistency of the model with the observational bound by Planck. Alongwith primordial fluctuations, the interacting scenario has been found to generate strong dissipative regime.

Scalar–tensor theory of gravity with nonlinear electromagnetic field, minimally coupled to gravity is considered and static black hole solutions are obtained. Namely, power-law and Born–Infeld nonlinear Lagrangians for the electromagnetic field are examined. Since the cosmological constant is taken into account, it allowed us to investigate the so-called topological black holes. Black hole thermodynamics is studied, in particular temperature of the black holes is calculated and examined and the first law of thermodynamics is obtained with help of Wald’s approach.

In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [arXiv:gr-qc/1904.09336] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant $\mathrm{\Lambda }$ and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).

Gravitational waves (GWs) are inevitably produced by second-order terms in cosmological perturbation theory. Most notably, the so-called induced (GWs) are a window to the small scales part of the primordial spectrum of fluctuations and a key counterpart to the primordial black hole (PBH) scenario. However, semi-analytical solutions are only known for matter and radiation domination eras. In this paper, we present new analytic integral formulas for the induced GWs on subhorizon scales in a general cosmological background with a constant equation-of-state. We also discuss applications to a peaked primordial scalar power spectrum and the PBH scenario.

We study the cosmological consequences of energy injection from the evaporation of Primordial Black Holes (PBHs) that are formed due to the collapse of the inhomogeneities that were generated during inflation in the early universe. By using the current results of the baryon–photon ratio obtained from BBN and CMB observations, we impose constraints on the spectral index of perturbations on those small scales that cannot be estimated through CMB anisotropy and CMB distortions. The masses of the PBHs constrained in this study lie in the range of $10^9$–$10^{11}$g, which corresponds to those PBHs whose maximal evaporation took place during the redshifts $10^6<z<10^9$. It is shown that the upper bound on the scalar spectral index, $n_s$ can be constrained for a given threshold value, ${\zeta }_{\mathrm{\text{th}}}$, of the curvature perturbations for PBHs formation. Using Planck results for cosmological parameters, we obtained $n_s<1.309$ for ${\zeta }_{\mathrm{\text{th}}}=0.7$ and $n_s<1.334$ for ${\zeta }_{\mathrm{\text{th}}}=1.2$, respectively. The density fraction that has contributed to the formation of PBHs has also been estimated.