International Journal of Modern Physics D

Einstein’s General theory of relativity (GR) successfully describes gravity. Although GR has been accurately tested in weak gravitational fields, it remains largely untested in the general strong field cases. One of the most fundamental predictions of GR is the existence of black holes (BHs). After the recent direct detection of gravitational waves by LIGO, there is now near conclusive evidence for the existence of stellar-mass BHs. In spite of this exciting discovery, there is not yet direct evidence of the existence of BHs using astronomical observations in the electromagnetic spectrum. Are BHs observable astrophysical objects? Does GR hold in its most extreme limit or are alternatives needed? The prime target to address these fundamental questions is in the center of our own Milky Way, which hosts the closest and best-constrained supermassive BH candidate in the universe, Sagittarius A* (Sgr A*). Three different types of experiments hold the promise to test GR in a strong-field regime using observations of Sgr A* with new-generation instruments. The first experiment consists of making a standard astronomical image of the synchrotron emission from the relativistic plasma accreting onto Sgr A*. This emission forms a “shadow” around the event horizon cast against the background, whose predicted size ($\sim 50\mu$as) can now be resolved by upcoming very long baseline radio interferometry experiments at mm-waves such as the event horizon telescope (EHT). The second experiment aims to monitor stars orbiting Sgr A* with the next-generation near-infrared (NIR) interferometer GRAVITY at the very large telescope (VLT). The third experiment aims to detect and study a radio pulsar in tight orbit about Sgr A* using radio telescopes (including the Atacama large millimeter array or ALMA). The BlackHoleCam project exploits the synergy between these three different techniques and contributes directly to them at different levels. These efforts will eventually enable us to measure fundamental BH parameters (mass, spin, and quadrupole moment) with sufficiently high precision to provide fundamental tests of GR (e.g. testing the no-hair theorem) and probe the spacetime around a BH in any metric theory of gravity. Here, we review our current knowledge of the physical properties of Sgr A* as well as the current status of such experimental efforts towards imaging the event horizon, measuring stellar orbits, and timing pulsars around Sgr A*. We conclude that the Galactic center provides a unique fundamental-physics laboratory for experimental tests of BH accretion and theories of gravity in their most extreme limits.

We briefly introduce the disadvantages for Type Ia supernovae (SNe Ia) as standard candles to measure the universe, and suggest Gamma-ray bursts (GRBs) can serve as a powerful tool for probing the properties of high redshift universe. We use GRBs as distance indicators in constructing the Hubble diagram at redshifts beyond the current reach of SNe Ia observations. Since the progenitors of long GRBs (LGRBs) are confirmed to be massive stars, they are deemed as an effective approach to study the cosmic star formation rate (SFR). A detailed representation of how to measure high-$z$ SFR using GRBs is presented. Moreover, first stars can form only in structures that are suitably dense, which can be parametrized by defining the minimum dark matter halo mass $M_{\mathrm{\text{min}}}$. $M_{\mathrm{\text{min}}}$ must play a crucial role in star formation. The association of LGRBs with the collapses of massive stars also indicates that the GRB data can be applied to constrain the minimum halo mass $M_{\mathrm{\text{min}}}$ and to investigate star formation in dark matter halos.

High energy transients make up a diverse and exotic class of objects, from terrestrial lightning to $\gamma$-ray bursts at cosmological distances. In this review, we provide a detailed look at some of the more exciting transients observed over the last few years by Swift and other high energy missions.

We investigate the quark deconfinement phase transition in cold ($T=0$) and hot $\beta$-stable hadronic matter. Assuming a first-order phase transition, we calculate and compare the nucleation rate and the nucleation time due to quantum and thermal nucleation mechanisms. We show that above a threshold value of the central pressure a pure hadronic star (HS) (i.e. a compact star with no fraction of deconfined quark matter (QM)) is metastable to the conversion to a quark star (QS) (i.e. a hybrid star or a strange star). This process liberates a huge amount of energy, of the order of 10${}^{53}$ erg, which produces a powerful neutrino burst, likely accompanied by intense gravitational waves emission, and possibly by a second delayed (with respect to the supernova explosion forming the HS) explosion which could be the energy source of a powerful gamma-ray burst (GRB). This stellar conversion process populates the QS branch of compact stars, thus one has in the universe two coexisting families of compact stars: HSs and QSs. We introduce the concept of critical mass $M_{\mathrm{\text{cr}}}$ for cold HSs and proto-hadronic stars (PHSs), and the concept of limiting conversion temperature for PHSs. We show that PHSs with a mass $M<M_{\mathrm{\text{cr}}}$ could survive the early stages of their evolution without decaying to QSs. Finally, we discuss the possible evolutionary paths of PHSs.

A new intrinsically-relativistic kinetic mechanism for generation of nonisotropic relativistic kinetic equilibria in collisionless $N$-body systems is pointed out. The theory is developed in the framework of the covariant Vlasov statistical description. The new effect is based on the constraints placed by the conservation laws of neutral single-particle dynamics in prescribed background curved-spacetimes demonstrating existence of Killing tensors. As an illustration, the particular case of the Kerr spacetime admitting the so-called Carter constant for the particle geodesic motion is considered. The general functional form of the equilibrium kinetic distribution function (KDF) is determined and an explicit realization in terms of Gaussian-like distributions is provided. It is shown that, due to the Carter constant, these equilibrium KDFs exhibit an anisotropic phase-space functional dependence in terms of the single-particle 4-velocity components, giving rise to corresponding nonisotropic continuum fluid fields. The qualitative properties of the equilibrium stress–energy tensor associated with these systems are discussed, with a particular emphasis on the related occurrence of temperature anisotropy effects. The theory is susceptible of astrophysical applications, including in particular the statistical properties of dark matter (DM) halos around stellar-mass or galactic-center black holes.

We present new anisotropic models for Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] type perfect fluid solution. For this purpose, we started with metric potential $e^{\lambda }$ same as Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] and $e^{\nu }$ is monotonically increasing function as suggested by Lake [K. Lake, Phys. Rev. D 67 (2003) 104015]. After that we determine the new pressure anisotropy factor $\mathrm{\Delta }$ with the help of both the metric potentials $e^{\lambda }$ and $e^{\nu }$ and propose new well behaved general solution for anisotropic fluid distribution. The physical quantities like energy density, radial and tangential pressures, velocity of sound and redshift etc. are positive and finite inside the compact star. In this connection, we have studied the stability of the models, which is most vital one and also we determined the equation of state $p=f(\rho )$ for the realistic compact star models. It is noted that the mass and radius of our models can represent the structure of realistic astrophysical objects such as Her X-1 and RXJ 1856-37.

The generated relic gravitational waves underwent several stages of evolution of the universe such as inflation and reheating. These stages were affected on the shape of spectrum of the waves. As well known, at the end of inflation, the scalar field $\varphi$ oscillates quickly around some point where potential $V(\varphi )=\lambda {\varphi }^n$ has a minimum. The end of inflation stage played a crucial role on the further evolution stages of the universe because particles were created and collisions of the created particles were responsible for reheating the universe. There is a general range for the frequency of the spectrum $\sim (0.3\times 10^{-18}-0.6\times 10^{10}$)Hz. It is shown that the reheating temperature can affect on the frequency of the spectrum as well. There is constraint on the temperature from cosmological observations based on WMAP-9 and Planck. Therefore, it is interesting to estimate allowed value of frequencies of the spectrum based on general range of reheating temperature like few MeV $\lesssim T_{rh}\lesssim 10^{16}$ GeV, WMAP-9 and Planck data then compare the spectrum with sensitivity of future detectors such as LISA, BBO and ultimate-DECIGIO. The obtained results of this comparison give us some more chance for detection of the relic gravitational waves.

We study the cosmological implications of the Nambu–Jona-Lasinio (NJL) model when the coupling constant is field dependent. The NJL model has a four-fermion interaction describing two different phases due to quantum interaction effects and determined by the strength of the coupling constant $g$. It describes massless fermions for weak coupling and a massive fermions and strong coupling, where a fermion condensate is formed. In the original NJL model, the coupling constant $g$ is indeed constant, and in this work we consider a modified version of the NJL model by introducing a dynamical field dependent coupling motivated by string theory. The effective potential as a function of the varying coupling (aimed to implement a natural phase transition) is seen to develop a negative divergence, i.e. becomes a “bottomless well” in certain limit region. Although we explain how an lower unbounded potential is not necessarily unacceptable in a cosmological context, the divergence can be removed if we consider a mass term for the coupling like field. We found that for a proper set of parameters, the total potential obtained has two minima, one located at the origin (the trivial solution, in which the fluid associated with the fields behave like matter); and the other related to the nontrivial solution. This last solution has three possibilities: (1) if the minimum is positive $V_{\mathrm{\text{min}}}>0$, the system behaves as a cosmological constant, thus leading eventually to an accelerated universe; (2) if the minimized potential vanishes $V_{\mathrm{\text{min}}}=0$, then we have matter with no acceleration; (3) finally a negative minimum $V_{\mathrm{\text{min}}}<0$ leads an eventually collapsing universe with a flat geometry. Therefore, a possible interpretation as dark matter (DM) or dark energy (DE) is allowed among the behaviors implicated in the model.

The nonminimal coupling of the kinetic term to Einstein’s tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parametrized post-Newtonian (PPN) parameters for the scalar–tensor theory of gravity with nonminimally derivative coupling. We find that under experimental constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein’s general relativity in the order of $10^{-20}$, and the effect of the nonminimal coupling is negligible if we take the scalar field as dynamical dark energy. With the assumed conditions that the background scalar field is spatially homogeneous and evolves only on cosmological timescales and the contribution to stress–energy in the solar system from the background scalar field is subdominant, the scalar field is required to be massless.

An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a generalization of unimodular gravity. In a cosmological context with ultrarelativistic or cold matter, the resulting field equations have only one solution, empty Minkowski spacetime (selected by the prior metric of the theory). The introduction of energy exchange between vacuum and matter gives rise to nonstatic cosmic solutions. It is found that Minkowski spacetime (from the prior metric) appears as an attractor of the dynamic equations. A further result is that energy–momentum conservation of any localized material system is violated in a nonconstant gravitational background. The impact for experiment appears, however, negligible if the vacuum-energy mass-scale is of order meV.

The interacting generalized ghost version of pilgrim dark energy (GGPDE) is discussed in the framework of loop quantum cosmology (LQC). We analyze the behavior of cosmological parameters (Hubble, equation of state (EoS), deceleration) and cosmological planes (${\omega }_D-{\omega }_D^{\prime }$ and $r$-$s$) in the present scenario (${\omega }_D$ represents the EoS parameter and ${\omega }_D^{\prime }$ indicates the evolution of the EoS parameter, $r$,$s$ are statefinder parameters). It is observed that the deceleration parameter corresponds to the accelerated expansion of the universe. The EoS parameter lies in vacuum and phantom regions for all cases of $u$ (pilgrim dark energy (PDE) parameter). The ${\omega }_D-{\omega }_D^{\prime }$ plane lies in thawing region for all cases of $u$. The $r-s$ plane corresponds to $\mathrm{\Lambda }$ cold dark matter (CDM) and Chaplygin gas model. We have also mentioned the constraints on calculated cosmological parameters and found that all the trajectories of cosmological parameters and planes show the consistence behavior with the observational schemes.

The late-time cosmic acceleration of the universe is explained in the framework of the Einstein-scalar-Gauss–Bonnet (GB) theory by considering different appropriate forms for the GB coupling parameter and the scalar field. The physical quantities such as the potential energy, the GB coupling parameter, the energy density, the pressure and the deceleration parameter are obtained in an exact parametric form of the volume scale factor of the universe. The behavior of the deceleration parameter shows a transition from the deceleration phase to the acceleration phase at the late times in agreement with the observational data. Finally, the GB energy density ratio is compared to the matter energy density and the scalar (the quintessence) field energy density in the early and late times.

If two particles collide inside the ergosphere, the energy in the center of mass frame can be made unbound provided at least one of particles has a large negative angular momentum [A. A. Grib and Yu. V. Pavlov, Europhys. Lett. 101 (2013) 20004]. We show that the same condition can give rise to unbounded Killing energy of debris at infinity, i.e. super-Penrose process. Proximity of the point of collision to the black hole horizon is not required.

We have examined the thermodynamic properties for a variety of spherically symmetric charged-AdS black hole (BH) solutions, including the charged AdS BH surrounded by quintessence dark energy and charged AdS BH in $f(R)$ gravity in extended phase-space. This framework involves treating the cosmological constant as thermodynamic variable (for example: thermodynamic pressure and thermodynamic volume). Then they should behave as an analog of Van-der-Waal (VdW) like systems. In the extended phase-space we have calculated the entropy product and thermodynamic volume product of all horizons. The mass (or enthalpy) independent nature of the said product signals they are universal quantities. The divergence of the specific heat indicates that the second-order phase transition occurs under certain condition. In Appendix A, we have studied the thermodynamic volume products for axisymmetric spacetime and it is shown to be not universal in nature. Finally, in Appendix B, we have studied the $P-V$ criticality of Cauchy horizon for charged-AdS BH and found to be an universal relation of critical values between two horizons as $P_c^{-}=P_c^{+}$, $v_c^{-}=v_c^{+}$, $T_c^{-}=-T_c^{+}$, ${\rho }_c^{-}=-{\rho }_c^{+}$. The symbols are defined in the main work.

In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann–Robertson–Walker (FRW) geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model, the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter $\beta$. We compute the scale factor expected value ($〈a〉$) for several values of $\beta$. For all of them, $〈a〉$ oscillates between maxima and minima values and never vanishes. It gives an initial indication that those models are free from singularities, at the quantum level. We improve this result by showing that if we subtract a quantity proportional to the standard deviation of $a$ from $〈a〉$, this quantity is still positive. The $〈a〉$ behavior, for the present model, is a drastic modification of the $〈a〉$ behavior in the corresponding commutative version of the present model. There, $〈a〉$ grows without limits with the time variable. Therefore, if the present model may represent the early stages of the universe, the results of the present paper give an indication that $〈a〉$ may have been, initially, bounded due to noncommutativity. We also compute the Bohmian trajectories for $a$, which are in accordance with $〈a〉$, and the quantum potential $Q$. From $Q$, we may understand why that model is free from singularities, at the quantum level.

In this paper, we consider tachyonic matter in spatially flat Friedmann–Robertson–Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.