International Journal of Modern Physics D

In this paper, we review recent theoretical results, demonstrating breakdown of the equivalence between active and passive gravitational masses and energy due to quantum effects in general relativity. In particular, we discuss the simplest composite quantum body — a hydrogen atom — and define its gravitational masses operators. Using Gedanken experiment, we show that the famous Einstein’s equation, $E=m{c}^2$, is broken with small probability for passive gravitational mass of the atom. It is important that the expectation values of both active and passive gravitational masses satisfy the above-mentioned equation for stationary quantum states. Nevertheless, we stress that, for quantum superpositions of stationary states in a hydrogen atom, where the expectation values of energy are constant, the expectation values of the masses oscillate in time and, thus, break the Einstein’s equation. We briefly discuss experimental possibility to observe the above-mentioned time-dependent oscillations. In this review, we also improve several drawbacks of the original pioneering works.

Cosmological and astrophysical observations lead to the emerging picture of a universe that is spatially flat and presently undertaking an accelerated expansion. The observations supporting this picture come from a range of measurements encompassing estimates of galaxy cluster masses, the Hubble diagram derived from type-Ia supernovae observations, the measurements of Cosmic Microwave Background radiation anisotropies, etc. The present accelerated expansion of the universe can be explained by admitting the existence of a cosmic fluid, with negative pressure. In the simplest scenario, this unknown component of the universe, the Dark Energy, is represented by the cosmological constant ($\mathrm{\Lambda }$), and accounts for about 70% of the global energy budget of the universe. The remaining 30% consist of a small fraction of baryons (4%) with the rest being Cold Dark Matter (CDM). The Lambda Cold Dark Matter ($\mathrm{\Lambda }$CDM) model, i.e. General Relativity with cosmological constant, is in good agreement with observations. It can be assumed as the first step towards a new standard cosmological model. However, despite the satisfying agreement with observations, the $\mathrm{\Lambda }$CDM model presents lack of congruence and shortcomings and therefore theories beyond Einstein’s General Relativity are called for. Many extensions of Einstein’s theory of gravity have been studied and proposed with various motivations like the quest for a quantum theory of gravity to extensions of anomalies in observations at the solar system, galactic and cosmological scales. These extensions include adding higher powers of Ricci curvature $R$, coupling the Ricci curvature with scalar fields and generalized functions of $R$. In addition, when viewed from the perspective of Supergravity (SUGRA), many of these theories may originate from the same SUGRA theory, but interpreted in different frames. SUGRA therefore serves as a good framework for organizing and generalizing theories of gravity beyond General Relativity. All these theories when applied to inflation (a rapid expansion of early universe in which primordial gravitational waves might be generated and might still be detectable by the imprint they left or by the ripples that persist today) can have distinct signatures in the Cosmic Microwave Background radiation temperature and polarization anisotropies. We give a review of $\mathrm{\Lambda }$CDM cosmology and survey the theories of gravity beyond Einstein’s General Relativity, specially which arise from SUGRA, and study the consequences of these theories in the context of inflation and put bounds on the theories and the parameters therein from the observational experiments like PLANCK, Keck/BICEP, etc. The possibility of testing these theories in the near future in CMB observations and new data coming from colliders like the LHC, provides an unique opportunity for constructing verifiable models of particle physics and General Relativity.

Rainbow gravity can be a suitable model to study the Friedmann–Robertson–Walker (FRW) universe in the realm of high energy physics. In rainbow gravity the radius of the apparent horizon is modified and it is used to derive the surface gravity and the temperature on the horizon. Inspired by the modified Friedmann equation in rainbow gravity and adopting the viewpoint that there is a deep connection between Friedmann equation and the first law of thermodynamics, the entropy on the horizon is obtained. It is interesting to be noted that the thermodynamical properties of the FRW universe depend on the energy of the probe, which is used by an observer to investigate the spacetime. Finally, it is shown that the validity of the generalized second law (GSL) of thermodynamics can be considered as a useful instrument to restrict the choice of rainbow gravity functions.

$Ad{S}_5$ Type IIb supergravity compactifications on five-dimensional Einstein manifolds ${{𝒱}}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) $Ad{S}_5$, they are expected to suffer Gregory–Laflamme instability with respect to localization on ${{𝒱}}_5$. Previously, the instability was demonstrated for gravitational dual of ${𝒩}=4$ SYM, where ${{𝒱}}_5=S^5$. We extend stability analysis to arbitrary ${{𝒱}}_5$. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is ${{𝒱}}_5$-sensitive, as it is governed by the lowest nonvanishing eigenvalue ${\lambda }_{\mathrm{\text{min}}}$ of its Laplacian.

In this paper, a detailed analysis for superradiant stability of the system composed by a $D$-dimensional Reissner–Nordström-anti-de Sitter (RN-AdS) black hole and a reflecting mirror under charged scalar perturbations are presented in the linear regime. It is found that the stability of the system is heavily affected by the mirror radius as well as the mass of the scalar perturbation, AdS radius and the dimension of spacetime. In a higher dimensional spacetime, the degree of instability of the superradiant modes will be severely weakened. Nevertheless, the degree of instability can be magnified significantly by choosing a suitable value of the mirror radius. Remarkably, when the mirror radius is smaller than a threshold value the system becomes stable. We also find that massive charged scalar fields cannot trigger the instabilities in the background of $D$-dimensional asymptotically flat RN black hole. For a given scalar charge, a small RN-AdS black hole can be superradiantly unstable, while a large one may be always stable under charged scalar field with or without a reflecting mirror. We also show that these results can be easily expounded and understood with the help of factorized potential analysis.

In this work, we study the gravitational collapsing process of a spherically symmetric star constitute of Dark Matter (DM), ${\rho }_M$, and Dark Energy (DE) $\rho$. In this model, we use anisotropic pressure with Equation of State (EoS) $p_t=\lambda \rho$ and $p_r=l\rho$, $(l+2\lambda <-1)$. It reveals that gravitational collapse of DM and DE with interaction leads to the formation of the black hole. When $l+2\lambda <-3$ (phantoms), dust and phantoms could be ejected from the death of white hole. This emitted matter again undergoes to collapsing process and becomes the black hole. This study gives the generalization for isotropy of pressure in the fluid to anisotropy when there will be interaction between DM and DE.

Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the anti-de Sitter (AdS) spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper, we suggest a prescription for the dS/MERA correspondence and recover a discrete version of dS Penrose diagram by using the MERA on conformal theories identified with the future/past boundaries (${{ℐ}}^{\pm }$) of the dS spacetime. In this case, as anticipated, time appears as the emergent direction. We comment on the possible interpretation that the dS cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.

A warm inflationary universe in the brane-world scenario is being studied by assuming the standard scalar and tachyon field models. For this purpose, the quartic potential ($\frac{\sigma {\varphi }^4}{4}$) is being utilized which is ruled out by current data in cold inflation but in our models it is analyzed that it is in agreement with recent observational data. Moreover, the generalized form of dissipative coefficient $(\mathrm{\Gamma }=a_0\frac{T^{\tilde{m}}}{{\varphi }^{\tilde{m}-1}})$ is being considered. Within this setup, the inflationary parameters in the weak dissipative regime are being analyzed. It is observed that the ranges of our results of tensor-to-scalar ratio, scalar spectral index and running of spectral favor observational data like BICEP2, WMAP9 and Planck.

We examine corrections to the standard Newton's law due to the presence of a spherically symmetric wormhole. We show that the Newtonian potential can be decomposed into two terms. The first term does not depend on the wormhole metric and corresponds to the standard law. It obeys to the conformal invariant equation. The second term explicitly depends on the wormhole metric and corresponds to corrections. We show that such corrections can be described in terms of a polarization energy density.

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller–Israel–Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

Killing tensors have been of interest historically primarily for generating first integrals for the geodesic equation and for their use in finding separable coordinate systems. A related notion, that of Killing spinors, has recently been shown to be important in the study of generalized symmetries of Maxwell's equations. In a given spacetime, the generalized symmetries depend on the existence of Killing spinors of the spacetime of certain valences. The existence of Killing spinors for the curved metric of Gödel's Universe is investigated. There are five (1,1) Killing spinors, 14 (2,2) and five (1,5) Killing spinors of the spacetime, in addition to the unique (0,2) and (0,4) Killing spinors which are exhibited here as well.

We investigate the propagation of gravitational waves in linearized Chern–Simons (CS) modified gravity by considering two nondynamical models for the coupling field $𝜃$: (i) a domain wall and (ii) a surface layer of $𝜃$, motivated by their relevance in condensed matter physics. We demonstrate that the metric and its first derivative become discontinuous for a domain wall of $𝜃$, and we determine the boundary conditions by realizing that the additional contribution to the wave equation corresponds to one of the self-adjoint extensions of the D'Alembert operator. Nevertheless, such discontinuous metric satisfies the area matching conditions introduced by Barrett. On the other hand, the propagation through a surface layer of $𝜃$ behaves similarly to the propagation of electromagnetic waves in CS extended electrodynamics. In both cases, we calculate the corresponding reflection and transmission amplitudes. As a consequence of the distributional character of the additional terms in the equations that describe wave propagation, the results obtained for the domain wall are not reproduced when the thickness of the surface layer goes to zero, as one could naively expect.

We study the phase-space dynamics of cosmological models in the theoretical formulations of nonminimal metric-torsion couplings with a scalar field, and investigate in particular the critical points (CPs) which yield stable solutions exhibiting cosmic acceleration driven by the dark energy (DE). The latter is so defined that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar–tensor cosmological setup, the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable CPs, we check their physical viability in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work [S. Sur and A. S. Bhatia, arXiv:1611.00654 [gr-qc]]. We not only examine the regions of physical relevance in the phase-space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively noninteracting scenarios, in both Einstein and Jordan frames.

We investigate the detectability of massive mode of polarization of Gravitational Waves (GWs) in $f(R)$ theory of gravity associated with Gamma Ray Bursts (GRBs) sources. We obtain the beam pattern function of Laser Interferometric Gravitational wave Observatory (LIGO) corresponding to the massive polarization of GWs and perform Bayesian analysis to study this polarization. It is found that the massive polarization component with a mass of $10^{-22}$eV/c² is too weak to be detected at LIGO with its current configuration.

The extended phase-space thermodynamics and heat engines for static spherically symmetric black hole solutions of four-dimensional conformal gravity are studied in detail. It is argued that the equation of states (EOS) for such black holes is always branched, any continuous thermodynamical process cannot drive the system from one branch of the EOS into another branch. Meanwhile, the thermodynamical volume is bounded from above, making the black holes always super-entropic in one branch and may also be super-entropic in another branch in certain range of the temperature. The Carnot and Stirling heat engines associated to such black holes are shown to be distinct from each other. For rectangular heat engines, the efficiency always approaches zero when the rectangle becomes extremely narrow, and given the highest and lowest working temperatures fixed, there is always a maximum for the efficiency of such engines.

The epochs of reheating and preheating are studied in a simple extension of the Starobinsky inflationary model, which consists of an $R^2$-correction to the Einstein–Hilbert action and an additional scalar field. We find that if the $R^2$-correction at the end of inflation is dynamically important, it affects the expansion rate and as a consequence, the reheating and preheating processes. While we find that the reheating temperature and duration of reheating are only slightly affected, the effect has to be taken into account when comparing the theory to data. In the case of preheating, the gravitational corrections can significantly affect the decay of the second field. We find that particle production is strongly affected for certain values of the parameters in the theory.

In the Ellis–Bronnikov wormhole (WH) metrics, the motion of a particle along the curved rotating channels is studied. By taking into account a prescribed shape of a trajectory, we derive the reduced 1 + 1 metrics, obtain the corresponding Langrangian of a free particle and analytically and numerically solve the corresponding equations of motion. We have shown that if the channels are twisted and lagged behind rotation, under certain conditions, beads might asymptotically reach infinity, leaving the WH, which is not possible for straight corotating trajectories. The analytical and numerical study is performed for two- and three-dimensional cases and initial conditions of particles are analyzed in the context of possibility of passing through the WH.