Abstract: Abstract An approximate realistic metric representing the spacetime of neutron stars is obtained by perturbing the Kerr metric. This metric has five parameters, namely the mass, spin or angular momentum, mass quadrupole, spin octupole and mass hexadecapole. Moreover, a version of the Hartle–Thorne metric containing these parameters is constructed by means of a series transformation between these spacetimes and solving the Einstein field equations. The form of the Pappas metric in Schwarzschild spherical coordinates is found. The three relativistic multipole structures are compared. PubDate: 2019-03-22 DOI: 10.1007/s10714-019-2530-5

Abstract: Abstract We consider a modified gravity model of the form \( f(R,\phi )=R e^{h(\phi )R} \) , where the strong gravity corrections are taken to all orders and \(\phi \) is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations. PubDate: 2019-03-18 DOI: 10.1007/s10714-019-2531-4

Abstract: Abstract Approximately 60 years ago, Herman Bondi took the major step in the study of gravitational radiation of introducing the use of null surfaces as coordinates for the study and integration of the Einstein equations. This led to the well-known Bondi mass loss theorem, the basis of the recent observation by the Ligo team of gravitational radiation. In Bondi’s approach to the integration procedure, he used special null surfaces (now referred to as Bondi null surfaces) where the null generators possessed (in general) non-vanishing asymptotic shear—the free radiation data. The use of this Bondi strategy over the years has become almost sacrosanct—being the central approach in almost all discussions of gravitational radiation issues. It led to the idea of an asymptotic symmetry—the BMS group. Eventually Bondi’s description of null infinity became elegantly formalized via Penrose’s future null infinity and associated structures. However recently an alternative picture of null infinity has been developed—now based on the similarity of the null surfaces to those of flat-space near null infinity. The new null surfaces, that are now asymptotically shear-free, are very different from the Bondi surfaces. These surfaces are as similar as possible to flat-space light cones near infinity. Totally new structures—e.g., the geometric asymptotically shear-free null geodesic congruences and even the physical classical equations of motion, now appear in this new picture. The Bondi–Sachs energy–momentum conservations laws remain but are augmented by angular momentum (orbital and spin) conservation laws. The BMS group again reappears, not as an asymptotic symmetry group, but as a transformation group acting on these new structures. An unanswered question arises: with this new point of view, have we lost the asymptotic symmetries of the BMS group' PubDate: 2019-03-16 DOI: 10.1007/s10714-019-2524-3

Abstract: Abstract One of the most interesting astrophysical phenomenon is the astrophysical flow near a 3D black hole. In this paper, we have adopted the Hamiltonian approach to investigate the matter accretion onto Einstein-power-Maxwell black hole in the presence of cosmological parameter l and the charge parameter Q. We analyze the accretion process for the case of isothermal flow when different test fluids are falling onto this black hole. Further, we calculate the general solution of equation of motion for the axial symmetric static black hole. The most interesting aspect of this paper is to discuss the effects parameters of black hole on the mass accretion rate, which we discussed by the graphical analysis. Moreover, it has been shown that the parameters \(\Lambda \) and Q play a dominant role for the maximum accretion rate. PubDate: 2019-03-13 DOI: 10.1007/s10714-019-2527-0

Abstract: Abstract In this work, we obtain the solution corresponding to a static spherically symmetric black hole surrounded by quintessence in pure Lovelock gravity. Some aspects of the thermodynamics of this black hole are investigated, with special emphasis on the Hawking temperature, entropy and heat capacity. The behaviors of these quantities are analyzed and the differences with respect to the ones in the Theory of General Relativity are pointed out. PubDate: 2019-03-13 DOI: 10.1007/s10714-019-2528-z

Abstract: Abstract In this work we use the latest observations on SNIa, H(z), BAO, \(f_{gas}\) in clusters and CMBR, to constrain three models showing an explicit interaction between dark matter and dark energy. In particular, we use the BOSS BAO measurements at \(z \simeq 0.32\) , 0.57 and 2.34, using the full 2-dimensional constraints on the angular and line of sight BAO scale. We find that using all five observational probes together, two of the interaction models show positive evidence at more than 3 \(\sigma \) . Although significant, further study is needed to establish this statement firmly. PubDate: 2019-03-13 DOI: 10.1007/s10714-019-2526-1

Abstract: Abstract For a general spherically-symmetric four-dimensional metric the notion of “circularity” of a family of equatorial geodesic trajectories is defined in geometrical terms. The main object turns out to be the angular-momentum function J obeying a consistency condition involving the mean extrinsic curvature of the submanifold containing the geodesics. The analysis of linear stability is reduced to a simple dynamical system. For static metrics the existence of such geodesics is given when \(J^2 > 0\) , and \((J^2)^{\prime } > 0\) for stability. The formalism is then applied to the Schwarzschild–de Sitter solution, both in its static and in its time-dependent cosmological version, as well to the Kerr–de Sitter solution. In addition we present an approximate solution to a cosmological metric containing a massive source and solving the Einstein field equation for a massless scalar. PubDate: 2019-03-11 DOI: 10.1007/s10714-018-2427-8

Abstract: Abstract In this paper we introduce a new general approach for the study of spacetimes admitting a standard static splitting. This approach allows us to give an alternative proof for the uniqueness of splitting in the spatially closed case to the first study made by Sánchez–Senovilla and later by Aledo–Romero–Rubio. However, our technique also allows us to obtain new uniqueness results for standard static models with complete (non necessarily compact) spacelike bases under some mild hypothesis, including some restrictions on the sectional curvature of such bases. PubDate: 2019-03-08 DOI: 10.1007/s10714-019-2525-2

Abstract: Abstract Close encounters between compact object binaries and a supermassive black hole are plausible at galactic centers. We present results from a numerical study of close to 13 million such encounters. Consistent with previous studies, we found that disrupted binaries produce bound extreme-mass-ratio binaries with eccentricities of \(\sim 0.97\) which circularize dramatically by the time they enter the classical LISA sensitivity band. We also investigated the regions of parameter space for binary survival and estimated the distribution of orbital parameters post-encounter. Our results showed that the semi-major axis of the population of surviving binaries is not significantly affected by the encounter. On the other hand, the eccentricity does; it increases in most cases. As a consequence, the encounter with the super-massive black hole accelerates the merger of the surviving binary, increasing the predicted merger rates by up to \(1\%\) . PubDate: 2019-03-05 DOI: 10.1007/s10714-019-2523-4

Abstract: Abstract The observation of a pulsar closely orbiting the galactic center supermassive black hole would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propagation delay in a Schwarzschild spacetime. We then compare this result to the propagation delays derived in the usually employed post-Newtonian approximation, in particular to the Shapiro delay up to the second post-Newtonian order. For edge-on orbits we also consider modifications of the Shapiro delay which take the lensing effects into account. Our results are then used to assess the accuracy of the different orders of the post-Newtonian approximation of the propagation delay. This comparison indicates that for (nearly) edge-on orbits the new exact delay formula should be used. PubDate: 2019-03-04 DOI: 10.1007/s10714-019-2517-2

Abstract: Abstract The interaction of a weak plane gravitational wave with a small gyroscope universal-mounted in a macroscopic gimbal is calculated. The microscopic gyroscope can be exemplified by a small hollow sphere with a massive spherical rotor inside. The macroscopic gimbal may be realized by a massless sphere with a rigidly coupled bar-bell of two masses. The gravitational wave causes a torque on the bar-bell, which is transferred to the gyroscope by the gimbal. For the proposed configuration the calculation results in a precession angle of the gyroscope proportional to \(\varGamma \times \omega _r / \omega _G\) where \(\varGamma \) is the amplitude of the gravitational wave, \(\omega _r\) is the angular velocity of the rotor and \(\omega _G\) is the frequency of the gravitational wave. The precession angle can be measured, in principle, by angular laser interferometry and leads for our configuration to a length difference of \(\varDelta L \approx 10^{-18}\text { m}\) which is comparable with the formal arm length difference of LIGO for the assumed gravitational wave amplitude \(\varGamma = 10^{-21} \text { with }\omega _G = 1 \text { Hz}\) . PubDate: 2019-03-02 DOI: 10.1007/s10714-019-2522-5

Abstract: Abstract We consider a charged Gauss–Bonnet black hole in d-dimensional spacetime and examine the effect of thermal fluctuations on the thermodynamics of the black hole. At first we take the first order logarithmic correction term in entropy and compute the thermodynamic potentials like Helmholtz free energy F, enthalpy H and Gibbs free energy G in the spherical, Ricci flat and hyperbolic topology of the black hole horizon, respectively. We also investigate the P–V criticality and calculate the critical volume \(V_{c}\) , critical pressure \(P_{c}\) and critical temperature \(T_{c}\) using different equations when P–V criticality appears and show that there is no critical point without thermal fluctuations for this type black hole. We find that the presence of logarithmic correction in it is necessary to have critical points and stable phases. Moreover, we study the stability of the black holes by employing the specific heat. Finally, we study the geometrothermodynamics and analyse the Ricci scalar of the Ruppeiner metric graphically for the same. PubDate: 2019-02-25 DOI: 10.1007/s10714-019-2520-7

Abstract: Abstract In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev black hole). In order to demonstrate that HPM is able to yield acceptable solutions for the null-geodesics with easily computable terms, the HPM is tested for the simple examples of spherically symmetric spacetimes such as Schwarzschild and Reissner–Nordström black holes. After that, the null-geodesics of light passing the vicinity of Kiselev black hole are studied via the HPM in two particular cases regarding the equation of state parameter of quintessence. In addition, a formula for the angle of deflection has been obtained via HPM in the form of a series which allows to calculate the angle with any accuracy without requirement of its smallness. PubDate: 2019-02-21 DOI: 10.1007/s10714-019-2521-6

Abstract: Abstract We examine the singularities of the wave fronts of null geodesics from point sources in the Kerr metric. We find that the wave fronts develop a tube like structure that collapses non-symmetrically, leading to cusp features in the wave front singularities. As the wave front advances, the cusps trace out an astroidal shaped caustic tube, which had been discovered previously using lens mapping and geodesic deviation methods. Thus, the wave front approach in this study helps to complete a picture of caustics and gravitational lensing in the Kerr geometry. PubDate: 2019-02-20 DOI: 10.1007/s10714-019-2518-1

Abstract: Abstract The standard \(\varLambda \hbox {CDM}\) model can be mimicked at the background and perturbative levels (linear and non-linear) by a class of gravitationally induced particle production cosmology dubbed CCDM cosmology. However, the radiation component in the CCDM model follows a slightly different temperature–redshift T(z)-law which depends on an extra parameter, \(\nu _r\) , describing the subdominant photon production rate. Here we perform a statistical analysis based on a compilation of 36 recent measurements of T(z) at low and intermediate redshifts. The likelihood of the production rate in CCDM cosmologies is constrained by \(\nu _r = 0.024^{+0.026}_{-0.024}\) ( \(1\sigma \) confidence level), thereby showing that \(\varLambda \) CDM ( \(\nu _r=0\) ) is still compatible with the adopted data sample. Although being hardly differentiated in the dynamic sector (cosmic history and matter fluctuations), the so-called thermal sector (temperature law, abundances of thermal relics and CMB power spectrum) offers a clear possibility for crucial tests confronting \(\varLambda \) CDM and CCDM cosmologies. PubDate: 2019-02-20 DOI: 10.1007/s10714-019-2516-3

Abstract: Abstract We use Hamilton–Jacobi formalism to study the curvature and isocurvature perturbations during inflation. This formalism is suitable for going beyond slow roll regime. We solve the equation of fields’ perturbations for some two-field models, and calculate their spectra. We next use \(\delta N\) formalism to calculate the curvature and isocurvature non-Gaussianity for a non-separable form of the Hubble expansion rate. Finally, using the sudden decay approximation, we obtain the link between the perturbations during inflation and after reheating for noninteracting fields. PubDate: 2019-02-19 DOI: 10.1007/s10714-019-2515-4

Abstract: Abstract A tidal disruption event (TDE) ensues when a star passes too close to a supermassive black hole (SMBH) in a galactic center, and is ripped apart by its tidal field. The gaseous debris produced in a TDE can power a bright electromagnetic flare as it is accreted by the SMBH; so far, several dozen TDE candidates have been observed. For SMBHs with masses above \(\sim 10^7 M_\odot \) , the tidal disruption of solar-type stars occurs within ten gravitational radii of the SMBH, implying that general relativity (GR) is needed to describe gravity. Three promising signatures of GR in TDEs are: (1) a super-exponential cutoff in the volumetric TDE rate for SMBH masses above \(\sim 10^8 M_\odot \) due to direct capture of tidal debris by the event horizon, (2) delays in accretion disk formation (and a consequent alteration of the early-time light curve) caused by the effects of relativistic nodal precession on stream circularization, and (3) quasi-periodic modulation of X-ray emission due to global precession of misaligned accretion disks and the jets they launch. We review theoretical models and simulations of TDEs in Newtonian gravity, then describe how relativistic modifications give rise to these proposed observational signatures, as well as more speculative effects of GR. We conclude with a brief summary of TDE observations and the extent to which they show indications of these predicted relativistic signatures. PubDate: 2019-02-12 DOI: 10.1007/s10714-019-2510-9

Abstract: Abstract The q-models are scenarios that may explain the smallness of the cosmological constant (Klinkhamer and Volovik in Phys Rev D 77:085015, 2008; Phys Rev D 78:063528, 2008; JETP Lett 88:289, 2008; Mod Phys Lett A 31(28):1650160, 2016; JETP Lett 91:259, 2010; Phys Rev D 79:063527, 2009; J Phys Conf Ser 314:012004, 2011). The vacuum in these theories is presented as a self-sustainable medium and include a new degree of freedom, the q-variable, which establishes the equilibrium of the quantum vacuum. In the present work, the Cauchy formulation for these models is studied in detail. It is known that there exist some limits in which these theories are described by an F(R) gravity model, and these models posses a well posed Cauchy problem. This paper shows that the Cauchy problem is well posed even not reaching this limit. By use of some mathematical theorems about second order non linear systems, it is shown that these scenarios admit a smooth solution for at least a finite time when some specific type of initial conditions are imposed. Some technical conditions of Ringstrom (The Cauchy problem in general relativity, European Mathematical Society, Warsaw, 2000) play an important role in this discussion. PubDate: 2019-02-09 DOI: 10.1007/s10714-019-2507-4

Abstract: Abstract We first calculate the holographic entanglement entropy of M5 branes on a circle and see that it has a phase transition when decreasing the compactified radius. In particular, it is shown that the entanglement entropy scales as \(N^3\) . Next, we investigate the holographic entanglement entropy of a \(D0+D4\) system on a circle and see that it scales as \(N^2\) at low energy, as in gauge theory with instantons. However, at high energy it transforms to a phase that scales as \(N^3\) , as an M5 brane system. We also present the general form of holographic entanglement entropy of Dp, \(D_p+D_{p+4}\) and M-branes on a circle and see some simple relations among them. Finally, we present an analytic method to prove that they all have phase transitions from connected to disconnected surfaces as one increases the line segment that divides the entangling regions. PubDate: 2019-02-07 DOI: 10.1007/s10714-019-2513-6

Abstract: Abstract A particular class of conformally flat spacetimes possessing isotropic and anisotropic pressure are investigated, using \(1+3\) formalism. We specialize the \(1+3\) equations obtained for the respective class of spacetimes to a compatible and simple equation of state where the energy per particle depends only on the particle density and the shear scalar. PubDate: 2019-02-07 DOI: 10.1007/s10714-019-2514-5