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In this paper, we focused on the study of anisotropic strange stars with anisotropic matter distribution in the framework of f ( T , T ) = α T ( r ) 2 + β T ( r ) model, where α , β are arbitrary constants, T and T represent the torsion scalar and trace of energy–momentum tensor, respectively. This model has interesting cosmological properties, in addition to providing an effective dark energy sector explanation (Harko et al., 2014). In order to achieve our goal, we considered the Krori-Barua space–time and utilize the off-diagonal tetrad components for deriving the corresponding set of field equations. We calculate the relation for the evaluation of effective density, effective radial and tangential pressure using the EoS of strange star i.e., MIT bag model p r ( r ) = 1 3 [ ρ ( r ) − 4 B g ] . The unknown constants appearing in the solution have been evaluated by using the conventional matching of interior and exterior space time. To check the feasibility of our proposed model we discuss the anisotropy, energy condition, TOV forces, abreu condition, EoS parameters, adiabatic index, mass function, compactness and redshift for different compact stars models namely, P S R J 1416 − 2230 , 4 U 1608 − 52 , C e n X − 3 , E X O 1785 − 248 and S M C X − 1 .

The fully parabolic cross-diffusion system { e u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) , v t = Δ v − v + u , is considered under homogneous Neumann boundary conditions in a ball Ω ⊂ R n , n ≥ 1 , for e ∈ ( 0 , 1 ) and χ > 0 . Previous literature has asserted global existence of certain generalized solutions whenever χ n ( n − 2 ) + , but no result on any unboundedness phenomenon seems available; only in a parabolic-elliptic simplification, some solutions are known to blow up in finite time when n ≥ 3 and χ > 2 n n − 2 . The present study examines the solution behavior in the singular limit e ↘ 0 , and based on an essentially well-known result on finite-time blow-up in an accordingly obtained nonlocal scalar parabolic problem, under the assumptions that n ≥ 3 and χ > n n − 2 a statement on spontaneous emergence of arbitrarily large values of u for appropriately small e is derived.

In this study, we investigate black hole solutions with toroidal horizons in scalar hair and dilaton gravity. First, we obtain the field equations in n-dimensions. Then, we propose different models (ansatz) and find the exact solutions for these types of ansatzs. These solutions are not asymptotically (anti) de Sitter or flat, except in one special case. We also show that the BTZand BTZ-like solutions emerge from some of these solutions as a special case. We also show that when the event horizon radius increases, the temperature will be the same in various dimensions. The only difference is noticeable near the origin (this statement is clear from the figures). For these solutions, we obtained a new version of the Smarr formula. In addition, we show that the presence of the scalar field makes the black holes more stable near the origin, except for the BTZ case. In general, the presence of a scalar field is an important factor in black hole stability investigations. In the critical behavior analysis, we find that there is no evidence to show the existence of P-V criticality. Here, we present a class of interior solutions corresponding to the solution in a scalar hair gravity exterior. The solution obtained in the linear case was regular and well-behaved at the stellar interior.

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic renormalization flow of multi-trace operators and stochastic $n$-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS$_6$. What we have found is that the stochastic time $t$ dependent 3-point function obtained from Langevin equation with its Euclidean action being given by $S_E=2I_{os}$ is identical to holographic renormalization group evolution of holographic triple trace operator as its energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi point functions and multi trace operators in each framework., Comment: 1+23 pages

We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator $O_k$ and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of $T^nO_k$ (being $T^n$ the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way., Comment: 23 pages

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin $J$ exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials., Textual improvements, updated bibliography. Version to appear in JHEP

We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times $t < \beta/2$ (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times $t, Comment: 44 pages, 17 figures, Comments about memory effect and some references are added

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars., 104 pages, 1 attached Mathematica notebook; V2: small adjustments, references added; V3: clarifications and some formulas corrected

The aim of this investigation is to examine the effect of gravitational modification, in particular, the f ( G , T ) gravitational field, for dynamically relativistic spherically symmetric systems in the existence of electromagnetic field. The theoretical analysis of dynamical variables linked with charged viscous anisotropic sphere with dissipation is formulated in these environments. We consider that with a relativistic matter, the non-static diagonally symmetric spherical structure is coupled. We linked the Weyl scalar, structure parameters including the charged terms with metric scale factors and mass function. To formulate general form of dynamical variables, we implemented Herrera’s methodology for the orthogonally decomposition of the Riemann tensor. The presence of these variables in the behavioral dynamics of radiating spheres is then analyzed. With the existence and exclusion of fixed f ( G , T ) values, the parameters essential for the occurrence of inhomogeneities have been studied. It is suggested that with generalized forms of scalar variables, the evolutionary periods of the spherical interiors can be well observed.

On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar charged fermions interacting by means of classical and phantom scalar fields. Based on the study of the microscopic dynamics of scalar charged particles, within the framework of the Lagrangian as well as Hamiltonian formalism, a function of the dynamic mass of scalar charged particles was constructed and it was shown that for the consistency of the theory, it is necessary to remove the nonnegativity condition for this function. On the basis of the Lagrangian formalism, equations of gravitational and scalar fields with singular sources are formulated and microscopic conservation laws are obtained. Within the framework of the general relativistic kinetic theory, macroscopic equations of gravitational and scalar fields are formulated and macroscopic conservation laws are obtained. These equations' full correspondence to microscopic equations with singular sources is shown. Further, on the basis of the obtained equations, a cosmological model for a degenerate system of scalarly charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which made it possible to significantly simplify the original system of equations. On the basis of the obtained solution of the constitutive equations, two fundamentally different cosmological models are formulated, one of which has two types of singly scalarly charged fermions, while the second has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamic system for a two-component model is carried out., 31 pages, 70 references

The superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is studied. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable. In the proof, we develop a new method which is based on the Descartes' rule of signs for the polynomial equations. Our results generalize the previous study that four-dimensional extremal Reissner-Nordstrom black hole is superradiantly stable under charged massive scalar perturbation., Comment: 15 pages, no figures

In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in an Einstein–Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner–Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a micro-canonical ensemble, scalarized solutions are always thermodynamically preferred over RNAdS black holes. However, the system has much richer phase structure and phase transitions in a canonical ensemble. In particular, we report a RNAdS BH/scalarized BH/RNAdS BH reentrant phase transition, which is composed of a zeroth-order phase transition and a second-order one.

We apply a recently developed 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation for the study of spherically symmetric, static black hole solutions of Horndeski scalar-tensor theory. Our discussion proceeds in an effective field theory (EFT) of modified gravity approach, with the action depending on metric and embedding scalars adapted to the nonorthogonal 2+1+1 decomposition. We prove that the most generic class of Horndeski Lagrangians compatible with observations can be expressed in this EFT form. By studying the first order perturbation of the EFT action we derive three equations of motion, which reduce to those derived earlier in an orthogonal 2+1+1 decomposition, and a fourth equation for the metric parameter N related to the nonorthogonality of the foliation. For the Horndeski class of theories with vanishing $G_3$ and $G_5$, but generic functions $G_2(\phi,X)$ (k-essence) and $G_4(\phi)$ (nonminimal coupling to the metric) we prove the unicity theorem that no action beyond Einstein--Hilbert allows for the Schwarzschild solution. Next we integrate the EFT field equations for the case with only one independent metric function obtaining new solutions characterized by a parameter interpreted as either mass or tidal charge, the cosmological constant and a third parameter. These solutions represent naked singularities, black holes with scalar hair or have the double horizon structure of the Schwarzschild--de Sitter spacetime. Solutions with homogeneous Kantowski--Sachs type regions also emerge. Finally, one of the solutions obtained for the function $G_4$ linear in the curvature coordinate, in certain parameter range exhibits an intriguing logarithmic singularity lying outside the horizon. The newly derived hairy black hole solutions evade previously known unicity theorems by being asymptotically nonflat, even in the absence of the cosmological constant., Comment: 20 pages, 4 figures

We consider solutions of the semi-classical Einstein-Klein-Gordon system with a cosmological constant $\Lambda\in\mathbb{R}$, where the spacetime is given by Einstein's static metric on $\mathbb{R}\times\mathbb{S}^3$ with a round sphere of radius $a>0$ and the state of the scalar quantum field has a two-point distribution $\omega_2$ that respects all the symmetries of the metric. We assume that the mass $m\ge0$ and scalar curvature coupling $\xi\in\mathbb{R}$ of the field satisfy $m^2+\xi R>0$, which entails the existence of a ground state. We do not require states to be Hadamard or quasi-free, but the quasi-free solutions are characterised in full detail. The set of solutions of the semi-classical Einstein-Klein-Gordon system depends on the choice of the parameters $(a,\Lambda,m,\xi)$ and on the renormalisation constants in the renormalised stress tensor of the scalar field. We show that the set of solutions is either (i) the empty set, or (ii) the singleton set containing only the ground state, or (iii) a set with infinitely many elements. We characterise the ranges of the parameters and renormalisation constants where each of these alternatives occur. We also show that all quasi-free solutions are given by density matrices in the ground state representation and we show that in cases (ii) and (iii) there is a unique quasi-free solution which minimises the von Neumann entropy. When $m=0$ this unique state is a $\beta$-KMS state. We argue that all these conclusions remain valid in the reduced order formulation of the semi-classical Einstein equation., Comment: 31p, v2: added reference and minor corrections

We prove unexpected decay of the L2-distance from the solution u(t) of a hyperbolic scalar conservation law, to some convex, flow-invariant target sets.

We study the bosonic pair production in time-dependent solitonic backgrounds, in which a charged scalar in the gauge potential or a massive scalar in the global de Sitter space has the frequency of the reflectionless Posch-Teller potential with a natural number that corresponds to the soliton number. Solving the quantum master equation for quadratic correlation functions in Phys. Rev. D 84, 1250028 (2011), we find the exact pair-production rates to be polynomials in the inverse square of hyperbolic cosine, which exhibit solitonic characteristics of a finite total pair production per unit volume and a non-oscillatory, exponentially decaying behavior for the entire period. An algebraic method that connects the quantum master equation to the soliton equation is advanced to confirm the exact result.

In this paper, we present the annihilation and creation operators for a moving scalar massive particle on 1 + 1-de Sitter space. This presentation is based on coherent states method and Hall-Mitchell approach about annihilation operator for a system which its phase space is $ S_{\mathcal {C}}^{n} $ . We show that these operators coincide with the Ladder operators for a quantum particle on circle which was presented by Kowalski-Rembielinski-Papaloucas (both cases have the same phase spaces).

We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L2. We then study the issue of global existence. We prove global existence for the KSE in the presence of advection for arbitrary data, provided the advecting velocity field v satisfies certain conditions that ensure the dissipation time of the associated hyperdiffusion-advection equation is sufficiently small. In the absence of advection, global existence can be shown only if the linearized operator does not admit any growing mode and for sufficiently small initial data.

We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) $\Sigma_2\times S^3$ and (ii) $\Sigma_3\times S^3$, where $\Sigma_2 = S^2/\Gamma$, $\mathbb{R}^2/\Gamma$, or $\mathbb{H}^2/\Gamma$, and $\Sigma_3 = S^3/\Gamma$, $\mathbb{R}^3/\Gamma$, or $\mathbb{H}^3/\Gamma$, with $\Gamma$ a discrete group of symmetries, corresponding to NS5-branes wrapped on $\Sigma_2$ and $\Sigma_3$. The resulting theories are a $D=5$, $\mathcal{N}=4$ gauged supergravity coupled to three vector multiplets with scalar manifold $SO(1,1)\times SO(5,3)/(SO(5)\times SO(3))$ and gauge group $SO(2)\times\left(SO(2)\ltimes_{\Sigma_2}\mathbb{R}^4\right)$ which depends on the curvature of $\Sigma_2$, and a $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold $SU(1,1)/U(1)\times G_{2(2)}/SO(4)$ and gauge group $\mathbb{R}^+\times\mathbb{R}^+$ for truncations (i) and (ii) respectively. Instead of carrying out the truncations at the 10-dimensional level, we show that they can be obtained directly by performing In\"on\"u-Wigner contractions on the 5 and 4-dimensional gauged supergravity theories that come from consistent truncations of 11-dimensional supergravity associated with M5-branes wrapping $\Sigma_2$ and $\Sigma_3$. This suggests the existence of a broader class of lower-dimensional gauged supergravity theories related by group contractions that have a 10 or 11-dimensional origin., Comment: 2+73 pages, 1 figure; very minor changes, reference added, published version

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $\langle VV\mathcal{O}\rangle$ maps to photon-photon-massive amplitudes., 57 pages, 12 figures, latex; comments added, refs added; the version to appear on JHEP

In this paper, we give some application of scalar type operators to Decomposibility. In particular, we show that if H is of (α, α + 1) type R and that it generates a strongly continuous group on a Banach space, then its resolvent is Decomposable hence scalar type.

The field theoretic renormalization group (RG) is applied to the model of a near-equilibrium fluid coupled to a scalar field (like temperature or density of an impurity) which is active, that is, influencing the dynamics of the fluid itself. It is shown that the only possible nontrivial infrared (IR) asymptotic regimes are governed by "passive" fixed points of the RG equations, where the back reaction is irrelevant. This result reminds of that obtained in [Nandy and Bhattacharjee, J. Phys. A: Math. Gen. {\bf 31}, 2621 (1998)] in a model describing active convection by fully developed turbulence. Furthermore, we establish the existence of "exotic" fixed points with negative and complex effective couplings and transport coefficients that may suggest possible directions for future studies.

Considering marginally relevant and relevant deformations of the weakly coupled $(3+1)$-dimensional large $N$ conformal gauge theories introduced in arXiv:2011.13981, we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the $N\rightarrow\infty$ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. In certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global $\mathbb Z_2$ or $U(1)$ symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the masses (squared) added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the $N\rightarrow\infty$ limit., Comment: 40 pages

The varational method with the Hamiltonian formalism of quantum field theory (QFT) is used to study the bound state for scalar particle and antiparticle (bosons with spin 0) in a reformulated model. We first recall some points about the two-body ground state energy solutions in 3 + 1 dimensions. In this case, some approximations are needed to obtain numerical solutions. Then, we study the upper and lower bound states in zero dimensional space for the two-body problem using simple trial states. It is shown that when the dimension of space is zero some analytical (exact) solutions can be obtained when the interactions are small.

This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the advected scalar by up to one order of derivative. We also consider a non-degenerate modification of the endpoint case in which the velocity is less smooth than the advected scalar by slightly more than one order. The existence and uniqueness theory of these equations in the borderline Sobolev spaces is addressed, as well as the instantaneous smoothing effect of their corresponding solutions. In particular, it is shown that solutions emanating from initial data belonging to these Sobolev classes immediately enter a Gevrey class. Such results appear to be the first of its kind for a quasilinear parabolic equation whose coefficients are of higher order than its linear term; they rely on an approximation scheme which modifies the flux in such a way that preserves the underlying commutator structure lost by having to work in the critical space setting, as well as delicate adaptations of well-known commutator estimates to Gevrey classes., 34 pages and 1 figure

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index $n_s$ and the amplitude of the scalar perturbations $A_s$ and different values of the tensor-to-scalar ratio $r$., Comment: 11 pages, 5 figures, v2: minor corrections, references are added, to appear in EPJC

The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

In this paper, we investigate the approximate bound states solutions of Klein–Gordon equation with position-dependent mass for scalar and vector central Hulthen-type potentials by applying an approximation scheme to deal with the centrifugal potential for any l-states. The supersymmetric quantum mechanics (SUSYQM) and shape invariance approaches are used in the calculations. We obtain straightforwardly the relativistic energies and their corresponding normalized wavefunctions, expressed in terms of Jacobi polynomials. Special cases of interest of this problem are also deduced and it is found that our results are in good agreement with those obtained in the literature.

The tunneling characteristics at the cosmological and event horizons of Reissner–Nordström–de Sitter black hole with a global monopole are studied by using the modified Lorentz violation scalar field equation in curved space–time. Firstly, we get the modified Hamilton–Jacobi equation using the semi-classical approximation, then the Hawking radiation and thermodynamical properties of Reissner–Nordström–de Sitter black hole with a global monopole are computed based on the modified Hamilton–Jacobi equation. Our results show that Lorentz violation can lead to lower Hawking temperature and higher entropy of the black hole at the same time. This work improves the understanding of the physical nature of Lorentz violation in curved space–time.

In this paper, we examine the spatially homogeneous and anisotropic Kantowski–Sachs (KS) space–time with viscous Ricci dark energy in the framework of Saez and Ballester (Phys Lett A 113:467, 1986) scalar tensor theory of gravitation. To solve the field equations, we use (i) the relationship between metric potentials which is obtained from the condition that shear scalar of the model is proportional to the expansion scalar and (ii) the relationship between average scale factor (a(t)) and bulk viscous coefficient $$(\xi )$$ as $$\xi =\xi _0+\xi _1\big (\frac{\dot{a}}{a}\big )+\xi _2\big (\frac{\ddot{a}}{\dot{a}}\big )$$ , where $$\xi _0$$ , $$\xi _1$$ and $$\xi _2$$ are constants. Some well-known cosmological implications such as deceleration parameter, equation of state parameter, statefinder and Om diagnostic parameters of the model are constructed and analyzed through graphical representation. It is also observed that the KS viscous Ricci dark energy model presented here is compatible with the current cosmological observations.

We are interested in the long time asymptotic behaviour of solutions to the scalar Zakharov system $$\begin{aligned} \begin{array}{ll} i u_{t} + \Delta u = nu,\\ n_{tt} - \Delta n= \Delta |u|^2 \end{array} \end{aligned}$$ and the Klein–Gordon–Zakharov system $$\begin{aligned} \begin{array}{ll} u_{tt} - \Delta u + u = - nu,\\ n_{tt} - \Delta n= \Delta |u|^2 \end{array} \end{aligned}$$ in one dimension of space. For these two systems, we give two results proving decay of solutions for initial data in the energy space. The first result deals with decay over compact intervals assuming smallness and parity conditions (u odd). The second result proves decay in far field regions along curves for solutions whose growth can be dominated by an increasing $$C^1$$ function. No smallness condition is needed to prove this last result for the Zakharov system. We argue relying on the use of suitable virial identities appropriate for the equations and follow the technics of [22, 24] and [33].

In this present paper, a slowly rotating stat is investigated in shift symmetric scalar torsion theory framework using a nondiagonal tetrad that gives an axially symmetric spacetime. We present the general equations for a general Lagrangian in a spherical symmetric space time and then in an axially symmetric spacetime. The obtained equations will allow us to study the behaviour of a specific model at the center of the star and at large distance. We find that this particular model affects the behaviour at the center but it is not case for large value of the radial coordinate r. The integration of the equations of motion, for different realistic equations of state (EoS), confirms that the mass, the radius as well as the moment of inertia are effected by varying the parameters of the model. Finally, we examine the universal relation of normalized moment of inertia and the stellar compactness of neutron star in slow rotation approximation. We showed that for all values of parameters present in the model leads to a deviation from GR for all EoS with a relative deviation below $$10\%$$ 10 % .

A theory of gravitation with a massive graviton which was proposed by Visser is considered. An exact solution of this theory is found for the case when the source of the gravitational field is a scalar plane wave. Hamilton–Jacobi methods are used to obtain the laws of motion of massive and massless particles in this gravitational field.

Objective: To present a new solution to the field equations obtained for higher dimensional LRS Bianchi type-I universe generated by means of a cloud of strings with particles connected to them with bulk viscosity in general relativity. Methods: To obtain the solutions of field equations of higher dimensional LRS Bianchi type-I universe we consider that the shear scalar of the model is proportional to the scalar expansion of the model (saq ), which leads to, c=b^n. The physical and geometrical behaviors of the model universe are studied by comparing with the present cosmological scenario and observations. Findings: It is observed that our model is anisotropic, expanding and decelerates at early stage and then accelerates in late universe giving the inflation model universe. Novelty: We obtained new solution to the field equations for higher dimensional LRS Bianchi type-I generated by means of a cloud of strings with bulk viscous fluid in general relativity. Keywords: LRS Bianchi TypeI Metric; Bulk Viscous Fluid; Strings

Background/Objectives: With reference to the theory of general relativity, the rotating metrics can be designed with mass function ˆM (u; r) . Methods/Statistical analysis: The methods/analysis adapted is the theoretical and mathematical analysis on the theory of general relativity. Findings: The line element can be found out with the help of mass function ˆM(u; r) following the find of the covariant complex null tetrad vectors for the rotating metrics. Then, the NP spin — coefficients, the Ricci scalars, and the Weyl scalars for the rotating metrics can be found out. The expanded form of the mass function ˆM(u; r) with (a=0) can be shown from Wang and Wu (1999). From the expended form of the mass function ˆM(u; r)with (a = 0) , the NP coefficients can be derived. With the help of the scalar k, the surface gravity of the black hole is derived. Novelty/Applications: The findings of covariant complex null tetrad vectors for the rotating metrics, the NP spin — coefficients, the Ricci scalars, and the Weyl scalars are new analysis towards the theory of general relativity. Specific applications are the deep studies on the black hole and its surface gravity. It can be concluded that generally the rotating metric possesses a geodesic (k =e = 0), actually shear free (s = 0) , purely expanding (ˆq ( = 0) and a non-zero twistw 2 = 0) null vector la (Chandrasekhar, 1983). With the help of a scalar k, on a horizon of a Black hole, the surface gravity of the black hole is derived. Keywords: The Mass Function; NP Spin – Coefficients; The Ricci Scalars; The Weyl Scalars; The Surface Gravity of the Black Hole

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons.

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e+e− → dd¯¯¯. We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 → 2 + X scalar scattering process., Journal of High Energy Physics, 2021 (4), ISSN:1126-6708, ISSN:1029-8479

In this paper, we have examined the Kantowski–Sachs space-time in the presence of strange quark matter with the appearance and non-appearance of strings in f(R) gravity. Here, R is the Ricci scalar of the space-time. Exact solutions of the field equations are obtained by considering the following conditions (i) hybrid scale factor, (ii) the proportionality of shear scalar ( $$\sigma$$ ) with expansion scalar ( $$\theta$$ ) and (iii) power-law between the scalar-on function F(R) and average scale factor a(t). We have investigated some physical and geometrical properties of the models, and their behavior is thoroughly studied with the help of graphical representation.

Locally rotationally symmetric Bianchi type-I viscous and nonviscous cosmological models are explored in general relativity (GR) and in $$f(R,T)$$ gravity. Solutions are obtained by assuming that the expansion scalar is proportional to the shear scalar, which yields a constant value for the deceleration parameter ( $$q=2$$ ). Constraints are obtained by requiring physical viability of the solutions. A comparison is made between viscous and nonviscous models, and between the models in GR and in $$f(R,T)$$ gravity. The metric potentials remain the same in GR and in $$f(R,T)$$ gravity. Consequently, the geometrical behavior of the $$f(R,T)$$ gravity models remains the same as in GR. It is found that $$f(R,T)$$ gravity or bulk viscosity do not affect the behavior of effective matter which acts as a stiff fluid in all models. The individual fluids have a very rich behavior. In one of the viscous models, the matter either follows a semi-realistic EoS or exhibits a transition from stiff matter to phantom, depending on the values of the parameter. In another model, the matter describes radiation, dust, quintessence, phantom, and the cosmological constant for different values of the parameter. In general, $$f(R,T)$$ gravity diminishes the effect of bulk viscosity.

A viable model for inflation driven by a torsion function in a Friedmann background is presented. The scalar spectral index in the interval $0.92\lesssim n_{s}\lesssim 0.97$ is obtained in order to satisfy the initial conditions for inflation. The post inflationary phase is also studied, and the analytical solutions obtained for scale factor and energy density generalizes that ones for a matter dominated universe, indicating just a small deviation from the standard model evolution. The same kind of torsion function used also describes satisfactorily the recent acceleration of the universe, which could indicate a possible unification of different phases, apart form specific constants., Comment: 8 pages, 2 figures, submitted to EPJC

We consider a generalised gravitational theory that contains the Ricci scalar curvature and a scalar field coupled to the higher-derivative, quadratic Gauss-Bonnet gravitational term through an arbitrary coupling function $f(\phi)$. We review both of the existing no-hair theorems, the old and the novel, and show that these are easily evaded; this opens the way for black holes to emerge in the context of this theory. Indeed, we demonstrate that, under mild only assumptions for $f(\phi)$, we may construct asymptotic solutions that describe either a regular black-hole horizon or an asymptotically-flat solution. We then demonstrate, through numerical integration, that these asymptotic solutions may be smoothly connected and that novel, regular black-hole solutions with non-trivial scalar hair emerge for any form of the coupling function $f(\phi)$. We present and discuss the physical characteristics of a large number of such solutions for a plethora of coupling functions $f(\phi)$. Finally, we consider the pure scalar-Gauss-Bonnet theory, under the assumption that the Ricci scalar may be ignored, and we investigate whether novel black-hole solutions may arise in this case.

Introduction: when creating modern automatic control systems for various processes and objects operating in real time, very often one has to face the problem of solving various kinds of nonlinear scalar equations. In the first part of this work entitled “Dichotomy. Dichotomy? Dichotomy!: fundamentals, terminology problems and inspection analysis of the dichotomy method”, a modified version of the dichotomy method was proposed, which has all the main advantages of the modified method. This method has a number of advantages in comparison with other methods for solving nonlinear equations, but at present it has not found wide practical use. The main reason for its low popularity is a low rate of convergence of the sequence of approximate solutions, and a large amount of computation required to obtain sufficiently accurate solutions. Purpose of the study: to propose a modified version of the dichotomy method, which allows one to obtain more rapidly converging sequences of approximate solutions to nonlinear scalar equations and requires significantly less computations required to obtain solutions with the desired accuracy, to illustrate, a higher convergence rate of the sequence of approximate solutions calculated using the modified dichotomy method by solving a number of specific nonlinear equations and, thereby, to substantiate the advantage of the new method for its use in creating various automatic control and regulation systems. Results: a modification of the method for dividing a segment in half is proposed, which has all the main advantages of the modified method. The results of solving 4 nonlinear equations are presented illustrating a higher rate of convergence of solutions calculated using the proposed modification. Practical significance: the research results can be used in the development of modern automatic control systems for various technological processes and objects.

We study the regularity of minima of scalar variational integrals of $p$-growth, $1, Comment: arXiv admin note: text overlap with arXiv:1711.03284

The complete integration of scalar fourth-order ODEs with four-dimensional symmetry algebras is performed by utilizing Lie’s method which was invoked to integrate scalar second-order ODEs admitting two-dimensional symmetry algebras. We obtain a complete integration of all scalar fourth-order ODEs that possess four Lie point symmetries.

Boltzmann equation plays important roles in particle cosmology in studying the evolution of distribution functions (also called as occupation numbers) of various particles. For the case of the decay of a scalar condensation $\phi$ into a pair of scalar particles (called $\chi$), we point out that the system may not be well described by the Boltzmann equation when the occupation number of $\chi$ becomes large even in the so-called narrow resonance regime. We study the particle production including the possible enhancement due to a large occupation number of the final state particle, known as the stimulated emission or the parametric resonance. Based on the quantum field theory (QFT), we derive a set of equations which directly govern the evolution of the distribution function of $\chi$. Comparing the results of the QFT calculation and those from the Boltzmann equation, we find non-agreements in some cases. In particular, in the expanding Universe, the occupation number of $\chi$ based on the QFT may differ by many orders of magnitude from that from the Boltzmann equation. We also discuss a possible relation between the evolution equations based on the QFT and the Boltzmann equation., Comment: 21 pages, 5 figures, 2 tables, version to appear in JHEP

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordstr\"om geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $\Psi_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $\chi$ which relates the perturbations of the radiative Maxwell scalars $\varphi_2$ and the Weyl scalar $\Psi_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhar's book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordstr\"om spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal., Comment: 21 pages, 6 figures, 1 table

We study the model of Einstein-Maxwell theory minimally coupling to a massive charged self-interacting scalar field, parameterized by the quartic and hexic coupling, labelled by $\lambda$ and $\beta$, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moveover, we investigate the properties of full nonlinear solution with nonzero scalar field, and argue that, by assuming massive charged self-interacting scalar field with sufficiently large charge above one certain bound, these counterexamples can be removed. In particular, this bound on charge for self-interacting scalar field is no longer equal to the weak gravity bound for free scalar case. In the quartic case, the bounds are below free scalar case for $\lambda0$. Meanwhile, in the hexic case, the bounds are above free scalar case for both $\beta>0$ and $\beta, Comment: 19 pages, 7 figures

We consider the Yang-Mills problem on $\mathbb{R}^{1+4}$ with gauge group $SO(4)$. In an appropriate equivariant reduction, this Yang-Mills problem reduces to a single scalar semilinear wave equation. This semilinear equation admits a one-parameter family of solitons, each of which is a re-scaling of a fixed solution. In this work, we construct a class of solutions, each of which consists of a soliton whose length scale is asymptotically constant, coupled to large radiation, plus corrections which slowly decay to zero in the energy norm. Our class of solutions includes ones for which the radiation component is only "logarithmically" better than energy class. As such, the solutions are not constructed by apriori assuming the length scale to be constant. Instead, we use an approach similar to a previous work of the author regarding wave maps. In the setup of this work, the soliton length scale asymptoting to a constant is a necessary condition for the radiation profile to have finite energy. An interesting point of our construction is that, for each radiation profile, there exist one-parameter families of solutions consisting of the radiation profile coupled to a soliton, which has any asymptotic value of the length scale., This is the accepted version, no major changes relative to v2