Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory ofGravitation

In this paper we classify cylindrically symmetric static space-timesaccording to their teleparallel homothetic vector fields using directintegration technique. It turns out that the dimensions of the teleparallelhomothetic vector fields are 4, 5, 7 or 11, which are the same in numbers asin general relativity. In case of 4, 5 or 7 proper teleparallel homotheticvector fields exist for the special choice to the space-times. In the caseof 11 teleparallel homothetic vector fields the space-time becomes Minkowskiwith all the zero torsion components. Teleparallel homothetic vector fieldsin this case are exactly the same as in general relativity. It is importantto note that this classification also covers the plane symmetric static space-times.     

Swampland dS conjecture in mimetic f(R,T) gravity

In this paper, we study a theory of gravity called mimetic f(R, T) in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H(N) from f(R, T) = R + δT gravity model, in which R is Ricci scalar, and T denotes the trace of the energy–momentum tensor. Also, δ and N are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as n_s and r. Then we challenge the mentioned inflationary model from the swampland dS conjecture. We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data.     

On finding hypersurface orthogonal Killing fields

The conditions for a space-time to admit a hypersurface-orthogonal Killing vector field are studied. Tests are derived first for space-times that admit two commuting Killing vectors, both for the timelike-spacelike (TS) case and the spacelike-spacelike case (SS); these give the condition for linear combinations of the two known Killing vectors to be hypersurface orthogonal. Illustrations are given in some stationary axisymmetric (TS) metrics and cylindrically symmetric (SS) metrics. In the general case, conditions for static symmetry are already known. We give the similar conditions for a spacelike hypersurface-orthogonal Killing field.     

Redshift drift constraints on f(T) gravity

We explore the impact of the Sandage−Loeb (SL) test on the precision of cosmological constraints for f(T) gravity theories. The SL test is an important supplement to current cosmological observations because it measures the redshift drift in the Lyman-α forest in the spectra of distant quasars, covering the “redshift desert” of 2≲z≲5. To avoid data inconsistency, we use the best-fit models based on current combined observational data as fiducial models to simulate 30 mock SL test data. We quantify the impact of these SL test data on parameter estimation for f(T) gravity theories. Two typical f(T) models are considered, the power-law model f(T)_PL and the exponential-form model f(T)_EXP. The results show that the SL test can effectively break the existing strong degeneracy between the present-day matter density Ω_m and the Hubble constant H₀ in other cosmological observations. For the considered f(T) models, a 30-year observation of the SL test can improve the constraint precision of Ω_m and H₀ enormously but cannot effectively improve the constraint precision of the model parameters.     

A Note on Classification of Spatially Homogeneous Rotating Space-Times According to Their Teleparallel Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify spatially homogeneous rotating space-timesaccording to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields.     

Superconductivity of compressed platinum powder at very low temperatures

Superconductivity of compressed, high-purity platinum powder (average grain size 2–3 μm) was found by measurements of resistivity, AC susceptibility and magnetization. The transition temperature into the superconducting state T_c and the critical magnetic field B_c strongly depend on the packing fraction f of the samples: we found 0.62T_c(0)1.38 mK and 6.6B_c(0)67 μT for 0.8f0.5, respectively. The temperature dependence of the critical magnetic fields can be described by B_c(T)=B_c(0)(1−(T/T_c)²). The discussion of these results includes possible explanations for the origin of superconductivity in this new superconducting material.     

Bianchi type I in f(T) gravitational theories

A tetrad field that is homogeneous and anisotropic which contains two unknown functions A(t) and B(t) of cosmic time is applied to the field equations of f(T), where T is the torsion scalar, T = T~μ_(νρ)S_μ~(νρ). We calculate the equation of continuity and rewrite it as a product of two brackets, the first is a function of f(T) and the second is a function of the two unknowns A(t) and B(t). We use two different relations between the two unknown functions A(t) and B(t) in the second bracket to solve it. Both of these relations give constant scalar torsion and solutions coincide with the de Sitter one. So,another assumption related to the contents of the matter fields is postulated. This assumption enables us to drive a solution with a non-constant value of the scalar torsion and a form of f(T) which represents ΛCDM.     

Radial conformal killing vectors in spherically symmetric shear-free space-times

The existence of “radial” conformai Killing (RCK) vector fields is discussed for metrics describing spherically symmetric, shear-free, perfect fluids. It is shown that conformally flat metrics admit three RCK fields, while nonconformally flat metrics might admit, at most, one such field. An RCK vector parallel to the 4-velocity of the fluid occurs in a subclass of conformally flat metrics containing the Friedmann-Robertson-Walker space-times as particular cases. A new class of nonconformally flat, self-similarity solutions is found. The necessary conditions for the existence of an RCK field in other nonconformally flat metrics are given in full.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Symmetry mappings in Einstein-Maxwell space-times

General properties of Einstein-Maxwell spaces, with both null and nonnull source-free Maxwell fields, are examined when these space-times admit various kinds of symmetry mappings. These include Killing, homothetic and conformal vector fields, curvature and Ricci collineations, and mappings belonging to the family of contracted Ricci collineations. In particular, the behavior of the electromagnetic field tensor is examined under these symmetry mappings. Examples are given of such space-times which admit proper curvature and proper Ricci collineations. Examples are also given of such space-times in which the metric tensor admits homothetic and other motions, but in which the corresponding Lie derivatives of the electromagnetic Maxwell tensor are not just proportional to the Maxwell tensor.On leave from Mathematics Department, Monash University, Clayton, Victoria, 3168, Australia.     

A Note on Classification of Teleparallel Conformal Vector Fields in Cylindrically Symmetric Static Space-Times in the Teleparallel Theory of Gravitation

In this paper we explored teleparallel conformal vector fields in cylindrically symmetric static space-times in the teleparallel theory of gravitation by using the direct integration technique. It turns out that the dimension of teleparallel conformal vector fields are 8, 9, 10 or 11. The case VI in which the space-time becomes conformally flat admits eleven independent teleparallel conformal vector fields.     

Energy conditions of the f(T,B) gravity dark energy model with the validity of thermodynamics

In this article, the analysis of Tsallis holographic dark energy(which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f(T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=αT~m+βB~n, made possible by the fact that the model is purely accelerating,corresponds to q=-0.54(Mamon and Das 2017 Eur. Phys.J.C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe.With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter,whereas it appears when the model is in the quintessence dominated era.     

Conformal Killing vectors and FRW spacetimes

Fluid space-times which admit a conformal Killing vector (CKV) are studied. It is shown that even in a perfect fluid space-time a conformal motion will not, in general, map the fluid flow lines onto fluid flow lines; consequently, perfect fluid space-times and, in particular, the simplest perfect fluid space-times known to admit a CKV, namely the Friedmann-Robertson-Walker (FRW) space-times, are studied. A direct proof that there do not exist any special CKV in FRW space-times will be given, thereby motivating the study of the physically more relevant proper CKV. Indeed, one of the principal motivations of the present work is the study of the symmetry inheritance problem for proper CKV. Since the FRW metric can, in general, satisfy the Einstein field equations for a non-comoving imperfect fluid, the relationship between the FRW models (and in particular the standard comoving perfect fluid models) and the conditions under which conformal motions (and in addition homothetic motions) map fluid flow lines onto fluid flow lines are investigated. Finally, further properties of fluid space-times which admit a proper CKV, and in particular space-times in which the CKV is parallel to the fluid four-velocity, are discussed.     

LETTER: Conformal Ricci Collineations of Space-Times

We study conformal vector fields on space-times which in addition are compatible with the Ricci tensor (so-called conformal Ricci collineations). In the case of Einstein metrics any conformal vector field is automatically a Ricci collineation as well. For Riemannian manifolds, conformal Ricci collineation were called concircular vector fields and studied in the relationship with the geometry of geodesic circles. Here we obtain a partial classification of space-times carrying proper conformal Ricci collineations. There are examples which are not Einstein metrics.     

Constant scalar curvature and warped product globally null manifolds

This paper deals with the curvature properties of a class of globally null manifolds (M,g) which admit a global null vector field and a complete Riemannian hypersurface. Using the warped product technique we study the fundamental problem of finding a warped function such that the degenerate metric g admits a constant scalar curvature on M. Our work has an interplay with the static vacuum solutions of the Einstein equations of general relativity.     

The Lynden-Bell and Katz definition of gravitational energy: Applications to singular solutions

We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and spherically symmetric space-times which admit a curvature singularity. These are the Tolman V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th of the gravitational radius. We show that the LK definition can still be applied to these solutions despite the presence of a singularity which nonetheless appears to carry no energy in the LK sense. While in the solutions that we mentioned the KL gravitational energy is positive definite everywhere in space time, this is not the case for the overcharged Reissner-Nordström space-time. In the latter case in fact the LK energy density becomes negative sufficiently close to the singularity hence we use the positivity criterion to impose a more stringent limit of validity to the Reissner-Nordström solution.     

Field-induced parameters of re-entrant magnets and concentrated spin glasses

We have used electron spin resonance measurements to derive the temperature and frequency dependences of the field-induced magnetization [M(T, f)] and anisotropy field [H_an (T)] in a number of amorphous alloys belonging to the series (Fe_pNi_1−p)₇₅P₁₆B₆Al₃. In re-entrant (p > p_c, the critical concentration for ferromagnetism) alloys at hi gh frequencies (f = 35 GHz, field ≈ 12 kOe) M reduces as T^3/2 at high T and as T below ≈ 40 K, the deviation from T^3/2 becoming more marked as p → p⁺_c. For p close to p_c, lowering the frequency first causes the T term to increase and ultimately ( ≈ 4 GHz) changes the variation of M with T to that discovered previously for concentrated spin glasses, namely M is constant at low T and drops linearly at high temperatures. For the re-entrants, the results are interpreted on the basis of a model which invokes an energy gap in the spin-wave spectrum, introduces a non-zero density of states of the gap energy and takes into consideration a low-q cut-off in the spin-wave integral in thelow-T (T) regime.In the concentrated spin glasses [M (0) - M (T)]/ M (0) is well represented by the function [exp (Δ / T) - 1]^-1, where Δ has values close to the corresponding Curie-Weiss temperatures θ_p but much larger than the respective spin glass transition temperatures T_SG. The temperature dependence of H_an is largely given by the function (1 - T/T^*), where T^* is equal to the zero-field freezing temperature for the re-entrants and T_SG for the spin glasses, respectively.     

Vacuum type N space-times admitting homothetic vector fields with isolated fixed points

We consider vacuum space-times (M, g) which are of Petrov type N on an open dense subset ofM, and which admit (proper) homothetic vector fields with isolated fixed points. We prove that if such is the case then, at the fixed point, (M,g) is flat and the homothetic bivector,X _[a;b] , is necessarily simple-timelike. Furthermore, we prove that if the homothetic bivector remains simple-timelike in some neighbourhood of the fixed point then, around the fixed point, the space-time in question is a pp-wave. The paper ends with a local characterization and some examples of space-tunes satisfying these conditions.     

Conformal Vector Fields and Conformal–Type Collineations in Space-Times

Some restrictions on the existence of homothetic and conformal vector fields in space-times which already admit some Killing symmetry are established. In particular, the behaviour of Weyl invariants and the nature of the Petrov type of the Weyl tensor along the integral curves of conformal vector fields are studied. This results in important restrictions between conformal vector fields and Killing orbits. A brief remark is made on Weyl collineations.     

Reconstructing f(T) modified gravity from ECHDE and ECNADE models

We investigate alternative candidates to dark energy (DE) that can explain the current state of the Universe in the framework of the generalized teleparallel theory of gravity f(T), where T denotes the torsion scalar. To achieve this, we carry out a series of reconstructions taking into account the ordinary and entropy-corrected versions of the holographic and new agegraphic DE models. These models are used as alternatives to DE in the literature in order to describe the current state of our Universe. It is remarked that the proposed models indicate behavior akin to phantom or quintessence models. Furthermore, we also generate the parameters of the equation of state associated with entropy-corrected models and we observe a phase transition between the quintessence state and phantom state as it is shown by the recent observational data. We also investigate the stability of these models and we create the $\{r-s\}$ trajectories and compare with the ΛCDM limit. The behavior of certain physical parameters such as the speed of sound and the Statefinder diagnostic pair $\{r-s\}$ is compatible with the current observational data.