We develop a symmetric teleparallel gravity model in a space-time with only the nonmetricity is nonzero, in terms of a Lagrangian quadratic in the non-metricity tensor. We present a detailed discussion of the variations that may be used for any gravitational formulation. We seek Schwarzschild-type solutions because of its observational significance and obtain a class of solutions that includes Schwarzschild-type, Schwarzschild-de Sitter-type and ReissnerNordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.

We investigate the non-minimal couplings between the electromagnetic fields and gravity through the natural logarithm of the curvature scalar. After we give the Lagrangian formulation of the non-minimally coupled theory, we derive field equations by a first order variational principle using the method of Lagrange multipliers. We look at static, spherically symmetric solutions that are asymptotically flat. We discuss the nature of horizons for some candidate black hole solutions according to various values of the parameters R 0 and a 1 .

In this paper we elaborate on the symmetric teleparallel gravity (STPG) written in a nonRiemannian spacetime with nonzero nonmetricity, but zero torsion and zero curvature.Firstly we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry the autoparallel curves coincides with those of the Riemannian spacetimes. Subsequently we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for certain values of coupling coefficients. Thus we arrive at calculating the field equations via independent variations. Then we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally we discuss a minimal coupling of a spin-1/2 field to STPG.

The purpose of this study was to investigate the effect of "with goalkeeper" (SSGwith) and "without goalkeeper" (SSGwithout) conditions on players' physiological responses and time-motion characteristics in small-sided games. Sixteen young soccer players (age: 16.5 ± 1.5 years; height: 175.5 ± 5.2 cm; body mass: 63.0 ± 6.9 kg; training experience: 6.3 ± 1.3 years) participated in 2 different 2-a-side, 3-a-side, and 4-a-side games: SSGwith and SSGwithout. The players underwent anthropometric measurements (height and body mass) followed by the Yo-Yo intermittent recovery test (level 1). Then they played 2-a-side, 3-a-side, and 4-a-side SSGwith and SSGwithout soccer-specific SSGs in random order at 2-day intervals. Heart rate (HR) responses and distance covered in different speed zones (walking [WLK, 0-6.9 km·h(-1)], low-intensity running [LIR, 7.0-12.9 km·h(-1)], moderate-intensity running [MIR, 13.0-17.9 km·h(-1)], and high-intensity running [HIR, >18 km·h(-1)]) were measured during the SSGs, whereas the rating of perceived exertion (RPE) and blood lactate (La) were determined at the end of the last bout of each SSG. During the SSGwithout players showed higher %HR, La, and RPE (p ≤ 0.05), greater distance covered in LIR, MIR, HIR, and total distance (p ≤ 0.05) compared with the SSGwith during the 2-a-side, 3-a-side, and 4-a-side games. The results of this study suggest that both SSGwith and SSGwithout could be used for the physiological adaptations required for soccer-specific aerobic endurance. However, if coaches want both higher physiological responses and greater distance covered in the intensity running zone from their teams, SSGwithout should be organized. In addition, this study also suggests that smaller format games (i.e., 2-a-side) may promote some anaerobic adaptations for youth soccer players.

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