We investigate galactic rotation curves in f( T) gravity, where T represents a torsional quantity. Our study centers on the particular Lagrangian [equation], where [equation] and [equation]is a...

Gravitomagnetism characterizes phenomena in the weak-field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theories of gravity may have an important impact on these effects which may constrain potential models within these theories.

Teleparallel and symmetric teleparallel gravity offer platforms in which gravity can be formulated in interesting geometric approaches, respectively given by torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a $$3+1$$3 + 1 decomposition of the teleparallel equivalent of general relativity and the symmetric teleparallel equivalent of general relativity which are both dynamically equivalent to curvature based general relativity. By splitting the spacetime metric and corresponding tetrad into their spatial and temporal parts as well as through finding the Gauss-like equations, it is possible to set up a general foundation for the different formulations of gravity. Based on these results, general 3-tetrad and 3-metric evolution equations are derived. Finally through the choice of the two respective connections, the metric $$3+1$$3 + 1 formulation for general relativity is recovered as well as the tetrad $$3+1$$3 + 1 formulation of the teleparallel equivalent of general relativity and the metric $$3+1$$3 + 1 formulation of symmetric teleparallel equivalent of general relativity. The approach is capable, in principle, of resolving common features of the various formulations of general relativity at a fundamental level and pointing out characteristics that extensions and alternatives to the various formulations can present.

The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler’s third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

Background: ¹⁸F-fluorodeoxyglucose (¹⁸FDG) PET is commonly used to quantify brown adipose tissue (BAT) mass/activity in humans but requires cold exposure. Rodent brown (BAds) but not white adipocytes (WAds) exhibit high choline content, thus we hypothesised that human BAT would demonstrate substantial ¹⁸F-fluorocholine (¹⁸FCH) uptake in vivo during warm and cold conditions. Methods: (1) Six male volunteers (age 21.4±1.1y, BMI 23.2±0.7kg/m²) with detectable BAT by ¹⁸FDG-PET underwent ¹⁸FCH-PET/MR scanning during warm (~23°C) and cold (17°C) exposure in a randomised crossover design. (2) ¹⁸FCH uptake by supraclavicular (SCVAT) and abdominal white adipose tissue (WAT) depots were quantified in patients with prostate cancer who had undergone ¹⁸FCH-PET/CT scanning at room temperature as part of their clinical care. (3) Choline transporter expression levels were measured in human BAds and WAds. (4) Human BAds were incubated with ¹⁵N-choline and incorporation into ¹⁵N-metabolites was analysed by LC-MS/MS. Results: (1) Cold exposure increased circulating noradrenaline, non-esterified fatty acids and decreased supraclavicular and sternal skin temperature without changing insulin or glucose levels. There was detectable ¹⁸FCH uptake by supraclavicular BAT in all subjects during warm and cold exposure. Cold exposure increased ¹⁸FCH-detected BAT volume (by ~100%) and total BAT activity (by ~50%); ¹⁸FCH detected substantially lower BAT though than ¹⁸FDG during both conditions. (2) ¹⁸FCH uptake was ~2.5-fold higher in human SCVAT compared to abdominal subcutaneous WAT in patients scanned at room temperature. (3) In parallel with the in vivo data, mRNA levels of the choline transporter SLC44A2 were higher in BAds than WAds. (4) ¹⁵N-Choline tracing revealed that choline was incorporated into multiple phosphatidylcholine species in BAds. Conclusion: ¹⁸FCH can be used to detect human BAT and acute cold exposure increases choline uptake by BAT. Human BAT utilises choline to synthesise phosphatidylcholines that may play an important role in optimal BAT function.

The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.