Exact mathematical Formula that connect 6 dimensionless physical constants

In this paper are a new formula for the Planck length ℓpℓ and a new formula for the Avogadro number NA. Also 9 Mathematical formulas that connect dimensionless physical constants. The 6 dimensionless physical constants are the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν1 of electric force to gravitational force between electron and proton,the Avogadro number NA,the Gravitational coupling constant αG for the electron and the gravitational coupling constant αG(p) of proton.

Stellar Structure in a Newtonian Theory with Variable G

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane–Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter ω, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed.

Spherically symmetric charged black holes with wavy scalar hair

We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating “wave packet” and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.

Gravitating Cho–Maison monopole

We study numerical solutions corresponding to spherically symmetric gravitating electroweak monopole and magnetically charged black holes of the Einstein–Weinberg–Salam theory. The gravitating electroweak monopole solutions are quite identical to the gravitating monopole solution in SU(2) Einstein–Yang–Mills–Higgs theory, but with distinctive characteristics. We also found solutions representing radially excited monopole, which has no counterpart in flat space. Both of these solutions exist up to a maximal gravitational coupling before they cease to exist. Lastly we also report on magnetically charged non-Abelian black holes solutions that is closely related to the regular monopole solutions, which represents counterexample to the ‘no-hair’ conjecture.

The Hawking black-hole radiation spectrum has a short tail

It is proved that the Hawking emission spectrum of a semiclassical Schwarzschild black hole of mass [Formula: see text] has a sharp cut at the frequency scale [Formula: see text]. In particular, taking into account the nonlinear gravitational coupling between the tunneled Hawking quanta and the emitting black hole, it is explicitly shown that the upper bound [Formula: see text] on the energies of the emitted Hawking quanta is a direct consequence of the famous Thorne hoop relation.

$$\varLambda $$CDM suitably embedded in f(R) with a non-minimal coupling to matter

In this work, we further study a metric modified theory of gravity which contains a non-minimal coupling to matter, more precisely, we assume two functions of the scalar curvature, $$f_1$$ f 1 and $$f_2$$ f 2 , where the first one generalises the Hilbert–Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a $$\varLambda $$ Λ CDM background, we calculate analytical solutions for the functions $$f_1$$ f 1 and $$f_2$$ f 2 . We consider two setups: on the first one, we fix $$f_2$$ f 2 and compute $$f_1$$ f 1 and on the second one, we fix $$f_1$$ f 1 and compute $$f_2$$ f 2 . Moreover, we do the analysis for two different energy density contents, a matter dominated universe and a general perfect fluid with a constant equation of state fuelling the universe expansion. On the other hand, we complete our study by performing a cosmographic analysis for $$f_1$$ f 1 and $$f_2$$ f 2 . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.

Classical gravitational self-energy from double copy

We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling GN by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion.

Holography and unitarity

If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling G. The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero G, raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don’t close in the usual fashion expected for a boundary theory.