The homotopy analysis method (HAM) is a useful to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl coupled with Maxwell field and obtain approximation for charged by using HAM. It found that are sufficiently accurate entire spacetime outside hole’s event horizon also consistent numerical ones Einstein–Maxwell–Weyl gra...

we investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the Newtonian and cosmological constants. We have shown that screening or antiscreening behaviour of the gravitational coupling depends cricially on the choice ...

Why are there no fundamental scalar fields actually observed in physics today? Scalars are the simplest fields, but once we go beyond Galilean-Newtonian physics they appear only in speculations, as possible determinants of the gravitational constants in the so-called Scalar-Tensor theories in non-quantum physics, and as Higgs particles, dilatons, etc., in quantum physics. Actually, scalar field...

On the macroscopical level, Einstein’s general relativity has passed every test “with flying colors", see Will [67] for a recent review. However, Einstein’s theory sofar has resisted any attempt of quantization, e.g. it is known to be perturbatively nonrenormalizable, partially due to its dimensional coupling constant2. String theory or brane scenarios with extra dimensions have been proposed a...

the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long time a mystery to be conquered. accordingly, the aim of this expository article is to present (i) the einstein relativistic vector addition, (ii) the resulting einstein scalar multiplication, (iii) the einstein rel...

We study static black hole solutions in Einstein and Einstein–Gauss–Bonnet gravity with the topology of the product of two spheres,Sn × Sn, in higher dimensions. There is an unusual new feature of the Gauss–Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of > 0. For an Einstein–Gauss–Bonnet black hole a limited window of ne...

We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or T 4 , they describe an equivalent class of a trio of the Einstein-Kähler forms (the hyperkähler forms). We calculate the dimensions of these moduli spaces by using the Atiyah-Singer Index theorem. We mention the partition function and the possibility of t...

Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge-invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reas...

Starting with the 2 + 1 Einstein–Maxwell–Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding 1 + 0 σ–model. It is shown that, for general values of the coupling parameters, the T –duality group is SL(2, R), which coincides with the group of linear coordinate transformations along the Killing orbits. This duality, along with a sui...

From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability o...