Related papers: The Birkhoff Theorem in Multidimensional Gravity

We explain the need for a theory of quantum gravity and some general ideas about string theory, including the idea of the derivation of the Hawking Bekenstein entropy formula for extremal black holes. We then give a general description of…

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any…

In this paper, we investigate capacity preserving transformations and their ergodicity. We show that for any measurable transformation $\theta$ there always exists a $\theta$-invariant capacity. We investigate some limit properties under…

Within the framework of relativistic theory of gravitation the exact spherically-symmetric wave solution is received. It is shown that this solution possesses the positive-definite energy and momentum deriving with the Fock energy-momentum…

Exact solutions of spherically symmetric black hole and gravitational wave are explored in $f(R)$ gravity in arbitrary dimension. We find two exact solutions for the radiation and absorption of null dust. In the framework of general…

We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined…

I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive…

Quasi-topological gravities (QTGs) are higher-curvature extensions of Einstein gravity in $D\geq 5$ spacetime dimensions. Throughout the years, different notions of QTGs constructed from analytic functions of polynomial curvature invariants…

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…

We show that the theorem of the three perpendiculars holds in any n-dimensional space form.

Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in…

A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…

The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily…

We define various Born-Infeld gravity theories in 3+1 dimensions which reduce to Horava's model at the quadratic level in small curvature expansion. In their exact forms, our actions provide z->(infinity) extensions of Horava's gravity, but…

We give an overview of the derivation of multipolar equations of motion of extended test bodies for a wide set of gravitational theories beyond the standard general relativistic framework. The classes of theories covered range from simple…

Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…

Variational formalism in the extended phase space for fields is applied to gravity. It is shown that the requirement of invariance under arbitrary local inertial frames implies a coupling of torsion to a 3-form of matter fields on the one…

An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are…

We give a detailed canonical analysis of the $n$-dimensional $f$(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer-Marsden form which is amenable to identifying the…