Related papers: The general solution of the quantum Einstein equat…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
We solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest ever obtained for quaternionic quantum theories, and the…
In this essay, we argue that the problem of time should not be regarded as an issue to be resolved within the prevailing framework for studying quantum gravity, but rather as an indication that there is an issue within the framework itself.…
These notes summarize the lectures delivered in the V Mexican School of Particle Physics, at the University of Guanajuato. We give a survey of the application of Ashtekar's variables to the quantization of General Relativity in four…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
In previous papers I expounded non-linear Schrodingerist quantum mechanics as a solution of the Measurement Problem. Here I show that NLQM is compatible with Einstein's theory of General Relativity. The extension to curved space-times…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities.…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of…
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
In this work, we give a general class of solutions of the spinning cosmic string in Einstein's theory of gravity. After treating same problem in Einstein Cartan (EC) theory of gravity, the exact solution satisfying both exterior and…
We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension…
The generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical…
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…