Self-dual Spacetime Research Articles

Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime

In this paper, we calculate the frequencies of geodesic orbits in self-dual spacetime on the equatorial plane and obtain the leading-order effects of loop quantum parameters P on the energy flux and angular momentum flux in eccentric extreme mass ratio inspirals. The gravitational waveform under different eccentricity is carried out by improved “analytic-kludge” method. We calculate the waveform mismatches for the LISA detector and the measurement error on loop quantum parameters. The constraint capability on P will be improved by a factor of 3 to 10, compared to the weak field experiments in the solar system.

Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the galactic center

One of remarkable features of loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In the mini-superspace approach based on the polymerization procedure in LQG, a quantum corrected black hole metric is constructed. This metric is also known as self-dual spacetime since the form of the metric is invariant under the exchange r ⟶ a 0/r with a 0 being proportional to the minimum area in LQG and r is the standard radial coordinate at asymptotic infinity. It modifies the Schwarzschild spacetime by the polymeric function P, purely due to the geometric quantum effects from LQG. Here P is related to the polymeric parameter δ which is introduced to define the paths one integrates the connection along to define the holonomies in the quantum corrected Hamiltonian constraint in the polymerization procedure in LQG. In this paper, we consider its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the central region of our Milky Way, and compare it with the publicly available astrometric and spectroscopic data, including the astrometric positions, the radial velocities, and the orbital precession for the S0-2 star. We perform Monte Carlo Markov Chain (MCMC) simulations to probe the possible LQG effects on the orbit of S0-2 star. No significant evidence of the self-dual spacetime arisIng from LQG is found. We thus place an upper bounds at 95% confidence level on the polymeric function P < 0.043 and P < 0.056, for Gaussian and uniform priors on orbital parameters, respectively.

Observational tests of the self-dual spacetime in loop quantum gravity

The self-dual spacetime was derived from the mini-superspace approach, based on the polymerization quantization procedure in loop quantum gravity (LQG). Its deviation from the Schwarzschild spacetime is characterized by the polymeric function $P$, purely due to the geometric quantum effects from LQG. In this paper, we consider the observational constraints imposed on $P$ by using the solar system experiments and observations. For this purpose, we calculate in detail the effects of $P$ on astronomical observations conducted in the Solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, and geodetic precession. The observational constraints are derived by confronting the theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the measurement of the gravitational time delay by the Cassini mission, which yields $0<P<5.5\times 10^{-6}$. In addition, we also discuss the potential constraint that can be obtained in the near future by the joint European-Japanese BepiColombo project and show that it could significantly improve the current constraints.

Stability of self-dual black holes

We study the stability properties of the Cauchy horizon for two different self-dual black hole solutions obtained in a model inspired by Loop Quantum Gravity. The self-dual spacetimes depend on a free dimensionless parameter called a polymeric parameter P. For the first metric the Cauchy horizon is stable for supermassive black holes only if this parameter is sufficiently small. For small black holes, however the stability is easily implemented. The second metric analyzed is not only self-dual but also form-invariant under the transformation r→r⁎2/r and r⁎=2mP. We find that this symmetry protects the Cauchy horizon for any value of the polymeric parameter.

Spacetime supersymmetry of extended fermionic strings in 2+2 dimensions

The N=2 fermionic string theory is revisited in the light of its recently proposed equivalence to the non-compact N=4 fermionic string model. The issues of spacetime Lorentz covariance and supersymmetry for the BRST quantized N=2 strings living in uncompactified 2+2 dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the spacetime symmetries of the extended fermionic strings and their interactions. The considerations support Siegel's (1992) ideas about the presence of SO(2,2) Lorentz symmetry as well as at least two self-dual spacetime supersymmetries in the theory of N=2(4) fermionic strings, though the authors do not have a compelling reason to argue for the necessity of maximal spacetime supersymmetry. The worldsheet arguments for the absence of all massive string modes in the physical spectrum and the vanishing of all string-loop amplitudes in the Polyakov (1981) approach, are given on the basis of the general consistency of the theory.

Gauge fields in algebraically special space-times

It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein–Yang–Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Bäcklund transformations is demonstrated. All the results apply for an arbitrary gauge group.

Non-self-dual nonlinear gravitons

Penrose has given a twistor description of all self-dual complex Riemannian space-times. We modify his construction to characterize all complex Riemannian space-times and all complex teleparallel space-times. This construction may be useful in finding non-self-dual solutions to the gravitational field equations (Einstein's or otherwise) without or with sources. It may also lead to a nonperturbative method for computing path integrals. Whereas Penrose shows that a self-dual space-time may be specified by a deformation of projective twistor space (the set of α planes in complex Minkowski space), we find that a Riemannian or teleparallel space-time may be described by a deformation of projective ambitwistor space (the set of null geodesics in complex Minkowski space).

Self-dual space-times with cosmological constant

It is shown that self-dual solutions of Einstein's equations, with cosmological constant λ, correspond to certain complex manifolds. This result generalizes the work of Penrose [1], who dealt with the case λ=0.

Yang-Mills instantons in self-dual spacetimes

The zero modes of a Yang-Mills instanton in a self-dual spacetime are related to the solutions of the zero mass Dirac equation in the adjoint representation. The index theorem is used to determined the number of parameters of instantons in such spacetimes. The result is illustrated by a calculation in Taub-NUT spacetime using the instanton constructed by the Charap and Duff prescription.